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                  Courses matching "Statistics Seminar"

                  Mathematical Statistics III

                  Statistical methods used in practice are based on a foundation of statistical theory. One branch of this theory uses the tools of probability to establish important distributional results that are used throughout statistics. Another major branch of statistical theory is statistical inference. It deals with issues such as how do we define a "good" estimator or hypothesis test, how do we recognise one and how do we construct one? This course is concerned with the fundamental theory of random variables and statistical inference. Topics covered are: calculus of distributions, moments, moment generating functions; multivariate distributions, marginal and conditional distributions, conditional expectation and variance operators, change of variable, multivariate normal distribution, exact distributions arising in statistics; weak convergence, convergence in distribution, weak law of large numbers, central limit theorem; statistical inference, likelihood, score and information; estimation, minimum variance unbiased estimation, the Cramer-Rao lower bound, exponential families, sufficient statistics, the Rao-Blackwell theorem, efficiency, consistency, maximum likelihood estimators, large sample properties; tests of hypotheses, most powerful tests, the Neyman-Pearson lemma, likelihood ratio, score and Wald tests, large sample properties.

                  More about this course...

                  Probability and Statistics

                  Probability theory is the branch of mathematics that deals with modelling uncertainty. It is important because of its direct application in areas such as genetics, finance and telecommunications. It also forms the fundamental basis for many other areas in the mathematical sciences including statistics, modern optimisation methods and risk modelling. This course provides an introduction to probability theory, random variables and Markov processes. Topics covered are: probability axioms, conditional probability; Bayes' theorem; discrete random variables, moments, bounding probabilities, probability generating functions, standard discrete distributions; continuous random variables, uniform, normal, Cauchy, exponential, gamma and chi-square distributions, transformations, the Poisson process; bivariate distributions, marginal and conditional distributions, independence, covariance and correlation, linear combinations of two random variables, bivariate normal distribution; sequences of independent random variables, the weak law of large numbers, the central limit theorem; definition and properties of a Markov chain and probability transition matrices; methods for solving equilibrium equations, absorbing Markov chains.

                  More about this course...

                  Events matching "Statistics Seminar"

                  TBA
                  00:00 Wed 30 Nov, -0001 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide

                  TBA
                  00:00 Wed 30 Nov, -0001 :: Ingkarni Wardli B17 :: Steve Rosenberg :: University of Adelaide / Boston University

                  Media...
                  TBA
                  Stability of time-periodic flows
                  15:10 Fri 10 Mar, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Andrew Bassom, School of Mathematics and Statistics, University of Western Australia

                  Time-periodic shear layers occur naturally in a wide range of applications from engineering to physiology. Transition to turbulence in such flows is of practical interest and there have been several papers dealing with the stability of flows composed of a steady component plus an oscillatory part with zero mean. In such flows a possible instability mechanism is associated with the mean component so that the stability of the flow can be examined using some sort of perturbation-type analysis. This strategy fails when the mean part of the flow is small compared with the oscillatory component which, of course, includes the case when the mean part is precisely zero.

                  This difficulty with analytical studies has meant that the stability of purely oscillatory flows has relied on various numerical methods. Until very recently such techniques have only ever predicted that the flow is stable, even though experiments suggest that they do become unstable at high enough speeds. In this talk I shall expand on this discrepancy with emphasis on the particular case of the so-called flat Stokes layer. This flow, which is generated in a deep layer of incompressible fluid lying above a flat plate which is oscillated in its own plane, represents one of the few exact solutions of the Navier-Stokes equations. We show theoretically that the flow does become unstable to waves which propagate relative to the basic motion although the theory predicts that this occurs much later than has been found in experiments. Reasons for this discrepancy are examined by reference to calculations for oscillatory flows in pipes and channels. Finally, we propose some new experiments that might reduce this disagreement between the theoretical predictions of instability and practical realisations of breakdown in oscillatory flows.
                  Making tertiary mathematics more interesting
                  15:10 Fri 24 Mar, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Emeritus Neville de Mestre, Faculty of Information Technology, Bond University

                  For the past few decades, calculus and linear algebra have provided the basis for many university courses in mathematics, science or engineering. However there are other courses, which could be given to motivate the students, particularly those with only a passing love of mathematics. One possible course could show the essential features of how mathematicians solve problems using many different analytical, cerebral and computer skills. In this seminar I will describe such a one-semester course (2 lectures, 2 labs each week), which includes hands-on problem solving and students eventually creating their own problems. One or two exciting problems at first-year level will be developed in detail.
                  How to draw a cube
                  11:10 Mon 26 Mar, 2007 :: Maths G08 :: Prof Mike Eastwood

                  Fibonacci: order, chaos, and the Holy Grail
                  11:10 Mon 30 Apr, 2007 :: Maths G08 :: Dr Alison Wolff :: School of Mathematical Sciences

                  The Great Big Jellyfish a.k.a. the Internet
                  11:10 Mon 28 May, 2007 :: Maths G08 :: A/Prof Matt Roughan

                  Trisection of an angle with ruler and compass
                  13:10 Fri 10 Aug, 2007 :: Maths G08 :: Dr John van der Hoek

                  It is well known that this construction is impossible, but an interesting question is whether this can be achieved to arbitrary accuracy. We show how this can be done. This construction generalizes to dividing angles into five equal parts, and so on.
                  Regression: a backwards step?
                  13:10 Fri 7 Sep, 2007 :: Maths G08 :: Dr Gary Glonek

                  Media...
                  Most students of high school mathematics will have encountered the technique of fitting a line to data by least squares. Those who have taken a university statistics course will also have heard this method referred to as regression. However, it is not obvious from common dictionary definitions why this should be the case. For example, "reversion to an earlier or less advanced state or form". In this talk, the mathematical phenomenon that gave regression its name will be explained and will be shown to have implications in some unexpected contexts.
                  Add one part chaos, one part topology, and stir well...
                  13:10 Fri 19 Oct, 2007 :: Engineering North 132 :: Dr Matt Finn :: School of Mathematical Sciences

                  Media...
                  Stirring and mixing of fluids occurs everywhere, from adding milk to a cup of coffee, right through to industrial-scale chemical blending. So why stir in the first place? Is it possible to do it badly? And how can you make sure you do it effectively? I will attempt to answer these questions using a few thought experiments, some dynamical systems theory and a little topology.
                  Counting fish
                  13:10 Wed 19 Mar, 2008 :: Napier 210 :: Mr Jono Tuke

                  Media...
                  How often have you asked yourself: "I wonder how many fish are in that lake?" Probably never, but if you ever did, then this is the lecture for you. The solution is easy (Seuss, 1960), but raises the question of how good the answer is. I will answer this by looking at confidence intervals. In the lecture, I will discuss what a confidence interval is and how to calculate it using techniques for calculating probabilities in poker. I will also look at how these ideas have been used in epidemiology, the study of disease, to estimate the number of people with diabetes. [1] Seuss, Dr. (1960). "One Fish Two Fish Red Fish Blue Fish". Random House Books.
                  Groundwater: using mathematics to solve our water crisis
                  13:10 Wed 9 Apr, 2008 :: Napier 210 :: Dr Michael Teubner

                  'The driest state in the driest continent' is how South Australia used to be described. And that was before the drought! Now we have severe water restrictions, dead lawns, and dying gardens. But this need not be the case. Mathematics to the rescue! Groundwater exists below much of the Adelaide metro area. We can store winter stormwater in the ground and use it when we need it in summer. But we need mathematical models to understand where groundwater exists, where we can inject stormwater and how much can be stored, and where we can extract it: all through mathematical models. Come along and see that we don't have a water problem, we have a water management problem.
                  Global and Local stationary modelling in finance: Theory and empirical evidence
                  14:10 Thu 10 Apr, 2008 :: G04 Napier Building University of Adelaide :: Prof. Dominique Guégan :: Universite Paris 1 Pantheon-Sorbonne

                  To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available.

                  Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.

                  Now non-stationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This non-stationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987).

                  Thus, using stationary unconditional moments suggest a global stationarity for the model, but using non-stationary unconditional moments or non-stationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior.

                  The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks.

                  1. What kinds of non-stationarity affect the major financial and economic data sets? How to detect them?

                  2. Local and global stationarities: How are they defined?

                  3. What is the impact of evidence of non-stationarity on the statistics computed from the global non stationary data sets?

                  4. How can we analyze data sets in the non-stationary global framework? Does the asymptotic theory work in non-stationary framework?

                  5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy?

                  These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.

                  The limits of proof
                  13:10 Wed 21 May, 2008 :: Napier 210 :: A/Prof Finnur Larusson

                  Media...
                  The job of the mathematician is to discover new truths about mathematical objects and their relationships. Such truths are established by proving them. This raises a fundamental question. Can every mathematical truth be proved (by a sufficiently clever being) or are there truths that will forever lie beyond the reach of proof? Mathematics can be turned on itself to investigate this question. In this talk, we will see that under certain assumptions about proofs, there are truths that cannot be proved. You must decide for yourself whether you think these assumptions are valid!
                  Something cool about primes
                  13:10 Wed 13 Aug, 2008 :: Napier 210 :: Mr David Butler

                  So far this year in the undergraduate seminars, we have seen how mathematics is useful for solving important problems, and how mathematics can be used to uncover profound truths. In this seminar I will show you something about prime numbers that is neither useful nor profound. I just think it is extremely cool.
                  Probabilistic models of human cognition
                  15:10 Fri 29 Aug, 2008 :: G03 Napier Building University of Adelaide :: Dr Daniel Navarro :: School of Psychology, University of Adelaide

                  Over the last 15 years a fairly substantial psychological literature has developed in which human reasoning and decision-making is viewed as the solution to a variety of statistical problems posed by the environments in which we operate. In this talk, I briefly outline the general approach to cognitive modelling that is adopted in this literature, which relies heavily on Bayesian statistics, and introduce a little of the current research in this field. In particular, I will discuss work by myself and others on the statistical basis of how people make simple inductive leaps and generalisations, and the links between these generalisations and how people acquire word meanings and learn new concepts. If time permits, the extensions of the work in which complex concepts may be characterised with the aid of nonparametric Bayesian tools such as Dirichlet processes will be briefly mentioned.
                  For the love of logs
                  13:10 Wed 10 Sep, 2008 :: Napier 210 :: Dr Paul McCann

                  Media...
                  The humble logarithm is a well known and dependable beast. In this talk we will provide a "greatest hits-tory" of the logarithm, highlighting some memorable moments from its first 400 years of life, and pondering some of the reasons why logarithms arise in so many diverse and unexpected situations. Finally, we will juggle some simple numerical coincidences to calculate a few choice logarithms from scratch.
                  Assisted reproduction technology: how maths can contribute
                  13:10 Wed 22 Oct, 2008 :: Napier 210 :: Dr Yvonne Stokes

                  Media...
                  Most people will have heard of IVF (in vitro fertilisation), a technology for helping infertile couples have a baby. Although there are many IVF babies, many will also know that the success rate is still low for the cost and inconvenience involved. The fact that some women cannot make use of IVF because of life-threatening consequences is less well known but motivates research into other technologies, including IVM (in vitro maturation). What has all this to do with maths? Come along and find out how mathematical modelling is contributing to understanding and improvement in this important and interesting field.
                  Direct "delay" reductions of the Toda equation
                  13:10 Fri 23 Jan, 2009 :: School Board Room :: Prof Nalini Joshi :: University of Sydney

                  A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated to this equation is obtained, also by reduction.
                  Big whirls
                  15:00 Fri 30 Jan, 2009 :: School Board Room :: A/Prof Richard Kelso :: University of Adelaide

                  Noncommutative geometry of odd-dimensional quantum spheres
                  13:10 Fri 27 Feb, 2009 :: School Board Room :: Dr Partha Chakraborty :: University of Adelaide

                  We will report on our attempts to understand noncommutative geometry in the lights of the example of quantum spheres. We will see how to produce an equivariant fundamental class and also indicate some of the limitations of isospectral deformations.
                  Impulsively generated drops
                  15:00 Fri 27 Feb, 2009 :: Napier LG29 :: Prof William Phillips :: Swinburne University of Technology

                  This talk is concerned with the evolution of an unbounded inviscid fluid-fluid interface subject to an axisymmetric impulse in pressure and how inertial, interfacial and gravitational forces affect that evolution. The construct was motivated by the occurrence of lung hemorrhage resulting from ultrasonic imaging and pursues the notion that bursts of ultrasound act to expel droplets that puncture the soft air-filled sacs in the lung plural surface allowing them to fill with blood. The evolution of the free surface is described by a boundary integral formulation which is integrated forward in time numerically. As the interface evolves, it is seen, depending upon the levels of gravity and surface tension, to form either axisymmetric surface jets, waves or droplets. Moreover the droplets may be spherical, inverted tear-shaped or pancake like. Also of interest is the finite time singularity which occurs when the drop pinches off; this is seen to be of the power law type with an exponent of 2/3.
                  Bibundles
                  13:10 Fri 6 Mar, 2009 :: School Board Room :: Prof Michael Murray :: University of Adelaide

                  The index theorem for projective families of elliptic operators
                  13:10 Fri 13 Mar, 2009 :: School Board Room :: Prof Mathai Varghese :: University of Adelaide

                  From histograms to multivariate polynomial histograms and shape estimation
                  12:10 Thu 19 Mar, 2009 :: Napier 210 :: A/Prof Inge Koch

                  Media...
                  Histograms are convenient and easy-to-use tools for estimating the shape of data, but they have serious problems which are magnified for multivariate data. We combine classic histograms with shape estimation by polynomials. The new relatives, `polynomial histograms', have surprisingly nice mathematical properties, which we will explore in this talk. We also show how they can be used for real data of 10-20 dimensions to analyse and understand the shape of these data.
                  Geometric analysis on the noncommutative torus
                  13:10 Fri 20 Mar, 2009 :: School Board Room :: Prof Jonathan Rosenberg :: University of Maryland

                  Noncommutative geometry (in the sense of Alain Connes) involves replacing a conventional space by a "space" in which the algebra of functions is noncommutative. The simplest truly non-trivial noncommutative manifold is the noncommutative 2-torus, whose algebra of functions is also called the irrational rotation algebra. I will discuss a number of recent results on geometric analysis on the noncommutative torus, including the study of nonlinear noncommutative elliptic PDEs (such as the noncommutative harmonic map equation) and noncommutative complex analysis (with noncommutative elliptic functions).
                  Understanding optimal linear transient growth in complex-geometry flows
                  15:00 Fri 27 Mar, 2009 :: Napier LG29 :: Associate Prof Hugh Blackburn :: Monash University

                  Tummy troubles
                  12:10 Thu 9 Apr, 2009 :: Napier 210 :: Dr Ben Binder

                  Media...
                  Hirschsprung's disease is relatively common, affecting roughly 1 in 5000 newly born babies each year in Australia. The disease occurs when there is an incomplete formation of the nervous system in the gut. Mathematical models can help in determining the underlying mechanisms that cause the disease. Comparisons between theoretical predictions and experimental results will be made.
                  Classification and compact complex manifolds I
                  13:10 Fri 17 Apr, 2009 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

                  Classification and compact complex manifolds II
                  13:10 Fri 24 Apr, 2009 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

                  Magnetorotational instabilities in cylindrical Taylor-Couette flow
                  15:00 Fri 24 Apr, 2009 :: Napier LG29 :: Dr Rainer Hollerbach :: University of Leeds

                  String structures and characteristic classes for loop group bundles
                  13:10 Fri 1 May, 2009 :: School Board Room :: Mr Raymond Vozzo :: University of Adelaide

                  The Chern-Weil homomorphism gives a geometric method for calculating characteristic classes for principal bundles. In infinite dimensions, however, the standard theory fails due to analytical problems. In this talk I shall give a geometric method for calculating characteristic classes for principal bundle with structure group the loop group of a compact group which side-steps these complications. This theory is inspired in some sense by results on the string class (a certain cohomology class on the base of a loop group bundle) which I shall outline.
                  How to see in higher dimensions
                  12:10 Thu 7 May, 2009 :: Napier 210 :: Prof Michael Murray

                  Media...
                  The human brain has evolved to be able to think intuitively in three dimensions. Unfortunately the real world is at least four and maybe 10, 11 or 26 dimensional. In this talk I will discuss some of the tricks mathematicians have devised to think about higher dimensional objects.
                  Four classes of complex manifolds
                  13:10 Fri 8 May, 2009 :: School Board Room :: A/Prof Finnur Larusson :: University of Adelaide

                  We introduce the four classes of complex manifolds defined by having few or many holomorphic maps to or from the complex plane. Two of these classes have played an important role in complex geometry for a long time. A third turns out to be too large to be of much interest. The fourth class has only recently emerged from work of Abel Prize winner Mikhail Gromov.
                  Wall turbulence: from the laboratory to the atmosphere
                  15:00 Fri 29 May, 2009 :: Napier LG29 :: Prof Ivan Marusic :: The University of Melbourne

                  The study of wall-bounded turbulent flows has received great attention over the past few years as a result of high Reynolds number experiments conducted in new high Reynolds number facilities such as the Princeton "superpipe", the NDF facility in Chicago and the HRNBLWT at the University of Melbourne. These experiments have brought into question the fundamental scaling laws of the turbulence and mean flow quantities as well as revealed high Reynolds number phenomena, which make extrapolation of low Reynolds number results highly questionable. In this talk these issues will be reviewed and new results from the HRNBLWT and atmospheric surface layer on the salt-flats of Utah will be presented documenting unique high Reynolds number phenomena. The implications for skin-friction drag reduction technologies and improved near-wall models for large-eddy simulation will be discussed.
                  Lagrangian fibrations on holomorphic symplectic manifolds I: Holomorphic Lagrangian fibrations
                  13:10 Fri 5 Jun, 2009 :: School Board Room :: Dr Justin Sawon :: Colorado State University

                  A compact K{\"a}hler manifold $X$ is a holomorphic symplectic manifold if it admits a non-degenerate holomorphic two-form $\sigma$. According to a theorem of Matsushita, fibrations on $X$ must be of a very restricted type: the fibres must be Lagrangian with respect to $\sigma$ and the generic fibre must be a complex torus. Moreover, it is expected that the base of the fibration must be complex projective space, and this has been proved by Hwang when $X$ is projective. The simplest example of these {\em Lagrangian fibrations\/} are elliptic K3 surfaces. In this talk we will explain the role of elliptic K3s in the classification of K3 surfaces, and the (conjectural) generalization to higher dimensions.
                  Chern-Simons classes on loop spaces and diffeomorphism groups
                  13:10 Fri 12 Jun, 2009 :: School Board Room :: Prof Steve Rosenberg :: Boston University

                  The loop space LM of a Riemannian manifold M comes with a family of Riemannian metrics indexed by a Sobolev parameter. We can construct characteristic classes for LM using the Wodzicki residue instead of the usual matrix trace. The Pontrjagin classes of LM vanish, but the secondary or Chern-Simons classes may be nonzero and may distinguish circle actions on M. There are similar results for diffeomorphism groups of manifolds.
                  Lagrangian fibrations on holomorphic symplectic manifolds II: Existence of Lagrangian fibrations
                  13:10 Fri 19 Jun, 2009 :: School Board Room :: Dr Justin Sawon :: Colorado State University

                  The Hilbert scheme ${\mathrm Hilb}^nS$ of points on a K3 surface $S$ is a well-known holomorphic symplectic manifold. When does ${\mathrm Hilb}^nS$ admit a Lagrangian fibration? The existence of a Lagrangian fibration places some conditions on the Hodge structure, since the pull back of a hyperplane from the base gives a special divisor on ${\mathrm Hilb}^nS$, and in turn a special divisor on $S$. The converse is more difficult, but using Fourier-Mukai transforms we will show that if $S$ admits a divisor of a certain degree then ${\mathrm Hilb}^nS$ admits a Lagrangian fibration.
                  Lagrangian fibrations on holomorphic symplectic manifolds III: Holomorphic coisotropic reduction
                  13:10 Fri 26 Jun, 2009 :: School Board Room :: Dr Justin Sawon :: Colorado State University

                  Given a certain kind of submanifold $Y$ of a symplectic manifold $(X,\omega)$ we can form its coisotropic reduction as follows. The null directions of $\omega|_Y$ define the characteristic foliation $F$ on $Y$. The space of leaves $Y/F$ then admits a symplectic form, descended from $\omega|_Y$. Locally, the coisotropic reduction $Y/F$ looks just like a symplectic quotient. This construction also work for holomorphic symplectic manifolds, though one of the main difficulties in practice is ensuring that the leaves of the foliation are compact. We will describe a criterion for compactness, and apply coisotropic reduction to produce a classification result for Lagrangian fibrations by Jacobians.
                  Nonlinear diffusion-driven flow in a stratified viscous fluid
                  15:00 Fri 26 Jun, 2009 :: Macbeth Lecture Theatre :: Associate Prof Michael Page :: Monash University

                  In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear density-stratified viscous fluid in a closed container demonstrated a slow flow can be generated simply due to the container having a sloping boundary surface This remarkable motion is generated as a result of the curvature of the lines of constant density near any sloping surface, which in turn enables a zero normal-flux condition on the density to be satisfied along that boundary. When the Rayleigh number is large (or equivalently Wunsch's parameter $R$ is small) this motion is concentrated in the near vicinity of the sloping surface, in a thin `buoyancy layer' that has many similarities to an Ekman layer in a rotating fluid.

                  A number of studies have since considered the consequences of this type of `diffusively-driven' flow in a semi-infinite domain, including in the deep ocean and with turbulent effects included. More recently, Page & Johnson (2008) described a steady linear theory for the broader-scale mass recirculation in a closed container and demonstrated that, unlike in previous studies, it is possible for the buoyancy layer to entrain fluid from that recirculation. That work has since been extended (Page & Johnson, 2009) to the nonlinear regime of the problem and some of the similarities to and differences from the linear case will be described in this talk. Simple and elegant analytical solutions in the limit as $R \to 0$ still exist in some situations, and they will be compared with numerical simulations in a tilted square container at small values of $R$. Further work on both the unsteady flow properties and the flow for other geometrical configurations will also be described.

                  Another proof of Gaboriau-Popa
                  13:10 Fri 3 Jul, 2009 :: School Board Room :: Prof Greg Hjorth :: University of Melbourne

                  Gaboriau and Popa showed that a non-abelian free group on finitely many generators has continuum many measure preserving, free, ergodic, actions on standard Borel probability spaces. The original proof used the notion of property (T). I will sketch how this can be replaced by an elementary, and apparently new, dynamical property.
                  Generalizations of the Stein-Tomas restriction theorem
                  13:10 Fri 7 Aug, 2009 :: School Board Room :: Prof Andrew Hassell :: Australian National University

                  The Stein-Tomas restriction theorem says that the Fourier transform of a function in L^p(R^n) restricts to an L^2 function on the unit sphere, for p in some range [1, 2(n+1)/(n+3)]. I will discuss geometric generalizations of this result, by interpreting it as a property of the spectral measure of the Laplace operator on R^n, and then generalizing to the Laplace-Beltrami operator on certain complete Riemannian manifolds. It turns out that dynamical properties of the geodesic flow play a crucial role in determining whether a restriction-type theorem holds for these manifolds.
                  Predicting turbulence
                  12:10 Wed 12 Aug, 2009 :: Napier 210 :: Dr Trent Mattner :: University of Adelaide

                  Media...
                  Turbulence is characterised by three-dimensional unsteady fluid motion over a wide range of spatial and temporal scales. It is important in many problems of technological and scientific interest, such as drag reduction, energy production and climate prediction. In this talk, I will explain why turbulent flows are difficult to predict and describe a modern mathematical model of turbulence based on a random collection of fluid vortices.
                  Asymmetric Cantor measures and sumsets
                  13:10 Fri 14 Aug, 2009 :: School Board Room :: Prof Gavin Brown :: Royal Institution of Australia and University of Adelaide

                  Weak Hopf algebras and Frobenius algebras
                  13:10 Fri 21 Aug, 2009 :: School Board Room :: Prof Ross Street :: Macquarie University

                  A basic example of a Hopf algebra is a group algebra: it is the vector space having the group as basis and having multiplication linearly extending that of the group. We can start with a category instead of a group, form the free vector space on the set of its morphisms, and define multiplication to be composition when possible and zero when not. The multiplication has an identity if the category has finitely many objects; this is a basic example of a weak bialgebra. It is a weak Hopf algebra when the category is a groupoid. Group algebras are also Frobenius algebras. We shall generalize weak bialgebras and Frobenius algebras to the context of monoidal categories and describe some of their theory using the geometry of string diagrams.
                  Moduli spaces of stable holomorphic vector bundles
                  13:10 Fri 28 Aug, 2009 :: School Board Room :: Dr Nicholas Buchdahl :: University of Adelaide

                  Modelling fluid-structure interactions in micro-devices
                  15:00 Thu 3 Sep, 2009 :: School Board Room :: Dr Richard Clarke :: University of Auckland

                  The flows generated in many modern micro-devices possess very little convective inertia, however, they can be highly unsteady and exert substantial hydrodynamic forces on the device components. Typically these components exhibit some degree of compliance, which traditionally has been treated using simple one-dimensional elastic beam models. However, recent findings have suggested that three-dimensional effects can be important and, accordingly, we consider the elastohydrodynamic response of a rapidly oscillating three-dimensional elastic plate that is immersed in a viscous fluid. In addition, a preliminary model will be presented which incorporates the presence of a nearby elastic wall.
                  Spin-up in a torus
                  16:00 Thu 3 Sep, 2009 :: School Board Room :: Dr Richard Hewitt :: University of Manchester

                  Defect formulae for integrals of pseudodifferential symbols: applications to dimensional regularisation and index theory
                  13:10 Fri 4 Sep, 2009 :: School Board Room :: Prof Sylvie Paycha :: Universite Blaise Pascal, Clermont-Ferrand, France

                  The ordinary integral on L^1 functions on R^d unfortunately does not extend to a translation invariant linear form on the whole algebra of pseudodifferential symbols on R^d, forcing to work with ordinary linear extensions which fail to be translation invariant. Defect formulae which express the difference between various linear extensions, show that they differ by local terms involving the noncommutative residue. In particular, we shall show how integrals regularised by a "dimensional regularisation" procedure familiar to physicists differ from Hadamard finite part (or "cut-off" regularised) integrals by a residue. When extended to pseudodifferential operators on closed manifolds, these defect formulae express the zeta regularised traces of a differential operator in terms of a residue of its logarithm. In particular, we shall express the index of a Dirac type operator on a closed manifold in terms of a logarithm of a generalized Laplacian, thus giving an a priori local description of the index and shall discuss further applications.
                  The Monster
                  12:10 Thu 10 Sep, 2009 :: Napier 210 :: Dr David Parrott :: University of Adelaide

                  Media...
                  The simple groups are the building blocks of all finite groups. The classification of finite simple groups is a towering achievement of 20th century mathematics. In addition to 18 infinite families of finite simple groups, there are 26 sporadic groups. The biggest sporadic group, dubbed The Monster, has about 10^54 elements. The talk will give a glimpse of this deep area of mathematics.
                  Covering spaces and algebra bundles
                  13:10 Fri 11 Sep, 2009 :: School Board Room :: Prof Keith Hannabuss :: University of Oxford

                  Bundles of C*-algebras over a topological space M can be classified by a Dixmier-Douady obstruction in H^3(M,Z). This talk will describe some recent work with Mathai investigating the relationship between algebra bundles on M and on its covering space, where there can be no obstruction, particularly when there is a group acting on M.
                  Stability of rotating boundary-layers
                  15:10 Wed 16 Sep, 2009 :: Napier LG29 :: Dr Christian Thomas :: University of Western Australia

                  Understanding hypersurfaces through tropical geometry
                  12:10 Fri 25 Sep, 2009 :: Napier 102 :: Dr Mohammed Abouzaid :: Massachusetts Institute of Technology

                  Given a polynomial in two or more variables, one may study the zero locus from the point of view of different mathematical subjects (number theory, algebraic geometry, ...). I will explain how tropical geometry allows to encode all topological aspects by elementary combinatorial objects called "tropical varieties." Mohammed Abouzaid received a B.S. in 2002 from the University of Richmond, and a Ph.D. in 2007 from the University of Chicago under the supervision of Paul Seidel. He is interested in symplectic topology and its interactions with algebraic geometry and differential topology, in particular the homological mirror symmetry conjecture. Since 2007 he has been a postdoctoral fellow at MIT, and a Clay Mathematics Institute Research Fellow.
                  Stable commutator length
                  13:40 Fri 25 Sep, 2009 :: Napier 102 :: Prof Danny Calegari :: California Institute of Technology

                  Stable commutator length answers the question: "what is the simplest surface in a given space with prescribed boundary?" where "simplest" is interpreted in topological terms. This topological definition is complemented by several equivalent definitions - in group theory, as a measure of non-commutativity of a group; and in linear programming, as the solution of a certain linear optimization problem. On the topological side, scl is concerned with questions such as computing the genus of a knot, or finding the simplest 4-manifold that bounds a given 3-manifold. On the linear programming side, scl is measured in terms of certain functions called quasimorphisms, which arise from hyperbolic geometry (negative curvature) and symplectic geometry (causal structures). In these talks we will discuss how scl in free and surface groups is connected to such diverse phenomena as the existence of closed surface subgroups in graphs of groups, rigidity and discreteness of symplectic representations, bounding immersed curves on a surface by immersed subsurfaces, and the theory of multi- dimensional continued fractions and Klein polyhedra. Danny Calegari is the Richard Merkin Professor of Mathematics at the California Institute of Technology, and is one of the recipients of the 2009 Clay Research Award for his work in geometric topology and geometric group theory. He received a B.A. in 1994 from the University of Melbourne, and a Ph.D. in 2000 from the University of California, Berkeley under the joint supervision of Andrew Casson and William Thurston. From 2000 to 2002 he was Benjamin Peirce Assistant Professor at Harvard University, after which he joined the Caltech faculty; he became Richard Merkin Professor in 2007.
                  Contemporary frontiers in statistics
                  15:10 Mon 28 Sep, 2009 :: Badger Labs G31 Macbeth Lectrue :: Prof. Peter Hall :: University of Melbourne

                  The availability of powerful computing equipment has had a dramatic impact on statistical methods and thinking, changing forever the way data are analysed. New data types, larger quantities of data, and new classes of research problem are all motivating new statistical methods. We shall give examples of each of these issues, and discuss the current and future directions of frontier problems in statistics.
                  A Fourier-Mukai transform for invariant differential cohomology
                  13:10 Fri 9 Oct, 2009 :: School Board Room :: Mr Richard Green :: University of Adelaide

                  Fourier-Mukai transforms are a geometric analogue of integral transforms playing an important role in algebraic geometry. Their name derives from the construction of Mukai involving the Poincare line bundle associated to an abelian variety. In this talk I will discuss recent work looking at an analogue of this original Fourier-Mukai transform in the context of differential geometry, which gives an isomorphism between the invariant differential cohomology of a real torus and its dual.
                  Irreducible subgroups of SO(2,n)
                  13:10 Fri 16 Oct, 2009 :: School Board Room :: Dr Thomas Leistner :: University of Adelaide

                  Berger's classification of irreducibly represented Lie groups that can occur as holonomy groups of semi-Riemannian manifolds is a remarkable result of modern differential geometry. What is remarkable about it is that it is so short and that only so few types of geometry can occur. In Riemannian signature this is even more remarkable, taking into account that any representation of a compact Lie group admits a positive definite invariant scalar product. Hence, for any not too small n there is an abundance of irreducible subgroups of SO(n). We show that in other signatures the situation is quite different with, for example, SO(1,n) having no proper irreducible subgroups. We will show how this and the corresponding result about irreducible subgroups of SO(2,n) follows from the Karpelevich-Mostov theorem. (This is joint work with Antonio J. Di Scala, Politecnico di Torino.)
                  Is the price really right?
                  12:10 Thu 22 Oct, 2009 :: Napier 210 :: Mr Sam Cohen :: University of Adelaide

                  Media...
                  Making decisions when outcomes are uncertain is a common problem we all face. In this talk I will outline some recent developments on this question from the mathematics of finance-the theory of risk measures and nonlinear expectations. I will also talk about how decisions are currently made in the finance industry, and how some simple mathematics can show where these systems are open to abuse.
                  Building centralisers in ~A_2 groups
                  13:10 Fri 23 Oct, 2009 :: School Board Room :: Prof Guyan Robertson :: University of Newcastle, UK

                  Analytic torsion for twisted de Rham complexes
                  13:10 Fri 30 Oct, 2009 :: School Board Room :: Prof Mathai Varghese :: University of Adelaide

                  We define analytic torsion for the twisted de Rham complex, consisting of differential forms on a compact Riemannian manifold X with coefficients in a flat vector bundle E, with a differential given by a flat connection on E plus a closed odd degree differential form on X. The definition in our case is more complicated than in the case discussed by Ray-Singer, as it uses pseudodifferential operators. We show that this analytic torsion is independent of the choice of metrics on X and E, establish some basic functorial properties, and compute it in many examples. We also establish the relationship of an invariant version of analytic torsion for T-dual circle bundles with closed 3-form flux. This is joint work with Siye Wu.
                  Eigen-analysis of fluid-loaded compliant panels
                  15:10 Wed 9 Dec, 2009 :: Santos Lecture Theatre :: Prof Tony Lucey :: Curtin University of Technology

                  This presentation concerns the fluid-structure interaction (FSI) that occurs between a fluid flow and an arbitrarily deforming flexible boundary considered to be a flexible panel or a compliant coating that comprises the wetted surface of a marine vehicle. We develop and deploy an approach that is a hybrid of computational and theoretical techniques. The system studied is two-dimensional and linearised disturbances are assumed. Of particular novelty in the present work is the ability of our methods to extract a full set of fluid-structure eigenmodes for systems that have strong spatial inhomogeneity in the structure of the flexible wall.

                  We first present the approach and some results of the system in which an ideal, zero-pressure gradient, flow interacts with a flexible plate held at both its ends. We use a combination of boundary-element and finite-difference methods to express the FSI system as a single matrix equation in the interfacial variable. This is then couched in state-space form and standard methods used to extract the system eigenvalues. It is then shown how the incorporation of spatial inhomogeneity in the stiffness of the plate can be either stabilising or destabilising. We also show that adding a further restraint within the streamwise extent of a homogeneous panel can trigger an additional type of hydroelastic instability at low flow speeds. The mechanism for the fluid-to-structure energy transfer that underpins this instability can be explained in terms of the pressure-signal phase relative to that of the wall motion and the effect on this relationship of the added wall restraint.

                  We then show how the ideal-flow approach can be conceptually extended to include boundary-layer effects. The flow field is now modelled by the continuity equation and the linearised perturbation momentum equation written in velocity-velocity form. The near-wall flow field is spatially discretised into rectangular elements on an Eulerian grid and a variant of the discrete-vortex method is applied. The entire fluid-structure system can again be assembled as a linear system for a single set of unknowns - the flow-field vorticity and the wall displacements - that admits the extraction of eigenvalues. We then show how stability diagrams for the fully-coupled finite flow-structure system can be assembled, in doing so identifying classes of wall-based or fluid-based and spatio-temporal wave behaviour.

                  Upper bounds for the essential dimension of the moduli stack of SL_n-bundles over a curve
                  11:10 Mon 14 Dec, 2009 :: School Board Room :: Dr Nicole Lemire :: University of Western Ontario, Canada

                  In joint work with Ajneet Dhillon, we find upper bounds for the essential dimension of various moduli stacks of SL_n-bundles over a curve. When n is a prime power, our calculation computes the essential dimension of the moduli stack of stable bundles exactly and the essential dimension is not equal to the dimension in this case.
                  Critical sets of products of linear forms
                  13:10 Mon 14 Dec, 2009 :: School Board Room :: Dr Graham Denham :: University of Western Ontario, Canada

                  Suppose $f_1,f_2,\ldots,f_n$ are linear polynomials in $\ell$ variables and $\lambda_1,\lambda_2,\ldots,\lambda_n$ are nonzero complex numbers. The product $$ \Phi_\lambda=\Prod_{i=1}^n f_1^{\lambda_i}, $$ called a master function, defines a (multivalued) function on $\ell$-dimensional complex space, or more precisely, on the complement of a set of hyperplanes. Then it is easy to ask (but harder to answer) what the set of critical points of a master function looks like, in terms of some properties of the input polynomials and $\lambda_i$'s. In my talk I will describe the motivation for considering such a question. Then I will indicate how the geometry and combinatorics of hyperplane arrangements can be used to provide at least a partial answer.
                  Hartogs-type holomorphic extensions
                  13:10 Tue 15 Dec, 2009 :: School Board Room :: Prof Roman Dwilewicz :: Missouri University of Science and Technology

                  We will review holomorphic extension problems starting with the famous Hartogs extension theorem (1906), via Severi-Kneser-Fichera-Martinelli theorems, up to some recent (partial) results of Al Boggess (Texas A&M Univ.), Zbigniew Slodkowski (Univ. Illinois at Chicago), and the speaker. The holomorphic extension problems for holomorphic or Cauchy-Riemann functions are fundamental problems in complex analysis of several variables. The talk will be very elementary, with many figures, and accessible to graduate and even advanced undergraduate students.
                  Group actions in complex geometry, I and II
                  13:10 Fri 8 Jan, 2010 :: School Board Room :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne

                  Media...
                  Group actions in complex geometry, III and IV
                  10:10 Fri 15 Jan, 2010 :: School Board Room :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne

                  Media...
                  Group actions in complex geometry, V and VI
                  10:10 Fri 22 Jan, 2010 :: School Board Room :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne

                  Media...
                  Group actions in complex geometry, VII and VIII
                  10:10 Fri 29 Jan, 2010 :: Napier LG 23 :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne

                  Media...
                  Oka manifolds and Oka maps
                  13:10 Fri 29 Jan, 2010 :: Napier LG 23 :: Prof Franc Forstneric :: University of Ljubljana

                  In this survey lecture I will discuss a new class of complex manifolds and of holomorphic maps between them which I introduced in 2009 (F. Forstneric, Oka Manifolds, C. R. Acad. Sci. Paris, Ser. I, 347 (2009) 1017-1020). Roughly speaking, a complex manifold Y is said to be an Oka manifold if Y admits plenty of holomorphic maps from any Stein manifold (or Stein space) X to Y, in a certain precise sense. In particular, the inclusion of the space of holomorphic maps of X to Y into the space of continuous maps must be a weak homotopy equivalence. One of the main results is that this class of manifolds can be characterized by a simple Runge approximation property for holomorphic maps from complex Euclidean spaces C^n to Y, with approximation on compact convex subsets of C^n. This answers in the affirmative a question posed by M. Gromov in 1989. I will also discuss the Oka properties of holomorphic maps and their characterization by approximation properties.
                  Proper holomorphic maps from strongly pseudoconvex domains to q-convex manifolds
                  13:10 Fri 5 Feb, 2010 :: School Board Room :: Prof Franc Forstneric :: University of Ljubljana

                  (Joint work with B. Drinovec Drnovsek, Amer. J. Math., in press.) I will discuss the existence of closed complex subvarieties of a complex manifold X that are proper holomorphic images of strongly pseudoconvex Stein domains. The main sufficient condition is expressed in terms of the Morse indices and of the number of positive Levi eigenvalues of an exhaustion function on X. Examples show that our condition cannot be weakened in general. I will describe optimal results for subvarieties of this type in complements of compact complex submanifolds with Griffiths positive normal bundle; in the projective case these generalize classical theorems of Remmert, Bishop and Narasimhan concerning proper holomorphic maps and embeddings to complex Euclidean spaces.
                  Conformal geometry of differential equations
                  13:10 Fri 12 Feb, 2010 :: School Board Room :: Dr Pawel Nurowski :: University of Warsaw

                  Integrable systems: noncommutative versus commutative
                  14:10 Thu 4 Mar, 2010 :: School Board Room :: Dr Cornelia Schiebold :: Mid Sweden University

                  After a general introduction to integrable systems, we will explain an approach to their solution theory, which is based on Banach space theory. The main point is first to shift attention to noncommutative integrable systems and then to extract information about the original setting via projection techniques. The resulting solution formulas turn out to be particularly well-suited to the qualitative study of certain solution classes. We will show how one can obtain a complete asymptotic description of the so called multiple pole solutions, a problem that was only treated for special cases before.
                  Convolution equations in A^{-\infty} for convex domains
                  13:10 Fri 5 Mar, 2010 :: School Board Room :: Dr Le Hai Khoi :: Nanyang Technological University, Singapore

                  Holomorphic extension on complex spaces
                  14:10 Fri 5 Mar, 2010 :: School Board Room :: Prof Egmont Porten :: Mid Sweden University

                  Infinite numbers: what are they and what are they good for?
                  13:10 Wed 17 Mar, 2010 :: Napier 210 :: A/Prof Finnur Larusson :: University of Adelaide

                  Media...
                  The sequence first, second, third,... can be continued with infinite ordinal numbers. I will explain what these infinite numbers are and how they can be used -- and sometimes must be used! -- to prove facts about ordinary, finite numbers.
                  Conformal structures with G_2 ambient metrics
                  13:10 Fri 19 Mar, 2010 :: School Board Room :: Dr Thomas Leistner :: University of Adelaide

                  The n-sphere considered as a conformal manifold can be viewed as the projectivisation of the light cone in n+2 Minkowski space. A construction that generalises this picture to arbitrary conformal classes is the ambient metric introduced by C. Fefferman and R. Graham. In the talk, I will explain the Fefferman-Graham ambient metric construction and how it detects the existence of certain metrics in the conformal class. Then I will present conformal classes of signature (3,2) for which the 7-dimensional ambient metric has the noncompact exceptional Lie group G_2 as its holonomy. This is joint work with P. Nurowski, Warsaw University.
                  The Jeffery–Hamel similarity solution and its relation to flow in a diverging channel
                  15:10 Fri 19 Mar, 2010 :: Santos Lecture Theatre :: Dr Phil Haines :: University of Adelaide

                  Jeffery–Hamel flows describe the steady two-dimensional flow of an incompressible viscous fluid between plane walls separated by an angle $\alpha$. They are often used to approximate the flow in domains of finite radial extent. However, whilst the base Jeffery–Hamel solution is characterised by a subcritical pitchfork bifurcation, studies in expanding channels of finite length typically find symmetry breaking via a supercritical bifurcation.

                  We use the finite element method to calculate solutions for flow in a two-dimensional wedge of finite length bounded by arcs of constant radii, $R_1$ and $R_2$. We present a comprehensive picture of the bifurcation structure and nonlinear states for a net radial outflow of fluid. We find a series of nested neutral curves in the Reynolds number-$\alpha$ plane corresponding to pitchfork bifurcations that break the midplane symmetry of the flow. We show that these finite domain bifurcations remain distinct from the similarity solution bifurcation even in the limit $R_2/R_1 \rightarrow \infty$.

                  We also discuss a class of stable steady solutions apparently related to a steady, spatially periodic, wave first observed by Tutty (1996). These solutions remain disconnected in our domain in the sense that they do not arise via a local bifurcation of the Stokes flow solution as the Reynolds number is increased.

                  American option pricing in a Markov chain market model
                  15:10 Fri 19 Mar, 2010 :: School Board Room :: Prof Robert Elliott :: School of Mathematical Sciences, University of Adelaide

                  This paper considers a model for asset pricing in a world where the randomness is modeled by a Markov chain rather than Brownian motion. In this paper we develop a theory of optimal stopping and related variational inequalities for American options in this model. A version of Saigal's Lemma is established and numerical algorithms developed. This is a joint work with John van der Hoek.
                  The fluid mechanics of gels used in tissue engineering
                  15:10 Fri 9 Apr, 2010 :: Santos Lecture Theatre :: Dr Edward Green :: University of Western Australia

                  Tissue engineering could be called 'the science of spare parts'. Although currently in its infancy, its long-term aim is to grow functional tissues and organs in vitro to replace those which have become defective through age, trauma or disease. Recent experiments have shown that mechanical interactions between cells and the materials in which they are grown have an important influence on tissue architecture, but in order to understand these effects, we first need to understand the mechanics of the gels themselves.

                  Many biological gels (e.g. collagen) used in tissue engineering have a fibrous microstructure which affects the way forces are transmitted through the material, and which in turn affects cell migration and other behaviours. I will present a simple continuum model of gel mechanics, based on treating the gel as a transversely isotropic viscous material. Two canonical problems are considered involving thin two-dimensional films: extensional flow, and squeezing flow of the fluid between two rigid plates. Neglecting inertia, gravity and surface tension, in each regime we can exploit the thin geometry to obtain a leading-order problem which is sufficiently tractable to allow the use of analytical methods. I discuss how these results could be exploited practically to determine the mechanical properties of real gels. If time permits, I will also talk about work currently in progress which explores the interaction between gel mechanics and cell behaviour.

                  Random walk integrals
                  13:10 Fri 16 Apr, 2010 :: School Board Room :: Prof Jonathan Borwein :: University of Newcastle

                  Following Pearson in 1905, we study the expected distance of a two-dimensional walk in the plane with unit steps in random directions---what Pearson called a "ramble". A series evaluation and recursions are obtained making it possible to explicitly determine this distance for small number of steps. Closed form expressions for all the moments of a 2-step and a 3-step walk are given, and a formula is conjectured for the 4-step walk. Heavy use is made of the analytic continuation of the underlying integral.
                  "The Emperor's New Mind": computers, minds, physics and biology
                  11:10 Wed 21 Apr, 2010 :: Napier 210 :: Prof Tony Roberts :: University of Adelaide

                  Media...
                  In the mid-1990s the computer 'Deep Blue' beat Kasparov, the world chess champion. Will computers soon overtake us humans in other endeavours of intelligence? Roger Penrose's thesis is that human intelligence is far more subtle than has previously been imagined, that the quest for human-like artificial intelligence in computers, the holy grail of artificial intelligence, is hopeless. The argument ranges from icily clear mathematics of computation, through the amazing shadows of quantum physics, and thence to new conjectures in biology.
                  Loop groups and characteristic classes
                  13:10 Fri 23 Apr, 2010 :: School Board Room :: Dr Raymond Vozzo :: University of Adelaide

                  Suppose $G$ is a compact Lie group, $LG$ its (free) loop group and $\Omega G \subseteq LG$ its based loop group. Let $P \to M$ be a principal bundle with structure group one of these loop groups. In general, differential form representatives of characteristic classes for principal bundles can be easily obtained using the Chern-Weil homomorphism, however for infinite-dimensional bundles such as $P$ this runs into analytical problems and classes are more difficult to construct. In this talk I will explain some new results on characteristic classes for loop group bundles which demonstrate how to construct certain classes---which we call string classes---for such bundles. These are obtained by making heavy use of a certain $G$-bundle associated to any loop group bundle (which allows us to avoid the problems of dealing with infinite-dimensional bundles). We shall see that the free loop group case naturally involves equivariant cohomology.
                  Moduli spaces of stable holomorphic vector bundles II
                  13:10 Fri 30 Apr, 2010 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

                  In this talk, I shall briefly review the notion of stability for holomorphic vector bundles on compact complex manifolds as discussed in the first part of this talk (28 August 2009). Then I shall attempt to compute some explicit examples in simple situations, illustrating the use of basic algebraic-geometric tools. The level of the talk will be appropriate for graduate students, particularly those who have been taking part in the algebraic geometry reading group meetings.
                  Estimation of sparse Bayesian networks using a score-based approach
                  15:10 Fri 30 Apr, 2010 :: School Board Room :: Dr Jessica Kasza :: University of Copenhagen

                  The estimation of Bayesian networks given high-dimensional data sets, with more variables than there are observations, has been the focus of much recent research. These structures provide a flexible framework for the representation of the conditional independence relationships of a set of variables, and can be particularly useful in the estimation of genetic regulatory networks given gene expression data.

                  In this talk, I will discuss some new research on learning sparse networks, that is, networks with many conditional independence restrictions, using a score-based approach. In the case of genetic regulatory networks, such sparsity reflects the view that each gene is regulated by relatively few other genes. The presented approach allows prior information about the overall sparsity of the underlying structure to be included in the analysis, as well as the incorporation of prior knowledge about the connectivity of individual nodes within the network.

                  The caloron transform
                  13:10 Fri 7 May, 2010 :: School Board Room :: Prof Michael Murray :: University of Adelaide

                  The caloron transform is a `fake' dimensional reduction which transforms a G-bundle over certain manifolds to a loop group of G bundle over a manifold of one lower dimension. This talk will review the caloron transform and show how it can be best understood using the language of pseudo-isomorphisms from category theory as well as considering its application to Bogomolny monopoles and string structures.
                  Two problems in porous media flow
                  15:10 Tue 11 May, 2010 :: Santos Lecture Theatre :: A/Prof Graeme Hocking :: Murdoch University

                  I will discuss two problems in porous media flow.

                  On a tropical island, fresh water may sit in the soil beneath the ground, floating on the ocean's salt water. This water is a valuable resource for the inhabitants, but requires sufficient rainfall to recharge the lens. In this paper, Green's functions are used to derive an integral equation to satisfy all of the conditions except those on the interfaces, which are then solved for numerically. Conditions under which the lens can be maintained will be described. This is work I did with an Honours student, Sue Chen, who is now at U. Melbourne.

                  In the second problem, I will discuss an "exact" solution to a problem in withdrawal from an unconfined aquifer. The problem formulation gives rise to a singular integral equation that can be solved using a nice orthogonality result I first met in airfoil theory. This is work with Hong Zhang from Griffith University.

                  Moduli spaces of stable holomorphic vector bundles III
                  13:10 Fri 14 May, 2010 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

                  This talk is a continuation of the talk on 30 April. The same abstract applies: In this talk, I shall briefly review the notion of stability for holomorphic vector bundles on compact complex manifolds as discussed in the first part of this talk (28 August 2009). Then I shall attempt to compute some explicit examples in simple situations, illustrating the use of basic algebraic-geometric tools. The level of the talk will be appropriate for graduate students, particularly those who have been taking part in the algebraic geometry reading group meetings.
                  Understanding convergence of meshless methods: Vortex methods and smoothed particle hydrodynamics
                  15:10 Fri 14 May, 2010 :: Santos Lecture Theatre :: A/Prof Lou Rossi :: University of Delaware

                  Meshless methods such as vortex methods (VMs) and smoothed particle hydrodynamics (SPH) schemes offer many advantages in fluid flow computations. Particle-based computations naturally adapt to complex flow geometries and so provide a high degree of computational efficiency. Also, particle based methods avoid CFL conditions because flow quantities are integrated along characteristics. There are many approaches to improving numerical methods, but one of the most effective routes is quantifying the error through the direct estimate of residual quantities. Understanding the residual for particle schemes requires a different approach than for meshless schemes but the rewards are significant. In this seminar, I will outline a general approach to understanding convergence that has been effective in creating high spatial accuracy vortex methods, and then I will discuss some recent investigations in the accuracy of diffusion operators used in SPH computations. Finally, I will provide some sample Navier-Stokes computations of high Reynolds number flows using BlobFlow, an open source implementation of the high precision vortex method.
                  Spot the difference: how to tell when two things are the same (and when they're not!)
                  13:10 Wed 19 May, 2010 :: Napier 210 :: Dr Raymond Vozzo :: University of Adelaide

                  Media...
                  High on a mathematician's to-do list is classifying objects and structures that arise in mathematics. We see patterns in things and want to know what other sorts of things behave similarly. This poses several problems. How can you tell when two seemingly different mathematical objects are the same? Can you even tell when two seemingly similar mathematical objects are the same? In fact, what does "the same" even mean? How can you tell if two things are the same when you can't even see them! In this talk, we will take a walk through some areas of maths known as algebraic topology and category theory and I will show you some of the ways mathematicians have devised to tell when two things are "the same".
                  Functorial 2-connected covers
                  13:10 Fri 21 May, 2010 :: School Board Room :: David Roberts :: University of Adelaide

                  The Whitehead tower of a topological space seeks to resolve that space by successively removing homotopy groups from the 'bottom up'. For a path-connected space with no 1-dimensional local pathologies the first stage in the tower can be chosen to be the universal (=1-connected) covering space. This construction also works in the category Diff of manifolds. However, further stages in the two known constructions of the Whitehead tower do not work in Diff, being purely topological - and one of these is non-functorial, depending on a large number of choices. This talk will survey results from my thesis which constructs a new, functorial model for the 2-connected cover which will lift to a generalised (2-)category of smooth objects. This talk contains joint work with Andrew Stacey of the Norwegian University of Science and Technology.
                  Interpolation of complex data using spatio-temporal compressive sensing
                  13:00 Fri 28 May, 2010 :: Santos Lecture Theatre :: A/Prof Matthew Roughan :: School of Mathematical Sciences, University of Adelaide

                  Many complex datasets suffer from missing data, and interpolating these missing elements is a key task in data analysis. Moreover, it is often the case that we see only a linear combination of the desired measurements, not the measurements themselves. For instance, in network management, it is easy to count the traffic on a link, but harder to measure the end-to-end flows. Additionally, typical interpolation algorithms treat either the spatial, or the temporal components of data separately, but in many real datasets have strong spatio-temporal structure that we would like to exploit in reconstructing the missing data. In this talk I will describe a novel reconstruction algorithm that exploits concepts from the growing area of compressive sensing to solve all of these problems and more. The approach works so well on Internet traffic matrices that we can obtain a reasonable reconstruction with as much as 98% of the original data missing.
                  On the uniqueness of almost-Kahler structures
                  13:10 Fri 28 May, 2010 :: School Board Room :: Dr Paul-Andi Nagy :: University of Auckland

                  We show uniqueness up to sign of positive, orthogonal almost-Kahler structures on any non-scalar flat Kahler-Einstein surface. This is joint work with A. J. di Scala.
                  A variance constraining ensemble Kalman filter: how to improve forecast using climatic data of unobserved variables
                  15:10 Fri 28 May, 2010 :: Santos Lecture Theatre :: A/Prof Georg Gottwald :: The University of Sydney

                  Data assimilation aims to solve one of the fundamental problems ofnumerical weather prediction - estimating the optimal state of the atmosphere given a numerical model of the dynamics, and sparse, noisy observations of the system. A standard tool in attacking this filtering problem is the Kalman filter.

                  We consider the problem when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. We derive the corresponding Kalman filter in a variational setting.

                  We analyze the variance constraining Kalman filter (VCKF) filter for a simple linear toy model and determine its range of optimal performance. We explore the variance constraining Kalman filter in an ensemble transform setting for the Lorenz-96 system, and show that incorporating the information on the variance on some un-observable variables can improve the skill and also increase the stability of the data assimilation procedure.

                  Using methods from dynamical systems theory we then systems where the un-observed variables evolve deterministically but chaotically on a fast time scale.

                  This is joint work with Lewis Mitchell and Sebastian Reich.

                  Vertex algebras and variational calculus I
                  13:10 Fri 4 Jun, 2010 :: School Board Room :: Dr Pedram Hekmati :: University of Adelaide

                  A basic operation in calculus of variations is the Euler-Lagrange variational derivative, whose kernel determines the extremals of functionals. There exists a natural resolution of this operator, called the variational complex. In this talk, I shall explain how to use tools from the theory of vertex algebras to explicitly construct the variational complex. This also provides a very convenient language for classifying and constructing integrable Hamiltonian evolution equations.
                  Vertex algebras and variational calculus II
                  13:10 Fri 11 Jun, 2010 :: School Board Room :: Dr Pedram Hekmati :: University of Adelaide

                  Last time I introduced the variational complex of an algebra of differential functions and gave a sketchy definition of a vertex algebra. This week I will make this notion more precise and explain how to apply it to the calculus of variations.
                  Some thoughts on wine production
                  15:05 Fri 18 Jun, 2010 :: School Board Room :: Prof Zbigniew Michalewicz :: School of Computer Science, University of Adelaide

                  In the modern information era, managers (e.g. winemakers) recognize the competitive opportunities represented by decision-support tools which can provide a significant cost savings & revenue increases for their businesses. Wineries make daily decisions on the processing of grapes, from harvest time (prediction of maturity of grapes, scheduling of equipment and labour, capacity planning, scheduling of crushers) through tank farm activities (planning and scheduling of wine and juice transfers on the tank farm) to packaging processes (bottling and storage activities). As such operation is quite complex, the whole area is loaded with interesting OR-related issues. These include the issues of global vs. local optimization, relationship between prediction and optimization, operating in dynamic environments, strategic vs. tactical optimization, and multi-objective optimization & trade-off analysis. During the talk we address the above issues; a few real-world applications will be shown and discussed to emphasize some of the presented material.
                  Topological chaos in two and three dimensions
                  15:10 Fri 18 Jun, 2010 :: Santos Lecture Theatre :: Dr Matt Finn :: School of Mathematical Sciences

                  Research into two-dimensional laminar fluid mixing has enjoyed a renaissance in the last decade since the realisation that the Thurston–Nielsen theory of surface homeomorphisms can assist in designing efficient "topologically chaotic" batch mixers. In this talk I will survey some tools used in topological fluid kinematics, including braid groups, train-tracks, dynamical systems and topological index formulae. I will then make some speculations about topological chaos in three dimensions.
                  On affine BMW algebras
                  13:10 Fri 25 Jun, 2010 :: Napier 208 :: Prof Arun Ram :: University of Melbourne

                  I will describe a family of algebras of tangles (which give rise to link invariants following the methods of Reshetikhin-Turaev and Jones) and describe some aspects of their structure and their representation theory. The main goal will be to explain how to use universal Verma modules for the symplectic group to compute the representation theory of affine BMW (Birman-Murakami-Wenzl) algebras.
                  Electrified film flow over topography
                  15:10 Mon 5 Jul, 2010 :: 5.58 Ingkarni Wardli :: Dr Mark Blyth :: University of East Anglia

                  Introduction to mirror symmetry and the Fukaya category I
                  13:10 Thu 15 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT

                  I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a two-hour talk.)
                  Introduction to mirror symmetry and the Fukaya category II
                  13:10 Fri 16 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT

                  I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a two-hour talk.)
                  Introduction to mirror symmetry and the Fukaya category III
                  13:10 Mon 19 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT

                  I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a two-hour talk.)
                  Introduction to mirror symmetry and the Fukaya category IV
                  13:10 Tue 20 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT

                  I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a two-hour talk.)
                  Introduction to mirror symmetry and the Fukaya category V
                  13:10 Wed 21 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT

                  I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a two-hour talk.)
                  Higher nonunital Quillen K'-theory
                  13:10 Fri 23 Jul, 2010 :: Engineering-Maths G06 :: Dr Snigdhayan Mahanta :: University of Adelaide

                  Quillen introduced a $K'_0$-theory for possibly nonunital rings and showed that it agrees with the usual algebraic $K_0$-theory if the ring is unital. We shall introduce higher $K'$-groups for $k$-algebras, where $k$ is a field, and discuss some elementary properties of this theory. We shall also show that for stable $C*$-algebras the higher $K'$-theory agrees with the topological $K$-theory. If time permits we shall explain how this provides a formalism to treat topological $\mathbb{T}$-dualities via Kasparov's bivariant $K$-theory.
                  Mathematica Seminar
                  15:10 Wed 28 Jul, 2010 :: Engineering Annex 314 :: Kim Schriefer :: Wolfram Research

                  The Mathematica Seminars 2010 offer an opportunity to experience the applicability, ease-of-use, as well as the advancements of Mathematica 7 in education and academic research. These seminars will highlight the latest directions in technical computing with Mathematica, and the impact this technology has across a wide range of academic fields, from maths, physics and biology to finance, economics and business. Those not yet familiar with Mathematica will gain an overview of the system and discover the breadth of applications it can address, while experts will get firsthand experience with recent advances in Mathematica like parallel computing, digital image processing, point-and-click palettes, built-in curated data, as well as courseware examples.
                  Dr
                  10:10 Thu 5 Aug, 2010 :: 10 Pulteney St :: Gary Glonek :: University of Adelaide

                  Gary will introduce Statistics without Parameters.
                  Eynard-Orantin invariants and enumerative geometry
                  13:10 Fri 6 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Paul Norbury :: University of Melbourne

                  As a tool for studying enumerative problems in geometry Eynard and Orantin associate multilinear differentials to any plane curve. Their work comes from matrix models but does not require matrix models (for understanding or calculations). In some sense they describe deformations of complex structures of a curve and conjectural relationships to deformations of Kahler structures of an associated object. I will give an introduction to their invariants via explicit examples, mainly to do with the moduli space of Riemann surfaces, in which the plane curve has genus zero.
                  Counting lattice points in polytopes and geometry
                  15:10 Fri 6 Aug, 2010 :: Napier G04 :: Dr Paul Norbury :: University of Melbourne

                  Counting lattice points in polytopes arises in many areas of pure and applied mathematics. A basic counting problem is this: how many different ways can one give change of 1 dollar into 5,10, 20 and 50 cent coins? This problem counts lattice points in a tetrahedron, and if there also must be exactly 10 coins then it counts lattice points in a triangle. The number of lattice points in polytopes can be used to measure the robustness of a computer network, or in statistics to test independence of characteristics of samples. I will describe the general structure of lattice point counts and the difficulty of calculations. I will then describe a particular lattice point count in which the structure simplifies considerably allowing one to calculate easily. I will spend a brief time at the end describing how this is related to the moduli space of Riemann surfaces.
                  The two envelope problem
                  12:10 Wed 11 Aug, 2010 :: Napier 210 :: A/Prof Gary Glonek :: University of Adelaide

                  Media...
                  The two envelope problem is a long standing paradox in probability theory. Although its formulation has elements in common with the celebrated Monty Hall problem, the underlying paradox is apparently far more subtle. In this talk, the problem will be explained and various aspects of the paradox will be discussed. Connections to Bayesian inference and other areas of statistics will be explored.
                  A spatial-temporal point process model for fine resolution multisite rainfall data from Roma, Italy
                  14:10 Thu 19 Aug, 2010 :: Napier G04 :: A/Prof Paul Cowpertwait :: Auckland University of Technology

                  A point process rainfall model is further developed that has storm origins occurring in space-time according to a Poisson process. Each storm origin has a random radius so that storms occur as circular regions in two-dimensional space, where the storm radii are taken to be independent exponential random variables. Storm origins are of random type z, where z follows a continuous probability distribution. Cell origins occur in a further spatial Poisson process and have arrival times that follow a Neyman-Scott point process. Cell origins have random radii so that cells form discs in two-dimensional space. Statistical properties up to third order are derived and used to fit the model to 10 min series taken from 23 sites across the Roma region, Italy. Distributional properties of the observed annual maxima are compared to equivalent values sampled from series that are simulated using the fitted model. The results indicate that the model will be of use in urban drainage projects for the Roma region.
                  Index theory in the noncommutative world
                  13:10 Fri 20 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Prof Alan Carey :: Australian National University

                  The aim of the talk is to give an overview of the noncommutative geometry approach to index theory.
                  A classical construction for simplicial sets revisited
                  13:10 Fri 27 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Danny Stevenson :: University of Glasgow

                  Simplicial sets became popular in the 1950s as a combinatorial way to study the homotopy theory of topological spaces. They are more robust than the older notion of simplicial complexes, which were introduced for the same purpose. In this talk, which will be as introductory as possible, we will review some classical functors arising in the theory of simplicial sets, some well-known, some not-so-well-known. We will re-examine the proof of an old theorem of Kan in light of these functors. We will try to keep all jargon to a minimum.
                  Compound and constrained regression analyses for EIV models
                  15:05 Fri 27 Aug, 2010 :: Napier LG28 :: Prof Wei Zhu :: State University of New York at Stony Brook

                  In linear regression analysis, randomness often exists in the independent variables and the resulting models are referred to errors-in-variables (EIV) models. The existing general EIV modeling framework, the structural model approach, is parametric and dependent on the usually unknown underlying distributions. In this work, we introduce a general non-parametric EIV modeling framework, the compound regression analysis, featuring an intuitive geometric representation and a 1-1 correspondence to the structural model. Properties, examples and further generalizations of this new modeling approach are discussed in this talk.
                  On some applications of higher Quillen K'-theory
                  13:10 Fri 3 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Snigdhayan Mahanta :: University of Adelaide

                  In my previous talk I introduced a functor from the category of k-algebras (k field) to abelian groups, called KQ-theory. In this talk I will explain its relationship with topological (homological) T-dualities and twisted K-theory.
                  Triangles, maps and curvature
                  13:10 Wed 8 Sep, 2010 :: Napier 210 :: Dr Thomas Leistner :: University of Adelaide

                  Euclidean space is flat but the real world is curved. This causes lots of problems for sailors, surveyors, mapmakers, and even geometers. In the talk I will explain how the notion of curvature evolved in mathematics starting off from practical applications such as geodesy and cartography and yielding less practical applications in modern physics.
                  Simultaneous confidence band and hypothesis test in generalised varying-coefficient models
                  15:05 Fri 10 Sep, 2010 :: Napier LG28 :: Prof Wenyang Zhang :: University of Bath

                  Generalised varying-coefficient models (GVC) are very important models. There are a considerable number of literature addressing these models. However, most of the existing literature are devoted to the estimation procedure. In this talk, I will systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. I will show the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient. I will compare different approaches for the construction of confidence band and hypothesis test. Finally, the proposed statistical inference methods are used to analyse the data from China about contraceptive use there, which leads to some interesting findings.
                  Contraction subgroups in locally compact groups
                  13:10 Fri 17 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Prof George Willis :: University of Newcastle

                  For each automorphism, $\alpha$, of the locally compact group $G$ there is a corresponding {\sl contraction subgroup\/}, $\hbox{con}(\alpha)$, which is the set of $x\in G$ such that $\alpha^n(x)$ converges to the identity as $n\to \infty$. Contractions subgroups are important in representation theory, through the Mautner phenomenon, and in the study of convolution semigroups. If $G$ is a Lie group, then $\hbox{con}(\alpha)$ is automatically closed, can be described in terms of eigenvalues of $\hbox{ad}(\alpha)$, and is nilpotent. Since any connected group may be approximated by Lie groups, contraction subgroups of connected groups are thus well understood. Following a general introduction, the talk will focus on contraction subgroups of totally disconnected groups. A criterion for non-triviality of $\hbox{con}(\alpha)$ will be described (joint work with U.~Baumgartner) and a structure theorem for $\hbox{con}(\alpha)$ when it is closed will be presented (joint with H.~Gl\"oeckner).
                  Hugs not drugs
                  15:10 Mon 20 Sep, 2010 :: Ingkarni Wardli B17 :: Dr Scott McCue :: Queensland University of Technology

                  I will discuss a model for drug diffusion that involves a Stefan problem with a "kinetic undercooling". I like Stefan problems, so I like this model. I like drugs too, but only legal ones of course. Anyway, it turns out that in some parameter regimes, this sophisticated moving boundary problem hardly works better than a simple linear undergraduate model (there's a lesson here for mathematical modelling). On the other hand, for certain polymer capsules, the results are interesting and suggest new means for controlled drug delivery. If time permits, I may discuss certain asymptotic limits that are of interest from a Stefan problem perspective. Finally, I won't bring any drugs with me to the seminar, but I'm willing to provide hugs if necessary.
                  The mathematics of smell
                  15:10 Wed 29 Sep, 2010 :: Ingkarni Wardli 5.57 :: Dr Michael Borgas :: CSIRO Light Metals Flagship; Marine and Atmospheric Research; Centre for Australian Weather and Clim

                  The sense of smell is important in nature, but the least well understood of our senses. A mathematical model of smell, which combines the transmission of volatile-organic-compound chemical signals (VOCs) on the wind, transduced by olfactory receptors in our noses into neural information, and assembled into our odour perception, is useful. Applications include regulations for odour nuisance, like German VDI protocols for calibrated noses, to the design of modern chemical sensors for extracting information from the environment and even for the perfume industry. This talk gives a broad overview of turbulent mixing in surface layers of the atmosphere, measurements of VOCs with PTR-MS (proton transfer reaction mass spectrometers), our noses, and integrated environmental models of the Alumina industry (a source of odour emissions) to help understand the science of smell.
                  At least four doors, numerous goats, a car, a frog, four lily pads and some probability
                  11:10 Wed 13 Oct, 2010 :: Napier 210 :: Dr Joshua Ross :: University of Adelaide

                  Media...
                  In the process of determining, amongst other things, the optimal strategy for playing a game show, and explaining the apparent persistence of a population that can be shown to die out with certainty, we will encounter a car, numerous goats, at least four doors, a frog, four lily pads, and some applied probability.
                  Some algebras associated with quantum gauge theories
                  13:10 Fri 15 Oct, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Keith Hannabuss :: Balliol College, Oxford

                  Classical gauge theories study sections of vector bundles and associated connections and curvature. The corresponding quantum gauge theories are normally written algebraically but can be understood as noncommutative geometries. This talk will describe one approach to the quantum gauge theories which uses braided categories.
                  IGA-AMSI Workshop: Dirac operators in geometry, topology, representation theory, and physics
                  10:00 Mon 18 Oct, 2010 :: 7.15 Ingkarni Wardli :: Prof Dan Freed :: University of Texas, Austin

                  Lecture Series by Dan Freed (University of Texas, Austin). Dirac introduced his eponymous operator to describe electrons in quantum theory. It was rediscovered by Atiyah and Singer in their study of the index problem on manifolds. In these lectures we explore new theorems and applications. Several of these also involve K-theory in its recent twisted and differential variations. These lectures will be supplemented by additional talks by invited speakers. For more details, please see the conference webpage: http://www.iga.adelaide.edu.au/workshops/WorkshopOct2010/
                  TBA
                  15:05 Fri 22 Oct, 2010 :: Napier LG28 :: Dr Andy Lian :: University of Adelaide

                  Statistical physics and behavioral adaptation to Creation's main stimuli: sex and food
                  15:10 Fri 29 Oct, 2010 :: E10 B17 Suite 1 :: Prof Laurent Seuront :: Flinders University and South Australian Research and Development Institute

                  Animals typically search for food and mates, while avoiding predators. This is particularly critical for keystone organisms such as intertidal gastropods and copepods (i.e. millimeter-scale crustaceans) as they typically rely on non-visual senses for detecting, identifying and locating mates in their two- and three-dimensional environments. Here, using stochastic methods derived from the field of nonlinear physics, we provide new insights into the nature (i.e. innate vs. acquired) of the motion behavior of gastropods and copepods, and demonstrate how changes in their behavioral properties can be used to identify the trade-offs between foraging for food or sex. The gastropod Littorina littorea hence moves according to fractional Brownian motions while foraging for food (in accordance with the fractal nature of food distributions), and switch to Brownian motion while foraging for sex. In contrast, the swimming behavior of the copepod Temora longicornis belongs to the class of multifractal random walks (MRW; i.e. a form of anomalous diffusion), characterized by a nonlinear moment scaling function for distance versus time. This clearly differs from the traditional Brownian and fractional Brownian walks expected or previously detected in animal behaviors. The divergence between MRW and Levy flight and walk is also discussed, and it is shown how copepod anomalous diffusion is enhanced by the presence and concentration of conspecific water-borne signals, and is dramatically increasing male-female encounter rates.
                  Arbitrage bounds for weighted variance swap prices
                  15:05 Fri 3 Dec, 2010 :: Napier LG28 :: Prof Mark Davis :: Imperial College London

                  This paper builds on earlier work by Davis and Hobson (Mathematical Finance, 2007) giving model-free---except for a 'frictionless markets' assumption--- necessary and sufficient conditions for absence of arbitrage given a set of current-time put and call options on some underlying asset. Here we suppose that the prices of a set of put options, all maturing at the same time, are given and satisfy the conditions for consistency with absence of arbitrage. We now add a path-dependent option, specifically a weighted variance swap, to the set of traded assets and ask what are the conditions on its time-0 price under which consistency with absence of arbitrage is maintained. In the present work, we work under the extra modelling assumption that the underlying asset price process has continuous paths. In general, we find that there is always a non- trivial lower bound to the range of arbitrage-free prices, but only in the case of a corridor swap do we obtain a finite upper bound. In the case of, say, the vanilla variance swap, a finite upper bound exists when there are additional traded European options which constrain the left wing of the volatility surface in appropriate ways.
                  Higher stacks and homotopy theory II: the motivic context
                  13:10 Thu 16 Dec, 2010 :: Ingkarni Wardli B21 :: Mr James Wallbridge :: University of Adelaide and Institut de mathematiques de Toulouse

                  In part I of this talk (JC seminar May 2008) we presented motivation and the basic definitions for building homotopy theory into an arbitrary category by introducing the notion of (higher) stacks. In part II we consider a specific example on the category of schemes to illustrate how the machinery works in practice. It will lead us into motivic territory (if we like it or not).
                  Complete quaternionic Kahler manifolds associated to cubic polynomials
                  13:10 Fri 11 Feb, 2011 :: Ingkarni Wardli B18 :: Prof Vicente Cortes :: University of Hamburg

                  We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h = 1} defined by a homogeneous cubic polynomial h such that -\partial^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler manifold defines a complete quaternionic Kahler manifold of negative scalar curvature. We classify all complete quaternionic Kahler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.
                  Queues with skill based routing under FCFS–ALIS regime
                  15:10 Fri 11 Feb, 2011 :: B17 Ingkarni Wardli :: Prof Gideon Weiss :: The University of Haifa, Israel

                  We consider a system where jobs of several types are served by servers of several types, and a bipartite graph between server types and job types describes feasible assignments. This is a common situation in manufacturing, call centers with skill based routing, matching of parent-child in adoption or matching in kidney transplants etc. We consider the case of first come first served policy: jobs are assigned to the first available feasible server in order of their arrivals. We consider two types of policies for assigning customers to idle servers - a random assignment and assignment to the longest idle server (ALIS) We survey some results for four different situations:

                  • For a loss system we find conditions for reversibility and insensitivity.
                  • For a manufacturing type system, in which there is enough capacity to serve all jobs, we discuss a product form solution and waiting times.
                  • For an infinite matching model in which an infinite sequence of customers of IID types, and infinite sequence of servers of IID types are matched according to first come first, we obtain a product form stationary distribution for this system, which we use to calculate matching rates.
                  • For a call center model with overload and abandonments we make some plausible observations.

                  This talk surveys joint work with Ivo Adan, Rene Caldentey, Cor Hurkens, Ed Kaplan and Damon Wischik, as well as work by Jeremy Visschers, Rishy Talreja and Ward Whitt.

                  Heat transfer scaling and emergence of three-dimensional flow in horizontal convection
                  15:10 Fri 25 Feb, 2011 :: Conference Room Level 7 Ingkarni Wardli :: Dr Greg Sheard :: Monash University

                  Horizontal convecton refers to flows driven by uneven heating on a horizontal forcing boundary. Flows exhibiting these characteristics are prevalent in nature, and include the North-South Hadley circulation within the atmosphere between warmer and more temperate latitudes, as well as ocean currents driven by non-uniform heating via solar radiation.

                  Here a model for these generic convection flows is established featuring a rectangular enclosure, insulated on the side and top walls, and driven by a linear temperature gradient applied along the bottom wall. Rayleigh number dependence of heat transfer through the forcing boundary is computed and compared with theory. Attention is given to transitions in the flow, including the development of unsteady flow and three-dimensional flow: the effect of these transitions on the Nusselt-Rayleigh number scaling exponents is described.

                  What is a p-adic number?
                  12:10 Mon 28 Feb, 2011 :: 5.57 Ingkarni Wardli :: Alexander Hanysz :: University of Adelaide

                  The p-adic numbers are: (a) something that visiting seminar speakers invoke when the want to frighten the audience; (b) a fascinating and useful concept in modern algebra; (c) alphabetically just before q-adic numbers? In this talk I hope to convince the audience that option (b) is worth considering. I will begin by reviewing how we get from integers via rational numbers to the real number system. Then we'll look at how this process can be "twisted" to produce something new.
                  Real analytic sets in complex manifolds I: holomorphic closure dimension
                  13:10 Fri 4 Mar, 2011 :: Mawson 208 :: Dr Rasul Shafikov :: University of Western Ontario

                  After a quick introduction to real and complex analytic sets, I will discuss possible notions of complex dimension of real sets, and then discuss a structure theorem for the holomorphic closure dimension which is defined as the dimension of the smallest complex analytic germ containing the real germ.
                  How are weather forecasts made?... and what role does mathematics play?
                  12:10 Mon 7 Mar, 2011 :: 5.57 Ingkarni Wardli :: Mika Peace :: University of Adelaide

                  Have you ever wondered where the weather forecast for the next seven days comes from? Come and find out! We will look at the basic laws of meteorology, leading in to the primitive equations, which are solved on supercomputers to produce the weather forecasts we see every day. We will finish by using the current numerical weather prediction charts to forecast our weather for the next few days.
                  Real analytic sets in complex manifolds II: complex dimension
                  13:10 Fri 11 Mar, 2011 :: Mawson 208 :: Dr Rasul Shafikov :: University of Western Ontario

                  Given a real analytic set R, denote by A the subset of R of points through which there is a nontrivial complex variety contained in R, i.e., A consists of points in R of positive complex dimension. I will discuss the structure of the set A.
                  Bioinspired computation in combinatorial optimization: algorithms and their computational complexity
                  15:10 Fri 11 Mar, 2011 :: 7.15 Ingkarni Wardli :: Dr Frank Neumann :: The University of Adelaide

                  Media...
                  Bioinspired computation methods, such as evolutionary algorithms and ant colony optimization, are being applied successfully to complex engineering and combinatorial optimization problems. The computational complexity analysis of this type of algorithms has significantly increased the theoretical understanding of these successful algorithms. In this talk, I will give an introduction into this field of research and present some important results that we achieved for problems from combinatorial optimization. These results can also be found in my recent textbook "Bioinspired Computation in Combinatorial Optimization -- Algorithms and Their Computational Complexity".
                  Tilings in the plane
                  12:10 Wed 16 Mar, 2011 :: Napier 210 :: Dr Susan Barwick :: University of Adelaide

                  Media...
                  We show that there are only three regular tilings of the plane, that is, tilings using a regular polygon tile, with tile vertices touching. We also classify the semiregular tilings; tilings using more than one type of regular polygon. These tilings all have many symmetries, in particular, we can translate the tiling, and it still looks the same. Sir Roger Penrose constructed a set of aperiodic tiles; a tiling using these Penrose tiles has no translational symmetry, that is, a translated copy will never match the original. We look at some of the interesting properties of these tiles.
                  Surface quotients of hyperbolic buildings
                  13:10 Fri 18 Mar, 2011 :: Mawson 208 :: Dr Anne Thomas :: University of Sydney

                  Let I(p,v) be Bourdon's building, the unique simply-connected 2-complex such that all 2-cells are regular right-angled hyperbolic p-gons, and the link at each vertex is the complete bipartite graph K_{v,v}. We investigate and mostly determine the set of triples (p,v,g) for which there is a discrete group acting on I(p,v) so that the quotient is a compact orientable surface of genus g. Surprisingly, the existence of such a quotient depends upon the value of v. The remaining cases lead to open questions in tessellations of surfaces and in number theory. We use elementary group theory, combinatorics, algebraic topology and number theory. This is joint work with David Futer.
                  To which extent the model of Black-Scholes can be applied in the financial market?
                  12:10 Mon 21 Mar, 2011 :: 5.57 Ingkarni Wardli :: Ahmed Hamada :: University of Adelaide

                  Black and Scholes have introduced a new approach to model the stock price dynamics about three decades ago. The so called Black Scholes model seems to be very adapted to the nature of market prices, mainly because the usage of the Brownian motion and the mathematical properties that follow from. Like every theoretical model, put in practice, it does not appear to be flawless, that means that new adaptations and extensions should be made so that engineers and marketers could utilise the Black Scholes models to trade and hedge risk on the market. A more detailed description with application will be given in the talk.
                  A mathematical investigation of methane encapsulation in carbon nanotubes.
                  12:10 Mon 21 Mar, 2011 :: 5.57 Ingkarni Wardli :: Olumide Adisa :: University of Adelaide

                  I hope we don't have to wait until oil and coal run out before we tackle that." - Thomas Edison, 1931. In a bid to resolve energy issues consistent with Thomas Edison's worries, scientists have been looking at other clean and sustainable sources of energy such as natural gas - methane. In this talk, the interaction between a methane molecule and carbon nanotubes is investigated mathematically, using two different models - first discrete and second, continuous. These models are analyzed to determine the dimensions of the particular nanotubes which will readily suck-up methane molecules. The results determine the minimum and maximum interaction energies required for methane encapsulation in different tube sizes, and establish the second model of the methane molecule as a simple and elegant model which might be exploited for other problems.
                  Lorentzian manifolds with special holonomy
                  13:10 Fri 25 Mar, 2011 :: Mawson 208 :: Mr Kordian Laerz :: Humboldt University, Berlin

                  A parallel lightlike vector field on a Lorentzian manifold X naturally defines a foliation of codimension 1 on X and a 1-dimensional subfoliation. In the first part we introduce Lorentzian metrics on the total space of certain circle bundles in order to construct weakly irreducible Lorentzian manifolds admitting a parallel lightlike vector field such that all leaves of the foliations are compact. Then we study which holonomy representations can be realized in this way. Finally, we consider the structure of arbitrary Lorentzian manifolds for which the leaves of the foliations are compact.
                  Heat transfer scaling and emergence of three-dimensional flow in horizontal convection
                  15:10 Fri 25 Mar, 2011 :: Conference Room Level 7 Ingkarni Wardli :: Dr Greg Sheard :: Monash University

                  Nanotechnology: The mathematics of gas storage in metal-organic frameworks.
                  12:10 Mon 28 Mar, 2011 :: 5.57 Ingkarni Wardli :: Wei Xian Lim :: University of Adelaide

                  Have you thought about what sort of car you would be driving in the future? Would it be a hybrid, solar, hydrogen or electric car? I would like to be driving a hydrogen car because my field of research may aid in their development! In my presentation I will introduce you to the world of metal-organic frameworks, which are an exciting new class of materials that have great potential in applications such as hydrogen gas storage. I will also discuss about the mathematical model that I am using to model the performance of metal-organic frameworks based on beryllium.
                  Operator algebra quantum groups
                  13:10 Fri 1 Apr, 2011 :: Mawson 208 :: Dr Snigdhayan Mahanta :: University of Adelaide

                  Woronowicz initiated the study of quantum groups using C*-algebras. His framework enabled him to deal with compact (linear) quantum groups. In this talk we shall introduce a notion of quantum groups that can handle infinite dimensional examples like SU(\infty). We shall also study some quantum homogeneous spaces associated to this group and compute their K-theory groups. This is joint work with V. Mathai.
                  Classification for high-dimensional data
                  15:10 Fri 1 Apr, 2011 :: Conference Room Level 7 Ingkarni Wardli :: Associate Prof Inge Koch :: The University of Adelaide

                  For two-class classification problems Fisher's discriminant rule performs well in many scenarios provided the dimension, d, is much smaller than the sample size n. As the dimension increases, Fisher's rule may no longer be adequate, and can perform as poorly as random guessing. In this talk we look at new ways of overcoming this poor performance for high-dimensional data by suitably modifying Fisher's rule, and in particular we describe the 'Features Annealed Independence Rule (FAIR)? of Fan and Fan (2008) and a rule based on canonical correlation analysis. I describe some theoretical developments, and also show analysis of data which illustrate the performance of these modified rule.
                  Modelling of Hydrological Persistence in the Murray-Darling Basin for the Management of Weirs
                  12:10 Mon 4 Apr, 2011 :: 5.57 Ingkarni Wardli :: Aiden Fisher :: University of Adelaide

                  The lakes and weirs along the lower Murray River in Australia are aggregated and considered as a sequence of five reservoirs. A seasonal Markov chain model for the system will be implemented, and a stochastic dynamic program will be used to find optimal release strategies, in terms of expected monetary value (EMV), for the competing demands on the water resource given the stochastic nature of inflows. Matrix analytic methods will be used to analyse the system further, and in particular enable the full distribution of first passage times between any groups of states to be calculated. The full distribution of first passage times can be used to provide a measure of the risk associated with optimum EMV strategies, such as conditional value at risk (CVaR). The sensitivity of the model, and risk, to changing rainfall scenarios will be investigated. The effect of decreasing the level of discretisation of the reservoirs will be explored. Also, the use of matrix analytic methods facilitates the use of hidden states to allow for hydrological persistence in the inflows. Evidence for hydrological persistence of inflows to the lower Murray system, and the effect of making allowance for this, will be discussed.
                  How round is your triangle, square, pentagon, ...?
                  12:10 Wed 6 Apr, 2011 :: Napier 210 :: Dr Barry Cox :: University of Adelaide

                  Media...
                  Most of us are familiar with the problem of making circular holes in wood or other material. For smaller diameter holes we typically use a drill, and for larger diameter holes a spade-bit, hole-saw or plunge router may be used. However for some applications, like mortise-and-tenon joints, what is needed is a tool that will produce a hole with a cross-section that is something other than a circle. In this talk we look at curves that may be used as the basis for a device that will produce holes with a cross-section of an equilateral triangle, square, or any regular polygon. Along the way we will touch on areas of engineering, algebra, geometry, calculus, Gothic art and architecture.
                  Spherical tube hypersurfaces
                  13:10 Fri 8 Apr, 2011 :: Mawson 208 :: Prof Alexander Isaev :: Australian National University

                  We consider smooth real hypersurfaces in a complex vector space. Specifically, we are interested in tube hypersurfaces, i.e., hypersurfaces represented as the direct product of the imaginary part of the space and hypersurfaces lying in its real part. Tube hypersurfaces arise, for instance, as the boundaries of tube domains. The study of tube domains is a classical subject in several complex variables and complex geometry, which goes back to the beginning of the 20th century. Indeed, already Siegel found it convenient to realise certain symmetric domains as tubes. One can endow a tube hypersurface with a so-called CR-structure, which is the remnant of the complex structure on the ambient vector space. We impose on the CR-structure the condition of sphericity. One way to state this condition is to require a certain curvature (called the CR-curvature of the hypersurface) to vanish identically. Spherical tube hypersurfaces possess remarkable properties and are of interest from both the complex-geometric and affine-geometric points of view. I my talk I will give an overview of the theory of such hypersurfaces. In particular, I will mention an algebraic construction arising from this theory that has applications in abstract commutative algebra and singularity theory. I will speak about these applications in detail in my colloquium talk later today.
                  How to value risk
                  12:10 Mon 11 Apr, 2011 :: 5.57 Ingkarni Wardli :: Leo Shen :: University of Adelaide

                  A key question in mathematical finance is: given a future random payoff X, what is its value today? If X represents a loss, one can ask how risky is X. To mitigate risk it must be modelled and quantified. The finance industry has used Value-at-Risk and conditional Value-at-Risk as measures. However, these measures are not time consistent and Value-at-Risk can penalize diversification. A modern theory of risk measures is being developed which is related to solutions of backward stochastic differential equations in continuous time and stochastic difference equations in discrete time. I first review risk measures used in mathematical finance, including static and dynamic risk measures. I recall results relating to backward stochastic difference equations (BSDEs) associated with a single jump process. Then I evaluate some numerical examples of the solutions of the backward stochastic difference equations and related risk measures. These concepts are new. I hope the examples will indicate how they might be used.
                  Centres of cyclotomic Hecke algebras
                  13:10 Fri 15 Apr, 2011 :: Mawson 208 :: A/Prof Andrew Francis :: University of Western Sydney

                  The cyclotomic Hecke algebras, or Ariki-Koike algebras $H(R,q)$, are deformations of the group algebras of certain complex reflection groups $G(r,1,n)$, and also are quotients of the ubiquitous affine Hecke algebra. The centre of the affine Hecke algebra has been understood since Bernstein in terms of the symmetric group action on the weight lattice. In this talk I will discuss the proof that over an arbitrary unital commutative ring $R$, the centre of the affine Hecke algebra maps \emph{onto} the centre of the cyclotomic Hecke algebra when $q-1$ is invertible in $R$. This is the analogue of the fact that the centre of the Hecke algebra of type $A$ is the set of symmetric polynomials in Jucys-Murphy elements (formerly known as he Dipper-James conjecture). Key components of the proof include the relationship between the trace functions on the affine Hecke algebra and on the cyclotomic Hecke algebra, and the link to the affine braid group. This is joint work with John Graham and Lenny Jones.
                  Comparison of Spectral and Wavelet Estimation of the Dynamic Linear System of a Wade Energy Device
                  12:10 Mon 2 May, 2011 :: 5.57 Ingkarni Wardli :: Mohd Aftar :: University of Adelaide

                  Renewable energy has been one of the main issues nowadays. The implications of fossil energy and nuclear energy along with its limited source have triggered researchers and industries to find another source of renewable energy for example hydro energy, wind energy and also wave energy. In this seminar, I will talk about the spectral estimation and wavelet estimation of a linear dynamical system of motion for a heaving buoy wave energy device. The spectral estimates was based on the Fourier transform, while the wavelet estimate was based on the wavelet transform. Comparisons between two spectral estimates with a wavelet estimate of the amplitude response operator(ARO) for the dynamical system of the wave energy device shows that the wavelet estimate ARO is much better for data with and without noise.
                  A strong Oka principle for embeddings of some planar domains into CxC*, I
                  13:10 Fri 6 May, 2011 :: Mawson 208 :: Mr Tyson Ritter :: University of Adelaide

                  The Oka principle refers to a collection of results in complex analysis which state that there are only topological obstructions to solving certain holomorphically defined problems involving Stein manifolds. For example, a basic version of Gromov's Oka principle states that every continuous map from a Stein manifold into an elliptic complex manifold is homotopic to a holomorphic map. In these two talks I will discuss a new result showing that if we restrict the class of source manifolds to circular domains and fix the target as CxC* we can obtain a much stronger Oka principle: every continuous map from a circular domain S into CxC* is homotopic to a proper holomorphic embedding. This result has close links with the long-standing and difficult problem of finding proper holomorphic embeddings of Riemann surfaces into C^2, with additional motivation from other sources.
                  On parameter estimation in population models
                  15:10 Fri 6 May, 2011 :: 715 Ingkarni Wardli :: Dr Joshua Ross :: The University of Adelaide

                  Essential to applying a mathematical model to a real-world application is calibrating the model to data. Methods for calibrating population models often become computationally infeasible when the populations size (more generally the size of the state space) becomes large, or other complexities such as time-dependent transition rates, or sampling error, are present. Here we will discuss the use of diffusion approximations to perform estimation in several scenarios, with successively reduced assumptions: (i) under the assumption of stationarity (the process had been evolving for a very long time with constant parameter values); (ii) transient dynamics (the assumption of stationarity is invalid, and thus only constant parameter values may be assumed); and, (iii) time-inhomogeneous chains (the parameters may vary with time) and accounting for observation error (a sample of the true state is observed).
                  The Cauchy integral formula
                  12:10 Mon 9 May, 2011 :: 5.57 Ingkarni Wardli :: Stephen Wade :: University of Adelaide

                  In this talk I will explain a simple method used for calculating the Hilbert transform of an analytic function, and provide some assurance that this isn't a bad thing to do in spite of the somewhat ominous presence of infinite areas. As it turns out this type of integral is not without an application, as will be demonstrated by one application to a problem in fluid mechanics.
                  When statistics meets bioinformatics
                  12:10 Wed 11 May, 2011 :: Napier 210 :: Prof Patty Solomon :: School of Mathematical Sciences

                  Media...
                  Bioinformatics is a new field of research which encompasses mathematics, computer science, biology, medicine and the physical sciences. It has arisen from the need to handle and analyse the vast amounts of data being generated by the new genomics technologies. The interface of these disciplines used to be information-poor, but is now information-mega-rich, and statistics plays a central role in processing this information and making it intelligible. In this talk, I will describe a published bioinformatics study which claimed to have developed a simple test for the early detection of ovarian cancer from a blood sample. The US Food and Drug Administration was on the verge of approving the test kits for market in 2004 when demonstrated flaws in the study design and analysis led to its withdrawal. We are still waiting for an effective early biomarker test for ovarian cancer.
                  A strong Oka principle for embeddings of some planar domains into CxC*, II
                  13:10 Fri 13 May, 2011 :: Mawson 208 :: Mr Tyson Ritter :: University of Adelaide

                  The Oka principle refers to a collection of results in complex analysis which state that there are only topological obstructions to solving certain holomorphically defined problems involving Stein manifolds. For example, a basic version of Gromov's Oka principle states that every continuous map from a Stein manifold into an elliptic complex manifold is homotopic to a holomorphic map. In these two talks I will discuss a new result showing that if we restrict the class of source manifolds to circular domains and fix the target as CxC* we can obtain a much stronger Oka principle: every continuous map from a circular domain S into CxC* is homotopic to a proper holomorphic embedding. This result has close links with the long-standing and difficult problem of finding proper holomorphic embeddings of Riemann surfaces into C^2, with additional motivation from other sources.
                  Change detection in rainfall time series for Perth, Western Australia
                  12:10 Mon 16 May, 2011 :: 5.57 Ingkarni Wardli :: Farah Mohd Isa :: University of Adelaide

                  There have been numerous reports that the rainfall in south Western Australia, particularly around Perth has observed a step change decrease, which is typically attributed to climate change. Four statistical tests are used to assess the empirical evidence for this claim on time series from five meteorological stations, all of which exceed 50 years. The tests used in this study are: the CUSUM; Bayesian Change Point analysis; consecutive t-test and the Hotelling’s T²-statistic. Results from multivariate Hotelling’s T² analysis are compared with those from the three univariate analyses. The issue of multiple comparisons is discussed. A summary of the empirical evidence for the claimed step change in Perth area is given.
                  Knots, posets and sheaves
                  13:10 Fri 20 May, 2011 :: Mawson 208 :: Dr Brent Everitt :: University of York

                  The Euler characteristic is a nice simple integer invariant that one can attach to a space. Unfortunately, it is not natural: maps between spaces do not induce maps between their Euler characteristics, because it makes no sense to talk of a map between integers. This shortcoming is fixed by homology. Maps between spaces induce maps between their homologies, with the Euler characteristic encoded inside the homology. Recently it has become possible to play the same game with knots and the Jones polynomial: the Khovanov homology of a knot both encodes the Jones polynomial and is a natural invariant of the knot. After saying what all this means, this talk will observe that Khovanov homology is just a special case of sheaf homology on a poset, and we will explore some of the ramifications of this observation. This is joint work with Paul Turner (Geneva/Fribourg).
                  Statistical challenges in molecular phylogenetics
                  15:10 Fri 20 May, 2011 :: Mawson Lab G19 lecture theatre :: Dr Barbara Holland :: University of Tasmania

                  Media...
                  This talk will give an introduction to the ways that mathematics and statistics gets used in the inference of evolutionary (phylogenetic) trees. Taking a model-based approach to estimating the relationships between species has proven to be an enormously effective, however, there are some tricky statistical challenges that remain. The increasingly plentiful amount of DNA sequence data is a boon, but it is also throwing a spotlight on some of the shortcomings of current best practice particularly in how we (1) assess the reliability of our phylogenetic estimates, and (2) how we choose appropriate models. This talk will aim to give a general introduction this area of research and will also highlight some results from two of my recent PhD students.
                  Statistical modelling in economic forecasting: semi-parametrically spatio-temporal approach
                  12:10 Mon 23 May, 2011 :: 5.57 Ingkarni Wardli :: Dawlah Alsulami :: University of Adelaide

                  How to model spatio-temporal variation of housing prices is an important and challenging problem as it is of vital importance for both investors and policy makersto assess any movement in housing prices. In this seminar I will talk about the proposed model to estimate any movement in housing prices and measure the risk more accurately.
                  Lifting principal bundles and abelian extensions
                  13:10 Fri 27 May, 2011 :: Mawson 208 :: Prof Michael Murray :: School of Mathematical Sciences

                  I will review what it means to lift the structure group of a principal bundle and the topological obstruction to this in the case of a central extension. I will then discuss some new results in the case of abelian extensions.
                  Permeability of heterogeneous porous media - experiments, mathematics and computations
                  15:10 Fri 27 May, 2011 :: B.21 Ingkarni Wardli :: Prof Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University

                  Permeability is a key parameter important to a variety of applications in geological engineering and in the environmental geosciences. The conventional definition of Darcy flow enables the estimation of permeability at different levels of detail. This lecture will focus on the measurement of surface permeability characteristics of a large cuboidal block of Indiana Limestone, using a surface permeameter. The paper discusses the theoretical developments, the solution of the resulting triple integral equations and associated computational treatments that enable the mapping of the near surface permeability of the cuboidal region. This data combined with a kriging procedure is used to develop results for the permeability distribution at the interior of the cuboidal region. Upon verification of the absence of dominant pathways for fluid flow through the cuboidal region, estimates are obtained for the "Effective Permeability" of the cuboid using estimates proposed by Wiener, Landau and Lifschitz, King, Matheron, Journel et al., Dagan and others. The results of these estimates are compared with the geometric mean, derived form the computational estimates.
                  Where is the best place in Australia to build an enhanced geothermal system?
                  12:10 Mon 30 May, 2011 :: 5.57 Ingkarni Wardli :: Ms Josephine Varney :: University of Adelaide

                  This week, my parents will join around 185,000 other Australians, in a significant move towards renewable energy, and install solar panels on the roof of their house. While solar energy is an important and useful form of renewable energy it is not able to provide power all the time. Opponents of renewable energy maintain that until renewable energy can provide energy all the time, traditional fossil-fuel generated power will be required to produce our base-load power. Geothermal energy is a renewable energy that can provide energy all the time. However, due to its special geological requirements, it can only be produced in a very small number of places in the world. An Enhanced Geothermal System (EGS) is a new technology which allows geothermal energy to be produced in a much wider range of places than traditional geothermal energy. Currently, there are ten different companies investigating possible EGS sties within Australia. This seminar investigates the question, that all these companies hope they have answered well, 'Where is the best place in Australia for an EGS facility?'
                  Optimal experimental design for stochastic population models
                  15:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Dan Pagendam :: CSIRO, Brisbane

                  Markov population processes are popular models for studying a wide range of phenomena including the spread of disease, the evolution of chemical reactions and the movements of organisms in population networks (metapopulations). Our ability to use these models effectively can be limited by our knowledge about parameters, such as disease transmission and recovery rates in an epidemic. Recently, there has been interest in devising optimal experimental designs for stochastic models, so that practitioners can collect data in a manner that maximises the precision of maximum likelihood estimates of the parameters for these models. I will discuss some recent work on optimal design for a variety of population models, beginning with some simple one-parameter models where the optimal design can be obtained analytically and moving on to more complicated multi-parameter models in epidemiology that involve latent states and non-exponentially distributed infectious periods. For these more complex models, the optimal design must be arrived at using computational methods and we rely on a Gaussian diffusion approximation to obtain analytical expressions for Fisher's information matrix, which is at the heart of most optimality criteria in experimental design. I will outline a simple cross-entropy algorithm that can be used for obtaining optimal designs for these models. We will also explore the improvements in experimental efficiency when using the optimal design over some simpler designs, such as the design where observations are spaced equidistantly in time.
                  Priority queueing systems with random switchover times and generalisations of the Kendall-Takacs equation
                  16:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

                  In this talk I will review existing analytical results for priority queueing systems with Poisson incoming flows, general service times and a single server which needs some (random) time to switch between requests of different priority. Specifically, I will discuss analytical results for the busy period and workload of such systems with a special structure of switchover times. The results related to the busy period can be seen as generalisations of the famous Kendall-Tak\'{a}cs functional equation for $M|G|1$: being formulated in terms of Laplace-Stieltjes transform, they represent systems of functional recurrent equations. I will present a methodology and algorithms of their numerical solution; the efficiency of these algorithms is achieved by acceleration of the numerical procedure of solving the classical Kendall-Tak\'{a}cs equation. At the end I will identify open problems with regard to such systems; these open problems are mainly related to the modelling of switchover times.
                  Natural operations on the Hochschild cochain complex
                  13:10 Fri 3 Jun, 2011 :: Mawson 208 :: Dr Michael Batanin :: Macquarie University

                  The Hochschild cochain complex of an associative algebra provides an important bridge between algebra and geometry. Algebraically, this is the derived center of the algebra. Geometrically, the Hochschild cohomology of the algebra of smooth functions on a manifold is isomorphic to the graduate space of polyvector fields on this manifold. There are many important operations acting on the Hochschild complex. It is, however, a tricky question to ask which operations are natural because the Hochschild complex is not a functor. In my talk I will explain how we can overcome this obstacle and compute all possible natural operations on the Hochschild complex. The result leads immediately to a proof of the Deligne conjecture on Hochschild cochains.
                  Inference and optimal design for percolation and general random graph models (Part I)
                  09:30 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

                  The problem of optimal arrangement of nodes of a random weighted graph is discussed in this workshop. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs.

                  We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity (geometric) graphs and numerical solution for graphs with threshold edge-probability functions.

                  We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice $\mathbb{Z}^d$ and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ëmostly populatedí designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Some of the obtained results may generalise to other lattices.

                  Inference and optimal design for percolation and general random graph models (Part II)
                  10:50 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

                  The problem of optimal arrangement of nodes of a random weighted graph is discussed in this workshop. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs.

                  We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity (geometric) graphs and numerical solution for graphs with threshold edge-probability functions.

                  We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice $\mathbb{Z}^d$ and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ëmostly populatedí designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Some of the obtained results may generalise to other lattices.

                  Probability density estimation by diffusion
                  15:10 Fri 10 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Dirk Kroese :: University of Queensland

                  Media...
                  One of the beautiful aspects of Mathematics is that seemingly disparate areas can often have deep connections. This talk is about the fundamental connection between probability density estimation, diffusion processes, and partial differential equations. Specifically, we show how to obtain efficient probability density estimators by solving partial differential equations related to diffusion processes. This new perspective leads, in combination with Fast Fourier techniques, to very fast and accurate algorithms for density estimation. Moreover, the diffusion formulation unifies most of the existing adaptive smoothing algorithms and provides a natural solution to the boundary bias of classical kernel density estimators. This talk covers topics in Statistics, Probability, Applied Mathematics, and Numerical Mathematics, with a surprise appearance of the theta function. This is joint work with Zdravko Botev and Joe Grotowski.
                  Quantitative proteomics: data analysis and statistical challenges
                  10:10 Thu 30 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Peter Hoffmann :: Adelaide Proteomics Centre

                  Introduction to functional data analysis with applications to proteomics data
                  11:10 Thu 30 Jun, 2011 :: 7.15 Ingkarni Wardli :: A/Prof Inge Koch :: School of Mathematical Sciences

                  Object oriented data analysis
                  14:10 Thu 30 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Steve Marron :: The University of North Carolina at Chapel Hill

                  Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie Groups and Symmetric Spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for Object Oriented Data Analysis create several potentially large new interfaces between mathematics and statistics. Even in situations where Euclidean analysis makes sense, there are statistical challenges because of the High Dimension Low Sample Size problem, which motivates a new type of asymptotics leading to non-standard mathematical statistics.
                  Object oriented data analysis of tree-structured data objects
                  15:10 Fri 1 Jul, 2011 :: 7.15 Ingkarni Wardli :: Prof Steve Marron :: The University of North Carolina at Chapel Hill

                  The field of Object Oriented Data Analysis has made a lot of progress on the statistical analysis of the variation in populations of complex objects. A particularly challenging example of this type is populations of tree-structured objects. Deep challenges arise, which involve a marriage of ideas from statistics, geometry, and numerical analysis, because the space of trees is strongly non-Euclidean in nature. These challenges, together with three completely different approaches to addressing them, are illustrated using a real data example, where each data point is the tree of blood arteries in one person's brain.
                  What is... a tensor?
                  12:10 Mon 25 Jul, 2011 :: 5.57 Ingkarni Wardli :: Mr Michael Albanese :: School of Mathematical Sciences

                  Tensors are important objects that are frequently used in a variety of fields including continuum mechanics, general relativity and differential geometry. Despite their importance, they are often defined poorly (if at all) which contributes to a lack of understanding. In this talk, I will give a concrete definition of a tensor and provide some familiar examples. For the remainder of the talk, I will discuss some applications—here I mean applications in the pure maths sense (i.e. more abstract nonsense, but hopefully still interesting).
                  The (dual) local cyclic homology valued Chern-Connes character for some infinite dimensional spaces
                  13:10 Fri 29 Jul, 2011 :: B.19 Ingkarni Wardli :: Dr Snigdhayan Mahanta :: School of Mathematical Sciences

                  I will explain how to construct a bivariant Chern-Connes character on the category of sigma-C*-algebras taking values in Puschnigg's local cyclic homology. Roughly, setting the first (resp. the second) variable to complex numbers one obtains the K-theoretic (resp. dual K-homological) Chern-Connes character in one variable. We shall focus on the dual K-homological Chern-Connes character and investigate it in the example of SU(infty).
                  Modelling computer network topologies through optimisation
                  12:10 Mon 1 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Rhys Bowden :: University of Adelaide

                  The core of the Internet is made up of many different computers (called routers) in many different interconnected networks, owned and operated by many different organisations. A popular and important field of study in the past has been "network topology": for instance, understanding which routers are connected to which other routers, or which networks are connected to which other networks; that is, studying and modelling the connection structure of the Internet. Previous study in this area has been plagued by unreliable or flawed experimental data and debate over appropriate models to use. The Internet Topology Zoo is a new source of network data created from the information that network operators make public. In order to better understand this body of network information we would like the ability to randomly generate network topologies resembling those in the zoo. Leveraging previous wisdom on networks produced as a result of optimisation processes, we propose a simple objective function based on possible economic constraints. By changing the relative costs in the objective function we can change the form of the resulting networks, and we compare these optimised networks to a variety of networks found in the Internet Topology Zoo.
                  The real thing
                  12:10 Wed 3 Aug, 2011 :: Napier 210 :: Dr Paul McCann :: School of Mathematical Sciences

                  Media...
                  Let x be a real number. This familiar and seemingly innocent assumption opens up a world of infinite variety and information. We use some simple techniques (powers of two, geometric series) to examine some interesting consequences of generating random real numbers, and encounter both the best flash drive and the worst flash drive you will ever meet. Come "hold infinity in the palm of your hand", and contemplate eternity for about half an hour. Almost nothing is assumed, almost everything is explained, and absolutely all are welcome.
                  Towards Rogers-Ramanujan identities for the Lie algebra A_n
                  13:10 Fri 5 Aug, 2011 :: B.19 Ingkarni Wardli :: Prof Ole Warnaar :: University of Queensland

                  The Rogers-Ramanujan identities are a pair of q-series identities proved by Leonard Rogers in 1894 which became famous two decades later as conjectures of Srinivasa Ramanujan. Since the 1980s it is known that the Rogers-Ramanujan identities are in fact identities for characters of certain modules for the affine Lie algebra A_1. This poses the obvious question as to whether there exist Rogers-Ramanujan identities for higher rank affine Lie algebras. In this talk I will describe some recent progress on this problem. I will also discuss a seemingly mysterious connection with the representation theory of quivers over finite fields.
                  Spectra alignment/matching for the classification of cancer and control patients
                  12:10 Mon 8 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide

                  Proteomic time-of-flight mass spectrometry produces a spectrum based on the peptides (chains of amino acids) in each patient’s serum sample. The spectra contain data points for an x-axis (peptide weight) and a y-axis (peptide frequency/count/intensity). It is our end goal to differentiate cancer (and sub-types) and control patients using these spectra. Before we can do this, peaks in these data must be found and common peptides to different spectra must be found. The data are noisy because of biotechnological variation and calibration error; data points for different peptide weights may in fact be same peptide. An algorithm needs to be employed to find common peptides between spectra, as performing alignment ‘by hand’ is almost infeasible. We borrow methods suggested in the literature by metabolomic gas chromatography-mass spectrometry and extend the methods for our purposes. In this talk I will go over the basic tenets of what we hope to achieve and the process towards this.
                  Horocycle flows at prime times
                  13:10 Wed 10 Aug, 2011 :: B.19 Ingkarni Wardli :: Prof Peter Sarnak :: Institute for Advanced Study, Princeton

                  The distribution of individual orbits of unipotent flows in homogeneous spaces are well understood thanks to the work work of Marina Ratner. It is conjectured that this property is preserved on restricting the times from the integers to primes, this being important in the study of prime numbers as well as in such dynamics. We review progress in understanding this conjecture, starting with Dirichlet (a finite system), Vinogradov (rotation of a circle or torus), Green and Tao (translation on a nilmanifold) and Ubis and Sarnak (horocycle flows in the semisimple case).
                  Boundaries of unsteady Lagrangian Coherent Structures
                  15:10 Wed 10 Aug, 2011 :: 5.57 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: Connecticut College, USA and the University of Adelaide

                  For steady flows, the boundaries of Lagrangian Coherent Structures are segments of manifolds connected to fixed points. In the general unsteady situation, these boundaries are time-varying manifolds of hyperbolic trajectories. Locating these boundaries, and attempting to meaningfully quantify fluid flux across them, is difficult since they are moving with time. This talk uses a newly developed tangential movement theory to locate these boundaries in nearly-steady compressible flows.
                  K3 surfaces: a crash course
                  13:10 Fri 12 Aug, 2011 :: B.19 Ingkarni Wardli :: A/Prof Nicholas Buchdahl :: University of Adelaide

                  Everything you have ever wanted to know about K3 surfaces! Two talks: 1:10 pm to 3:00 pm.
                  Textbooks go interactive but are they any better?
                  12:10 Mon 15 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Patrick Korbel :: University of Adelaide

                  Textbooks remain a central part of mathematics lessons in secondary schools. However, while textbooks are still formatted in the traditional way, they are including increasingly more sophisticated software packages to assist teachers and students. I will be demonstrating the different software packages available to students included with two South Australian textbooks. I will talk about how these new features fit into the current classroom environment and some of their potential positives and negatives. I would also like to encourage people to share their own experiences with textbooks, especially if they were used in a novel way or you have experience of mathematics classes in another country.
                  There are no magnetically charged particle-like solutions of the Einstein-Yang-Mills equations for models with Abelian residual groups
                  13:10 Fri 19 Aug, 2011 :: B.19 Ingkarni Wardli :: Dr Todd Oliynyk :: Monash University

                  According to a conjecture from the 90's, globally regular, static, spherically symmetric (i.e. particle-like) solutions with nonzero total magnetic charge are not expected to exist in Einstein-Yang-Mills theory. In this talk, I will describe recent work done in collaboration with M. Fisher where we establish the validity of this conjecture under certain restrictions on the residual gauge group. Of particular interest is that our non-existence results apply to the most widely studied models with Abelian residual groups.
                  Blood flow in the coiled umbilical cord
                  12:10 Mon 22 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr David Wilke :: University of Adelaide

                  The umbilical cord is the connecting cord between the developing embryo or fetus and the placenta. In a normal pregnancy it facilitates the supply of oxygen and nutrients from the placenta, in addition to the return of deoxygenated blood from the fetus. One of the most striking features of the umbilical cord is it's coiled structure, which allows the vasculature to withstand tensile and compressive forces in utero. The level of coiling also has a significant effect on the blood flow and cords exhibiting abnormally high or low levels are known to correlate well with adverse outcomes in pregancy, including fetal demise. In this talk I will discuss the complexities associated with numerically modeling blood flow within the umbilical cord, and provide an outline of the key features which will be investigated throughout my research.
                  Deformations of Oka manifolds
                  13:10 Fri 26 Aug, 2011 :: B.19 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

                  We discuss the behaviour of the Oka property with respect to deformations of compact complex manifolds. We have recently proved that in a family of compact complex manifolds, the set of Oka fibres corresponds to a G_delta subset of the base. We have also found a necessary and sufficient condition for the limit fibre of a sequence of Oka fibres to be Oka in terms of a new uniform Oka property. The special case when the fibres are tori will be considered, as well as the general case of holomorphic submersions with noncompact fibres.
                  Laplace's equation on multiply-connected domains
                  12:10 Mon 29 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide

                  Various physical processes take place on multiply-connected domains (domains with some number of 'holes'), such as the stirring of a fluid with paddles or the extrusion of material from a die. These systems may be described by partial differential equations (PDEs). However, standard numerical methods for solving PDEs are not well-suited to such examples: finite difference methods are difficult to implement on multiply-connected domains, especially when the boundaries are irregular or moving, while finite element methods are computationally expensive. In this talk I will describe a fast and accurate numerical method for solving certain PDEs on two-dimensional multiply-connected domains, considering Laplace's equation as an example. This method takes advantage of complex variable techniques which allow the solution to be found with spectral accuracy provided the boundary data is smooth. Other advantages over traditional numerical methods will also be discussed.
                  Oka properties of some hypersurface complements
                  13:10 Fri 2 Sep, 2011 :: B.19 Ingkarni Wardli :: Mr Alexander Hanysz :: University of Adelaide

                  Oka manifolds can be viewed as the "opposite" of Kobayashi hyperbolic manifolds. Kobayashi conjectured that the complement of a generic algebraic hypersurface of sufficiently high degree is hyperbolic. Therefore it is natural to ask whether the complement is Oka for the case of low degree or non-algebraic hypersurfaces. We provide a complete answer to this question for complements of hyperplane arrangements, and some results for graphs of meromorphic functions.
                  Alignment of time course gene expression data sets using Hidden Markov Models
                  12:10 Mon 5 Sep, 2011 :: 5.57 Ingkarni Wardli :: Mr Sean Robinson :: University of Adelaide

                  Time course microarray experiments allow for insight into biological processes by measuring gene expression over a time period of interest. This project is concerned with time course data from a microarray experiment conducted on a particular variety of grapevine over the development of the grape berries at a number of different vineyards in South Australia. The aim of the project is to construct a methodology for combining the data from the different vineyards in order to obtain more precise estimates of the underlying behaviour of the genes over the development process. A major issue in doing so is that the rate of development of the grape berries is different at different vineyards. Hidden Markov models (HMMs) are a well established methodology for modelling time series data in a number of domains and have been previously used for gene expression analysis. Modelling the grapevine data presents a unique modelling issue, namely the alignment of the expression profiles needed to combine the data from different vineyards. In this seminar, I will describe our problem, review HMMs, present an extension to HMMs and show some preliminary results modelling the grapevine data.
                  Twisted Morava K-theory
                  13:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne

                  Morava's extraordinary K-theories K(n) are a family of generalized cohomology theories which behave in some ways like K-theory (indeed, K(1) is mod 2 K-theory). Their construction exploits Quillen's description of cobordism in terms of formal group laws and Lubin-Tate's methods in class field theory for constructing abelian extensions of number fields. Constructed from homotopy-theoretic methods, they do not admit a geometric description (like deRham cohomology, K-theory, or cobordism), but are nonetheless subtle, computable invariants of topological spaces. In this talk, I will give an introduction to these theories, and explain how it is possible to define an analogue of twisted K-theory in this setting. Traditionally, K-theory is twisted by a three-dimensional cohomology class; in this case, K(n) admits twists by (n+2)-dimensional classes. This work is joint with Hisham Sati.
                  Mathematical modelling of lobster populations in South Australia
                  12:10 Mon 12 Sep, 2011 :: 5.57 Ingkarni Wardli :: Mr John Feenstra :: University of Adelaide

                  Just how many lobsters are there hanging around the South Australian coastline? How is this number changing over time? What is the demographic breakdown of this number? And what does it matter? Find out the answers to these questions in my upcoming talk. I will provide a brief flavour of the kinds of quantitative methods involved, showcasing relevant applications of regression, population modelling, estimation, as well as simulation. A product of these analyses are biological performance indicators which are used by government to help decide on fishery controls such as yearly total allowable catch quotas. This assists in maintaining the sustainability of the fishery and hence benefits both the fishers and the lobsters they catch.
                  Cohomology of higher-rank graphs and twisted C*-algebras
                  13:10 Fri 16 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Aidan Sims :: University of Wollongong

                  Higher-rank graphs and their $C^*$-algebras were introduced by Kumjian and Pask in 2000. They have provided a rich source of tractable examples of $C^*$-algebras, the most elementary of which are the commutative algebras $C(\mathbb{T}^k)$ of continuous functions on $k$-tori. In this talk we shall describe how to define the homology and cohomology of a higher-rank graph, and how to associate to each higher-rank graph $\Lambda$ and $\mathbb{T}$-valued cocycle on $\Lambda$ a twisted higher-rank graph $C^*$-algebra. As elementary examples, we obtain all noncommutative tori. This is a preleminary report on ongoing joint work with Alex Kumjian and David Pask.
                  Statistical analysis of metagenomic data from the microbial community involved in industrial bioleaching
                  12:10 Mon 19 Sep, 2011 :: 5.57 Ingkarni Wardli :: Ms Susana Soto-Rojo :: University of Adelaide

                  In the last two decades heap bioleaching has become established as a successful commercial option for recovering copper from low-grade secondary sulfide ores. Genetics-based approaches have recently been employed in the task of characterizing mineral processing bacteria. Data analysis is a key issue and thus the implementation of adequate mathematical and statistical tools is of fundamental importance to draw reliable conclusions. In this talk I will give a recount of two specific problems that we have been working on. The first regarding experimental design and the latter on modeling composition and activity of the microbial consortium.
                  Can statisticians do better than random guessing?
                  12:10 Tue 20 Sep, 2011 :: Napier 210 :: A/Prof Inge Koch :: School of Mathematical Sciences

                  In the finance or credit risk area, a bank may want to assess whether a client is going to default, or be able to meet the repayments. In the assessment of benign or malignant tumours, a correct diagnosis is required. In these and similar examples, we make decisions based on data. The classical t-tests provide a tool for making such decisions. However, many modern data sets have more variables than observations, and the classical rules may not be any better than random guessing. We consider Fisher's rule for classifying data into two groups, and show that it can break down for high-dimensional data. We then look at ways of overcoming some of the weaknesses of the classical rules, and I show how these "post-modern" rules perform in practice.
                  T-duality via bundle gerbes I
                  13:10 Fri 23 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

                  In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
                  Estimating disease prevalence in hidden populations
                  14:05 Wed 28 Sep, 2011 :: B.18 Ingkarni Wardli :: Dr Amber Tomas :: The University of Oxford

                  Estimating disease prevalence in "hidden" populations such as injecting drug users or men who have sex with men is an important public health issue. However, traditional design-based estimation methods are inappropriate because they assume that a list of all members of the population is available from which to select a sample. Respondent Driven Sampling (RDS) is a method developed over the last 15 years for sampling from hidden populations. Similarly to snowball sampling, it leverages the fact that members of hidden populations are often socially connected to one another. Although RDS is now used around the world, there are several common population characteristics which are known to cause estimates calculated from such samples to be significantly biased. In this talk I'll discuss the motivation for RDS, as well as some of the recent developments in methods of estimation.
                  Understanding the dynamics of event networks
                  15:00 Wed 28 Sep, 2011 :: B.18 Ingkarni Wardli :: Dr Amber Tomas :: The University of Oxford

                  Within many populations there are frequent communications between pairs of individuals. Such communications might be emails sent within a company, radio communications in a disaster zone or diplomatic communications between states. Often it is of interest to understand the factors that drive the observed patterns of such communications, or to study how these factors are changing over over time. Communications can be thought of as events occuring on the edges of a network which connects individuals in the population. In this talk I'll present a model for such communications which uses ideas from social network theory to account for the complex correlation structure between events. Applications to the Enron email corpus and the dynamics of hospital ward transfer patterns will be discussed.
                  TBA
                  15:10 Fri 30 Sep, 2011 :: Napier LG23 :: Prof Tony Roberts :: The University of Adelaide

                  Statistical analysis of school-based student performance data
                  12:10 Mon 10 Oct, 2011 :: 5.57 Ingkarni Wardli :: Ms Jessica Tan :: University of Adelaide

                  Join me in the journey of being a statistician for 15 minutes of your day (if you are not already one) and experience the task of data cleaning without having to get your own hands dirty. Most of you may have sat the Basic Skills Tests when at school or know someone who currently has to do the NAPLAN (National Assessment Program - Literacy and Numeracy) tests. Tests like these assess student progress and can be used to accurately measure school performance. In trying to answer the research question: "what conclusions about student progress and school performance can be drawn from NAPLAN data or data of a similar nature, using mathematical and statistical modelling and analysis techniques?", I have uncovered some interesting results about the data in my initial data analysis which I shall explain in this talk.
                  The Makerbot - desktop printing in 3D - and some of the maths that makes it work
                  12:10 Thu 13 Oct, 2011 :: Napier 210 :: A/Prof Matt Roughan :: School of Mathematical Sciences

                  For many years industry has used CNC (computer numerically controlled) machines to craft specialist items. CNC machines traditionally mill out metal objects with arbitrary shapes, but they are expensive, large and dangerous. In recent years a new type of CNC machine has appeared - a 3D printer - which makes 3D objects by printing layers of plastic. These can be made safe, cheap, and small enough to fit on a desktop. I will show off my 3D printer, and explain some of the maths that goes into it.
                  Statistical modelling for some problems in bioinformatics
                  11:10 Fri 14 Oct, 2011 :: B.17 Ingkarni Wardli :: Professor Geoff McLachlan :: The University of Queensland

                  Media...
                  In this talk we consider some statistical analyses of data arising in bioinformatics. The problems include the detection of differential expression in microarray gene-expression data, the clustering of time-course gene-expression data and, lastly, the analysis of modern-day cytometric data. Extensions are considered to the procedures proposed for these three problems in McLachlan et al. (Bioinformatics, 2006), Ng et al. (Bioinformatics, 2006), and Pyne et al. (PNAS, 2009), respectively. The latter references are available at http://www.maths.uq.edu.au/~gjm/.
                  On the role of mixture distributions in the modelling of heterogeneous data
                  15:10 Fri 14 Oct, 2011 :: 7.15 Ingkarni Wardli :: Prof Geoff McLachlan :: University of Queensland

                  Media...
                  We consider the role that finite mixture distributions have played in the modelling of heterogeneous data, in particular for clustering continuous data via mixtures of normal distributions. A very brief history is given starting with the seminal papers by Day and Wolfe in the sixties before the appearance of the EM algorithm. It was the publication in 1977 of the latter algorithm by Dempster, Laird, and Rubin that greatly stimulated interest in the use of finite mixture distributions to model heterogeneous data. This is because the fitting of mixture models by maximum likelihood is a classic example of a problem that is simplified considerably by the EM's conceptual unification of maximum likelihood estimation from data that can be viewed as being incomplete. In recent times there has been a proliferation of applications in which the number of experimental units n is comparatively small but the underlying dimension p is extremely large as, for example, in microarray-based genomics and other high-throughput experimental approaches. Hence there has been increasing attention given not only in bioinformatics and machine learning, but also in mainstream statistics, to the analysis of complex data in this situation where n is small relative to p. The latter part of the talk shall focus on the modelling of such high-dimensional data using mixture distributions.
                  TBA
                  12:10 Mon 17 Oct, 2011 :: 5.57 Ingkarni Wardli :: Mr Casey Briggs :: University of Adelaide

                  T-duality via bundle gerbes II
                  13:10 Fri 21 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

                  In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
                  TBA
                  12:10 Mon 24 Oct, 2011 :: 5.57 Ingkarni Wardli :: Ms Soo Young Lee :: University of Adelaide

                  Dirac operators on classifying spaces
                  13:10 Fri 28 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Pedram Hekmati :: University of Adelaide

                  The Dirac operator was introduced by Paul Dirac in 1928 as the formal square root of the D'Alembert operator. Thirty years later it was rediscovered in Euclidean signature by Atiyah and Singer in their seminal work on index theory. In this talk I will describe efforts to construct a Dirac type operator on the classifying space for odd complex K-theory. Ultimately the aim is to produce a projective family of Fredholm operators realising elements in twisted K-theory of a certain moduli stack.
                  Mathematical opportunities in molecular space
                  15:10 Fri 28 Oct, 2011 :: B.18 Ingkarni Wardli :: Dr Aaron Thornton :: CSIRO

                  The study of molecular motion, interaction and space at the nanoscale has become a powerful tool in the area of gas separation, storage and conversion for efficient energy solutions. Modeling in this field has typically involved highly iterative computational algorithms such as molecular dynamics, Monte Carlo and quantum mechanics. Mathematical formulae in the form of analytical solutions to this field offer a range of useful and insightful advantages including optimization, bifurcation analysis and standardization. Here we present a few case scenarios where mathematics has provided insight and opportunities for further investigation.
                  Staircase to heaven
                  13:10 Fri 4 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Burkard Polster :: Monash University

                  Media...
                  How much of an overhang can we produce by stacking identical rectangular blocks at the edge of a table? It has been known for at least 100 years that the overhang can be as large as desired: we arrange the blocks in the form of a staircase. With $n$ blocks of length 2 the overhang can be made to sum to $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\cdots+\frac{1}{n}$. Since the harmonic series diverges, it follows that the overhang can be arranged to be as large as desired, simply by using a suitably large number of blocks. Recently, a number of interesting twists have been added to this paradoxical staircase. I'll be talking about some of these new developments and in particular about a continuous counterpart of the staircase that I've been pondering together with my colleagues David Treeby and Marty Ross.
                  Metric geometry in data analysis
                  13:10 Fri 11 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Facundo Memoli :: University of Adelaide

                  The problem of object matching under invariances can be studied using certain tools from metric geometry. The central idea is to regard objects as metric spaces (or metric measure spaces). The type of invariance that one wishes to have in the matching is encoded by the choice of the metrics with which one endows the objects. The standard example is matching objects in Euclidean space under rigid isometries: in this situation one would endow the objects with the Euclidean metric. More general scenarios are possible in which the desired invariance cannot be reflected by the preservation of an ambient space metric. Several ideas due to M. Gromov are useful for approaching this problem. The Gromov-Hausdorff distance is a natural candidate for doing this. However, this metric leads to very hard combinatorial optimization problems and it is difficult to relate to previously reported practical approaches to the problem of object matching. I will discuss different variations of these ideas, and in particular will show a construction of an L^p version of the Gromov-Hausdorff metric, called the Gromov-Wassestein distance, which is based on mass transportation ideas. This new metric directly leads to quadratic optimization problems on continuous variables with linear constraints. As a consequence of establishing several lower bounds, it turns out that several invariants of metric measure spaces turn out to be quantitatively stable in the GW sense. These invariants provide practical tools for the discrimination of shapes and connect the GW ideas to a number of pre-existing approaches.
                  Oka theory of blow-ups
                  13:10 Fri 18 Nov, 2011 :: B.19 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

                  This talk is a continuation of my talk last August. I will discuss the recently-obtained answers to the open questions I described then.
                  Stability analysis of nonparallel unsteady flows via separation of variables
                  15:30 Fri 18 Nov, 2011 :: 7.15 Ingkarni Wardli :: Prof Georgy Burde :: Ben-Gurion University

                  Media...
                  The problem of variables separation in the linear stability equations, which govern the disturbance behavior in viscous incompressible fluid flows, is discussed. Stability of some unsteady nonparallel three-dimensional flows (exact solutions of the Navier-Stokes equations) is studied via separation of variables using a semi-analytical, semi-numerical approach. In this approach, a solution with separated variables is defined in a new coordinate system which is sought together with the solution form. As the result, the linear stability problems are reduced to eigenvalue problems for ordinary differential equations which can be solved numerically. In some specific cases, the eigenvalue problems can be solved analytically. Those unique examples of exact (explicit) solution of the nonparallel unsteady flow stability problems provide a very useful test for methods used in the hydrodynamic stability theory. Exact solutions of the stability problems for some stagnation-type flows are presented.
                  Applications of tropical geometry to groups and manifolds
                  13:10 Mon 21 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Stephan Tillmann :: University of Queensland

                  Tropical geometry is a young field with multiple origins. These include the work of Bergman on logarithmic limit sets of algebraic varieties; the work of the Brazilian computer scientist Simon on discrete mathematics; the work of Bieri, Neumann and Strebel on geometric invariants of groups; and, of course, the work of Newton on polynomials. Even though there is still need for a unified foundation of the field, there is an abundance of applications of tropical geometry in group theory, combinatorics, computational algebra and algebraic geometry. In this talk I will give an overview of (what I understand to be) tropical geometry with a bias towards applications to group theory and low-dimensional topology.
                  Space of 2D shapes and the Weil-Petersson metric: shapes, ideal fluid and Alzheimer's disease
                  13:10 Fri 25 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Sergey Kushnarev :: National University of Singapore

                  The Weil-Petersson metric is an exciting metric on a space of simple plane curves. In this talk the speaker will introduce the shape space and demonstrate the connection with the Euler-Poincare equations on the group of diffeomorphisms (EPDiff). A numerical method for finding geodesics between two shapes will be demonstrated and applied to the surface of the hippocampus to study the effects of Alzheimer's disease. As another application the speaker will discuss how to do statistics on the shape space and what should be done to improve it.
                  Fluid flows in microstructured optical fibre fabrication
                  15:10 Fri 25 Nov, 2011 :: B.17 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide

                  Optical fibres are used extensively in modern telecommunications as they allow the transmission of information at high speeds. Microstructured optical fibres are a relatively new fibre design in which a waveguide for light is created by a series of air channels running along the length of the material. The flexibility of this design allows optical fibres to be created with adaptable (and previously unrealised) optical properties. However, the fluid flows that arise during fabrication can greatly distort the geometry, which can reduce the effectiveness of a fibre or render it useless. I will present an overview of the manufacturing process and highlight the difficulties. I will then focus on surface-tension driven deformation of the macroscopic version of the fibre extruded from a reservoir of molten glass, occurring during fabrication, which will be treated as a two-dimensional Stokes flow problem. I will outline two different complex-variable numerical techniques for solving this problem along with comparisons of the results, both to other models and to experimental data.
                  Collision and instability in a rotating fluid-filled torus
                  15:10 Mon 12 Dec, 2011 :: Benham Lecture Theatre :: Dr Richard Clarke :: The University of Auckland

                  The simple experiment discussed in this talk, first conceived by Madden and Mullin (JFM, 1994) as part of their investigations into the non-uniqueness of decaying turbulent flow, consists of a fluid-filled torus which is rotated in an horizontal plane. Turbulence within the contained flow is triggered through a rapid change in its rotation rate. The flow instabilities which transition the flow to this turbulent state, however, are truly fascinating in their own right, and form the subject of this presentation. Flow features observed in both UK- and Auckland-based experiments will be highlighted, and explained through both boundary-layer analysis and full DNS. In concluding we argue that this flow regime, with its compact geometry and lack of cumbersome flow entry effects, presents an ideal regime in which to study many prototype flow behaviours, very much in the same spirit as Taylor-Couette flow.
                  Spinal Research at the University of Adelaide
                  11:10 Wed 14 Dec, 2011 :: B.17 Ingkarni Wardli :: Dr Robert Moore :: Adelaide Centre for Spinal Research

                  TBA
                  15:10 Mon 16 Jan, 2012 :: TBA :: Professsor Mike Foster :: Ohio State University

                  Noncritical holomorphic functions of finite growth on algebraic Riemann surfaces
                  13:10 Fri 3 Feb, 2012 :: B.20 Ingkarni Wardli :: Prof Franc Forstneric :: University of Ljubljana

                  Given a compact Riemann surface X and a point p in X, we construct a holomorphic function without critical points on the punctured (algebraic) Riemann surface R=X-p which is of finite order at the point p. In the case at hand this improves the 1967 theorem of Gunning and Rossi to the effect that every open Riemann surface admits a noncritical holomorphic function, but without any particular growth condition. (Joint work with Takeo Ohsawa.)
                  Embedding circle domains into the affine plane C^2
                  13:10 Fri 10 Feb, 2012 :: B.20 Ingkarni Wardli :: Prof Franc Forstneric :: University of Ljubljana

                  We prove that every circle domain in the Riemann sphere admits a proper holomorphic embedding into the affine plane C^2. By a circle domain we mean a domain obtained by removing from the Riemann sphere a finite or countable family of pairwise disjoint closed round discs. Our proof also applies to some circle domains with punctures. The uniformization theorem of He and Schramm (1996) says that every domain in the Riemann sphere with at most countably many boundary components is conformally equivalent to a circle domain, so our theorem embeds all such domains properly holomorphically in C^2. (Joint work with Erlend F. Wold.)
                  Spinal Research at the University of Adelaide
                  15:10 Fri 10 Feb, 2012 :: B.20 Ingkarni Wardli :: Dr Robert Moore :: Adelaide Centre for Spinal Research

                  Plurisubharmonic subextensions as envelopes of disc functionals
                  13:10 Fri 2 Mar, 2012 :: B.20 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

                  I will describe new joint work with Evgeny Poletsky. We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient is a complex manifold with a local biholomorphism to $X$, except it need not be Hausdorff. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension.
                  IGA Workshop: The mathematical implications of gauge-string dualities
                  09:30 Mon 5 Mar, 2012 :: 7.15 Ingkarni Wardli :: Prof Rajesh Gopakumar :: Harish-Chandra Research Institute

                  Media...
                  Lecture series by Rajesh Gopakumar (Harish-Chandra Research Institute). The lectures will be supplemented by talks by other invited speakers.
                  The Lorentzian conformal analogue of Calabi-Yau manifolds
                  13:10 Fri 16 Mar, 2012 :: B.20 Ingkarni Wardli :: Prof Helga Baum :: Humboldt University

                  Calabi-Yau manifolds are Riemannian manifolds with holonomy group SU(m). They are Ricci-flat and Kahler and admit a 2-parameter family of parallel spinors. In the talk we will discuss the Lorentzian conformal analogue of this situation. If on a manifold a class of conformally equivalent metrics [g] is given, then one can consider the holonomy group of the conformal manifold (M,[g]), which is a subgroup of O(p+1,q+1) if the metric g has signature (p,q). There is a close relation between algebraic properties of the conformal holonomy group and the existence of Einstein metrics in the conformal class as well as to the existence of conformal Killing spinors. In the talk I will explain classification results for conformal holonomy groups of Lorentzian manifolds. In particular, I will describe Lorentzian manifolds (M,g) with conformal holonomy group SU(1,m), which can be viewed as the conformal analogue of Calabi-Yau manifolds. Such Lorentzian metrics g, known as Fefferman metrics, appear on S^1-bundles over strictly pseudoconvex CR spin manifolds and admit a 2-parameter family of conformal Killing spinors.
                  IGA Workshop: Dualities in field theories and the role of K-theory
                  09:30 Mon 19 Mar, 2012 :: 7.15 Ingkarni Wardli :: Prof Jonathan Rosenberg :: University of Maryland

                  Media...
                  Lecture series by Jonathan Rosenberg (University of Maryland). There will be additional talks by other invited speakers.
                  The de Rham Complex
                  12:10 Mon 19 Mar, 2012 :: 5.57 Ingkarni Wardli :: Mr Michael Albanese :: University of Adelaide

                  Media...
                  The de Rham complex is of fundamental importance in differential geometry. After first introducing differential forms (in the familiar setting of Euclidean space), I will demonstrate how the de Rham complex elegantly encodes one half (in a sense which will become apparent) of the results from vector calculus. If there is time, I will indicate how results from the remaining half of the theory can be concisely expressed by a single, far more general theorem.
                  Fluid mechanics: what's maths got to do with it?
                  13:10 Tue 20 Mar, 2012 :: 7.15 Ingkarni Wardli :: A/Prof Jim Denier :: School of Mathematical Sciences

                  Media...
                  We've all heard about the grand challenges in mathematics. There was the Poincare Conjecture, which has now been resolved. There is the Riemann Hypothesis which many are seeking to prove. But one of the most intriguing is the so called "Navier-Stokes Equations" problem, intriguing because it not only involves some wickedly difficult mathematics but also involves questions about our deep understanding of nature as encountered in the flow of fluids. This talk will introduce the problem (without the wickedly difficult mathematics) and discuss some of the consequences of its resolution.
                  Financial risk measures - the theory and applications of backward stochastic difference/differential equations with respect to the single jump process
                  12:10 Mon 26 Mar, 2012 :: 5.57 Ingkarni Wardli :: Mr Bin Shen :: University of Adelaide

                  Media...
                  This is my PhD thesis submitted one month ago. Chapter 1 introduces the backgrounds of the research fields. Then each chapter is a published or an accepted paper. Chapter 2, to appear in Methodology and Computing in Applied Probability, establishes the theory of Backward Stochastic Difference Equations with respect to the single jump process in discrete time. Chapter 3, published in Stochastic Analysis and Applications, establishes the theory of Backward Stochastic Differential Equations with respect to the single jump process in continuous time. Chapter 2 and 3 consist of Part I Theory. Chapter 4, published in Expert Systems With Applications, gives some examples about how to measure financial risks by the theory established in Chapter 2. Chapter 5, accepted by Journal of Applied Probability, considers the question of an optimal transaction between two investors to minimize their risks. It's the applications of the theory established in Chapter 3. Chapter 4 and 5 consist of Part II Applications.
                  Instability in standing waves in inhomogeneous nonlinear Schrodinger equations
                  13:10 Fri 30 Mar, 2012 :: B.17 Ingkarni Wardli :: Dr Robert Marangell :: The University of Sydney

                  Media...
                  In this talk, I will describe a mechanism for determining instability of standing wave solutions to a class of inhomogeneous nonlinear Schrodinger (NLS) equations. The inhomogeneity in this case means that the equations will spatially alternate between NLS and the so-called Gross-Pitaevskii equation. Such equations are useful in 1-D models of Bose-Einstein Condensates (BECs). The mechanism is inherently topological and therefore robust, leading to its application to a number of different soliton solutions, such as gap solitons, surface gap solitons, and dark soliton among others.
                  Bundle gerbes and the Faddeev-Mickelsson-Shatashvili anomaly
                  13:10 Fri 30 Mar, 2012 :: B.20 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

                  The Faddeev-Mickelsson-Shatashvili anomaly arises in the quantisation of fermions interacting with external gauge potentials. Mathematically, it can be described as a certain lifting problem for an extension of groups. The theory of bundle gerbes is very useful for studying lifting problems, however it only applies in the case of a central extension whereas in the study of the FMS anomaly the relevant extension is non-central. In this talk I will explain how to describe this anomaly indirectly using bundle gerbes and how to use a generalisation of bundle gerbes to describe the (non-central) lifting problem directly. This is joint work with Pedram Hekmati, Michael Murray and Danny Stevenson.
                  The Kazdan-Warner equation
                  12:10 Mon 2 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Damien Warman :: University of Adelaide

                  Media...
                  We look at an equation arising from the differential-geometric problem of specifying the scalar curvature of a manifold.
                  Fast-track study of viscous flow over topography using 'Smoothed Particle Hydrodynamics'
                  12:10 Mon 16 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Stephen Wade :: University of Adelaide

                  Media...
                  Motivated by certain tea room discussions, I am going to (attempt to) model the flow of a viscous fluid under gravity over conical topography. The method used is 'Smoothed Particle Hydrodynamics' (SPH), which is an easy-to-use but perhaps limited-accuracy computational method. The model could be extended to include solidification and thermodynamic effects that can also be implemented within the framework of SPH, and this has the obvious practical application to the modelling of the coverage of ice cream with ice magic, I mean, lava flows. If I fail to achieve this within the next 4 weeks, I will have to go through a talk on SPH that I gave during honours instead.
                  New examples of totally disconnected, locally compact groups
                  13:10 Fri 20 Apr, 2012 :: B.20 Ingkarni Wardli :: Dr Murray Elder :: University of Newcastle

                  I will attempt to explain what a totally disconnected, locally compact group is, and then describe some new work with George Willis on an attempt to create new examples based on Baumslag-Solitar groups, which are well known, tried and tested examples/counterexamples in geometric/combinatorial group theory. I will describe how to compute invariants of scale and flat rank for these groups.
                  Correcting Errors in RSA Private Keys
                  12:10 Mon 23 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Wilko Henecka :: University of Adelaide

                  Media...
                  Let pk=(N,e) be an RSA public key with corresponding secret key sk=(d,p,q,...). Assume that we obtain partial error-free information of sk, e.g., assume that we obtain half of the most significant bits of p. Then there are well-known algorithms to recover the full secret key. As opposed to these algorithms that allow for correcting erasures of the key sk, we present for the first time a heuristic probabilistic algorithm that is capable of correcting errors in sk provided that e is small. That is, on input of a full but error-prone secret key sk' we reconstruct the original sk by correcting the faults. More precisely, consider an error rate of d in [0,1), where we flip each bit in sk with probability d resulting in an erroneous key sk'. Our Las-Vegas type algorithm allows to recover sk from sk' in expected time polynomial in logN with success probability close to 1, provided that d is strictly less than 0.237. We also obtain a polynomial time Las-Vegas factorization algorithm for recovering the factorization (p,q) from an erroneous version with error rate d strictly less than 0.084.
                  Revenge of the undead statistician part II
                  13:10 Tue 24 Apr, 2012 :: 7.15 Ingkarni Wardli :: Mr Jono Tuke :: School of Mathematical Sciences

                  Media...
                  If you only go to one undergraduate seminar this year, then you should have gone to Jim Denier's - it was cracking, but if you decide to go to another, then this one has cholera, Bayesian statistics, random networks and zombies. Warning: may contain an overuse of pop culture references to motivate an interest in statistics.
                  A Problem of Siegel
                  13:10 Fri 27 Apr, 2012 :: B.20 Ingkarni Wardli :: Dr Brent Everitt :: University of York

                  The first explicit examples of orientable hyperbolic 3-manifolds were constructed by Weber, Siefert, and Lobell in the early 1930's. In the subsequent decades the world of hyperbolic n-manifolds has grown into an extraordinarily rich one. Its sociology is best understood through the eyes of invariants, and for hyperbolic manifolds the most important invariant is volume. Viewed this way the n-dimensional hyperbolic manifolds, for fixed n, look like a well-ordered subset of the reals (a discrete set even, when n is not 3). So we are naturally led to the (manifold) Siegel problem: for a given n, determine the minimum possible volume obtained by an orientable hyperbolic n-manifold. It is a problem with a long and venerable history. In this talk I will describe a unified solution to the problem in low even dimensions, one of which at least is new. Joint work with John Ratcliffe and Steve Tschantz (Vanderbilt).
                  Spatial-point data sets and the Polya distribution
                  15:10 Fri 27 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Benjamin Binder :: The University of Adelaide

                  Media...
                  Spatial-point data sets, generated from a wide range of physical systems and mathematical models, can be analyzed by counting the number of objects in equally sized bins. We find that the bin counts are related to the Polya distribution. New indexes are developed which quantify whether or not a spatial data set is at its most evenly distributed state. Using three case studies (Lagrangian fluid particles in chaotic laminar flows, cellular automata agents in discrete models, and biological cells within colonies), we calculate the indexes and predict the spatial-state of the system.
                  Mathematical modelling of the surface adsorption for methane on carbon nanostructures
                  12:10 Mon 30 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Olumide Adisa :: University of Adelaide

                  Media...
                  In this talk, methane (CH4) adsorption is investigated on both graphite and in the region between two aligned single-walled carbon nanotubes, which we refer to as the groove site. The Lennard–Jones potential function and the continuous approximation is exploited to determine surface binding energies between a single CH4 molecule and graphite and between a single CH4 and two aligned single-walled carbon nanotubes. The modelling indicates that for a CH4 molecule interacting with graphite, the binding energy of the system is minimized when the CH4 carbon is 3.83 angstroms above the surface of the graphitic carbon, while the binding energy of the CH4–groove site system is minimized when the CH4 carbon is 5.17 angstroms away from the common axis shared by the two aligned single-walled carbon nanotubes. These results confirm the current view that for larger groove sites, CH4 molecules in grooves are likely to move towards the outer surfaces of one of the single-walled carbon nanotubes. The results presented in this talk are computationally efficient and are in good agreement with experiments and molecular dynamics simulations, and show that CH4 adsorption on graphite and groove surfaces is more favourable at lower temperatures and higher pressures.
                  Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds
                  13:10 Fri 4 May, 2012 :: Napier LG28 :: Dr Tyson Ritter :: University of Adelaide

                  In complex geometry a manifold is Stein if there are, in a certain sense, "many" holomorphic maps from the manifold into C^n. While this has long been well understood, a fruitful definition of the dual notion has until recently been elusive. In Oka theory, a manifold is Oka if it satisfies several equivalent definitions, each stating that the manifold has "many" holomorphic maps into it from C^n. Related to this is the geometric condition of ellipticity due to Gromov, who showed that it implies a complex manifold is Oka. We present recent contributions to three open questions involving elliptic and Oka manifolds. We show that affine quotients of C^n are elliptic, and combine this with an example of Margulis to construct new elliptic manifolds of interesting homotopy types. It follows that every open Riemann surface properly acyclically embeds into an elliptic manifold, extending an existing result for open Riemann surfaces with abelian fundamental group.
                  Are Immigrants Discriminated in the Australian Labour Market?
                  12:10 Mon 7 May, 2012 :: 5.57 Ingkarni Wardli :: Ms Wei Xian Lim :: University of Adelaide

                  Media...
                  In this talk, I will present what I did in my honours project, which was to determine if immigrants, categorised as immigrants from English speaking countries and Non-English speaking countries, are discriminated in the Australian labour market. To determine if discrimination exists, a decomposition of the wage function is applied and analysed via regression analysis. Two different methods of estimating the unknown parameters in the wage function will be discussed: 1. the Ordinary Least Square method, 2. the Quantile Regression method. This is your rare chance of hearing me talk about non-nanomathematics related stuff!
                  Index type invariants for twisted signature complexes
                  13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide

                  Atiyah-Patodi-Singer proved an index theorem for non-local boundary conditions in the 1970's that has been widely used in mathematics and mathematical physics. A key application of their theory gives the index theorem for signature operators on oriented manifolds with boundary. As a consequence, they defined certain secondary invariants that were metric independent. I will discuss some recent work with Benameur where we extend the APS theory to signature operators twisted by an odd degree closed differential form, and study the corresponding secondary invariants.
                  Change detection in rainfall times series for Perth, Western Australia
                  12:10 Mon 14 May, 2012 :: 5.57 Ingkarni Wardli :: Ms Farah Mohd Isa :: University of Adelaide

                  Media...
                  There have been numerous reports that the rainfall in south Western Australia, particularly around Perth has observed a step change decrease, which is typically attributed to climate change. Four statistical tests are used to assess the empirical evidence for this claim on time series from five meteorological stations, all of which exceed 50 years. The tests used in this study are: the CUSUM; Bayesian Change Point analysis; consecutive t-test and the Hotelling's T^2-statistic. Results from multivariate Hotelling's T^2 analysis are compared with those from the three univariate analyses. The issue of multiple comparisons is discussed. A summary of the empirical evidence for the claimed step change in Perth area is given.
                  Computational complexity, taut structures and triangulations
                  13:10 Fri 18 May, 2012 :: Napier LG28 :: Dr Benjamin Burton :: University of Queensland

                  There are many interesting and difficult algorithmic problems in low-dimensional topology. Here we study the problem of finding a taut structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting taut structures is "hard", in the sense that it is NP-complete. We also prove that detecting taut structures is "not too hard", by showing it to be fixed-parameter tractable. This is joint work with Jonathan Spreer.
                  The classification of Dynkin diagrams
                  12:10 Mon 21 May, 2012 :: 5.57 Ingkarni Wardli :: Mr Alexander Hanysz :: University of Adelaide

                  Media...
                  The idea of continuous symmetry is often described in mathematics via Lie groups. These groups can be classified by their root systems: collections of vectors satisfying certain symmetry properties. The root systems are described in a concise way by Dynkin diagrams, and it turns out, roughly speaking, that there are only seven possible shapes for a Dynkin diagram. In this talk I'll describe some simple examples of Lie groups, explain what a root system is, and show how a Dynkin diagram encodes this information. Then I'll give a very brief sketch of the methods used to classify Dynkin diagrams.
                  P or NP: this is the question
                  13:10 Tue 22 May, 2012 :: 7.15 Ingkarni Wardli :: Dr Ali Eshragh :: School of Mathematical Sciences

                  Media...
                  Up to early 70's, the main concentration of mathematicians was the design of algorithms. However, the advent of computers changed this focus from not just the design of an algorithm but also to the most efficient algorithm. This created a new field of research, namely the complexity of algorithms, and the associated problem "Is P equal to NP?" was born. The latter question has been unknown for more than four decades and is one of the most famous open problems of the 21st century. Any person who can solve this problem will be awarded US$1,000,000 by the Clay Institute. In this talk, we are going to introduce this problem through simple examples and explain one of the intriguing approaches that may help to solve it.
                  On the full holonomy group of special Lorentzian manifolds
                  13:10 Fri 25 May, 2012 :: Napier LG28 :: Dr Thomas Leistner :: University of Adelaide

                  The holonomy group of a semi-Riemannian manifold is defined as the group of parallel transports along loops based at a point. Its connected component, the `restricted holonomy group', is given by restricting in this definition to contractible loops. The restricted holonomy can essentially be described by its Lie algebra and many classification results are obtained in this way. In contrast, the `full' holonomy group is a more global object and classification results are out of reach. In the talk I will describe recent results with H. Baum and K. Laerz (both HU Berlin) about the full holonomy group of so-called `indecomposable' Lorentzian manifolds. I will explain a construction method that arises from analysing the effects on holonomy when dividing the manifold by the action of a properly discontinuous group of isometries and present several examples of Lorentzian manifolds with disconnected holonomy groups.
                  Evaluation and comparison of the performance of Australian and New Zealand intensive care units
                  14:10 Fri 25 May, 2012 :: 7.15 Ingkarni Wardli :: Dr Jessica Kasza :: The University of Adelaide

                  Media...
                  Recently, the Australian Government has emphasised the need for monitoring and comparing the performance of Australian hospitals. Evaluating the performance of intensive care units (ICUs) is of particular importance, given that the most severe cases are treated in these units. Indeed, ICU performance can be thought of as a proxy for the overall performance of a hospital. We compare the performance of the ICUs contributing to the Australian and New Zealand Intensive Care Society (ANZICS) Adult Patient Database, the largest of its kind in the world, and identify those ICUs with unusual performance. It is well-known that there are many statistical issues that must be accounted for in the evaluation of healthcare provider performance. Indicators of performance must be appropriately selected and estimated, investigators must adequately adjust for casemix, statistical variation must be fully accounted for, and adjustment for multiple comparisons must be made. Our basis for dealing with these issues is the estimation of a hierarchical logistic model for the in-hospital death of each patient, with patients clustered within ICUs. Both patient- and ICU-level covariates are adjusted for, with a random intercept and random coefficient for the APACHE III severity score. Given that we expect most ICUs to have similar performance after adjustment for these covariates, we follow Ohlssen et al., JRSS A (2007), and estimate a null model that we expect the majority of ICUs to follow. This methodology allows us to rigorously account for the aforementioned statistical issues, and accurately identify those ICUs contributing to the ANZICS database that have comparatively unusual performance. This is joint work with Prof. Patty Solomon and Assoc. Prof. John Moran.
                  The change of probability measure for jump processes
                  12:10 Mon 28 May, 2012 :: 5.57 Ingkarni Wardli :: Mr Ahmed Hamada :: University of Adelaide

                  Media...
                  In financial derivatives pricing theory, it is very common to change the probability measure from historical measure "real world" into a Risk-Neutral measure as a development of the non arbitrage condition. Girsanov theorem is the most known example of this technique and is used when prices randomness is modelled by Brownian motions. Other genuine candidates for modelling market randomness that have proved efficiency in recent literature are jump process, so how can a change of measure be performed for such processes? This talk will address this question by introducing the non arbitrage condition, discussing Girsanov theorem for diffusion and jump processes and presenting a concrete example.
                  Geometric modular representation theory
                  13:10 Fri 1 Jun, 2012 :: Napier LG28 :: Dr Anthony Henderson :: University of Sydney

                  Representation theory is one of the oldest areas of algebra, but many basic questions in it are still unanswered. This is especially true in the modular case, where one considers vector spaces over a field F of positive characteristic; typically, complications arise for particular small values of the characteristic. For example, from a vector space V one can construct the symmetric square S^2(V), which is one easy example of a representation of the group GL(V). One would like to say that this representation is irreducible, but that statement is not always true: if F has characteristic 2, there is a nontrivial invariant subspace. Even for GL(V), we do not know the dimensions of all irreducible representations in all characteristics. In this talk, I will introduce some of the main ideas of geometric modular representation theory, a more recent approach which is making progress on some of these old problems. Essentially, the strategy is to re-formulate everything in terms of homology of various topological spaces, where F appears only as the field of coefficients and the spaces themselves are independent of F; thus, the modular anomalies in representation theory arise because homology with modular coefficients is detecting something about the topology that rational coefficients do not. In practice, the spaces are usually varieties over the complex numbers, and homology is replaced by intersection cohomology to take into account the singularities of these varieties.
                  Model turbulent floods based upon the Smagorinski large eddy closure
                  12:10 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Meng Cao :: University of Adelaide

                  Media...
                  Rivers, floods and tsunamis are often very turbulent. Conventional models of such environmental fluids are typically based on depth-averaged inviscid irrotational flow equations. We explore changing such a base to the turbulent Smagorinski large eddy closure. The aim is to more appropriately model the fluid dynamics of such complex environmental fluids by using such a turbulent closure. Large changes in fluid depth are allowed. Computer algebra constructs the slow manifold of the flow in terms of the fluid depth h and the mean turbulent lateral velocities u and v. The major challenge is to deal with the nonlinear stress tensor in the Smagorinski closure. The model integrates the effects of inertia, self-advection, bed drag, gravitational forcing and turbulent dissipation with minimal assumptions. Although the resultant model is close to established models, the real outcome is creating a sound basis for the modelling so others, in their modelling of more complex situations, can systematically include more complex physical processes.
                  A brief introduction to Support Vector Machines
                  12:30 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide

                  Media...
                  Support Vector Machines (SVMs) are used in a variety of contexts for a range of purposes including regression, feature selection and classification. To convey the basic principles of SVMs, this presentation will focus on the application of SVMs to classification. Classification (or discrimination), in a statistical sense, is supervised model creation for the purpose of assigning future observations to a group or class. An example might be determining healthy or diseased labels to patients from p characteristics obtained from a blood sample. While SVMs are widely used, they are most successful when the data have one or more of the following properties: The data are not consistent with a standard probability distribution. The number of observations, n, used to create the model is less than the number of predictive features, p. (The so-called small-n, big-p problem.) The decision boundary between the classes is likely to be non-linear in the feature space. I will present a short overview of how SVMs are constructed, keeping in mind their purpose. As this presentation is part of a double post-grad seminar, I will keep it to a maximum of 15 minutes.
                  Epidemiological consequences of household-based antiviral prophylaxis for pandemic influenza
                  14:10 Fri 8 Jun, 2012 :: 7.15 Ingkarni Wardli :: Dr Joshua Ross :: The University of Adelaide

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                  Antiviral treatment offers a fast acting alternative to vaccination. It is viewed as a first-line of defence against pandemic influenza, protecting families and household members once infection has been detected. In clinical trials antiviral treatment has been shown to be efficacious in preventing infection, limiting disease and reducing transmission, yet their impact at containing the 2009 influenza A(H1N1)pdm outbreak was limited. I will describe some of our work, which attempts to understand this seeming discrepancy, through the development of a general model and computationally efficient methodology for studying household-based interventions. This is joint work with Dr Andrew Black (Adelaide), and Prof. Matt Keeling and Dr Thomas House (Warwick, U.K.).
                  IGA Workshop: Dendroidal sets
                  14:00 Tue 12 Jun, 2012 :: Ingkarni Wardli B17 :: Dr Ittay Weiss :: University of the South Pacific

                  Media...
                  A series of four 2-hour lectures by Dr. Ittay Weiss. The theory of dendroidal sets was introduced by Moerdijk and Weiss in 2007 in the study of homotopy operads in algebraic topology. In the five years that have past since then several fundamental and highly non-trivial results were established. For instance, it was established that dendroidal sets provide models for homotopy operads in a way that extends the Joyal-Lurie approach to homotopy categories. It can be shown that dendroidal sets provide new models in the study of n-fold loop spaces. And it is very recently shown that dendroidal sets model all connective spectra in a way that extends the modeling of certain spectra by Picard groupoids. The aim of the lecture series will be to introduce the concepts mentioned above, present the elementary theory, and understand the scope of the results mentioned as well as discuss the potential for further applications. Sources for the course will include the article "From Operads to Dendroidal Sets" (in the AMS volume on mathematical foundations of quantum field theory (also on the arXiv)) and the lecture notes by Ieke Moerdijk "simplicial methods for operads and algebraic geometry" which resulted from an advanced course given in Barcelona 3 years ago. No prior knowledge of operads will be assumed nor any knowledge of homotopy theory that is more advanced then what is required for the definition of the fundamental group. The basics of the language of presheaf categories will be recalled quickly and used freely.
                  Introduction to quantales via axiomatic analysis
                  13:10 Fri 15 Jun, 2012 :: Napier LG28 :: Dr Ittay Weiss :: University of the South Pacific

                  Quantales were introduced by Mulvey in 1986 in the context of non-commutative topology with the aim of providing a concrete non-commutative framework for the foundations of quantum mechanics. Since then quantales found applications in other areas as well, among others in the work of Flagg. Flagg considers certain special quantales, called value quantales, that are desigend to capture the essential properties of ([0,\infty],\le,+) that are relevant for analysis. The result is a well behaved theory of value quantale enriched metric spaces. I will introduce the notion of quantales as if they were desigend for just this purpose, review most of the known results (since there are not too many), and address a some new results, conjectures, and questions.
                  Comparison of spectral and wavelet estimators of transfer function for linear systems
                  12:10 Mon 18 Jun, 2012 :: B.21 Ingkarni Wardli :: Mr Mohd Aftar Abu Bakar :: University of Adelaide

                  Media...
                  We compare spectral and wavelet estimators of the response amplitude operator (RAO) of a linear system, with various input signals and added noise scenarios. The comparison is based on a model of a heaving buoy wave energy device (HBWED), which oscillates vertically as a single mode of vibration linear system. HBWEDs and other single degree of freedom wave energy devices such as the oscillating wave surge convertors (OWSC) are currently deployed in the ocean, making single degree of freedom wave energy devices important systems to both model and analyse in some detail. However, the results of the comparison relate to any linear system. It was found that the wavelet estimator of the RAO offers no advantage over the spectral estimators if both input and response time series data are noise free and long time series are available. If there is noise on only the response time series, only the wavelet estimator or the spectral estimator that uses the cross-spectrum of the input and response signals in the numerator should be used. For the case of noise on only the input time series, only the spectral estimator that uses the cross-spectrum in the denominator gives a sensible estimate of the RAO. If both the input and response signals are corrupted with noise, a modification to both the input and response spectrum estimates can provide a good estimator of the RAO. However, a combination of wavelet and spectral methods is introduced as an alternative RAO estimator. The conclusions apply for autoregressive emulators of sea surface elevation, impulse, and pseudorandom binary sequences (PRBS) inputs. However, a wavelet estimator is needed in the special case of a chirp input where the signal has a continuously varying frequency.
                  Three Minute Thesis
                  14:00 Mon 2 Jul, 2012 :: B.21 Ingkarni Wardli

                  Media...
                  This session will feature the The School of Mathematical Sciences Three Minute Thesis competition. Each postgraduate participating will have three minutes to explain their thesis at a level appropriate for a non-specialist audience. The competition is open to all postgraduates within the School. All staff are welcome to attend.
                  K-theory and unbounded Fredholm operators
                  13:10 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Dr Jerry Kaminker :: University of California, Davis

                  There are several ways of viewing elements of K^1(X). One of these is via families of unbounded self-adjoint Fredholm operators on X. Each operator will have discrete spectrum, with infinitely many positive and negative eigenvalues of finite multiplicity. One can associate to such a family a geometric object, its graph, and the Chern character and other invariants of the family can be studied from this perspective. By restricting the dimension of the eigenspaces one may sometimes use algebraic topology to completely determine the family up to equivalence. This talk will describe the general framework and some applications to families on low-dimensional manifolds where the methods work well. Various notions related to spectral flow, the index gerbe and Berry phase play roles which will be discussed. This is joint work with Ron Douglas.
                  Complex geometry and operator theory
                  14:10 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Prof Ron Douglas :: Texas A&M University

                  In the study of bounded operators on Hilbert spaces of holomorphic functions, concepts and techniques from complex geometry are important. An anti-holomorphic bundle exists on which one can define the Chern connection. Its curvature turns out to be a complete invariant and various operator notions can't be reframed in terms of geometrical ones which leads to the solution of some problems. We will discuss this approach with an emphasis on natural examples in the one and multivariable case.
                  Inquiry-based learning: yesterday and today
                  15:30 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Prof Ron Douglas :: Texas A&M University

                  Media...
                  The speaker will report on a project to develop and promote approaches to mathematics instruction closely related to the Moore method -- methods which are called inquiry-based learning -- as well as on his personal experience of the Moore method. For background, see the speaker's article in the May 2012 issue of the Notices of the American Mathematical Society. To download the article, click on "Media" above.
                  The Four Colour Theorem
                  11:10 Mon 23 Jul, 2012 :: B.17 Ingkarni Wardli :: Mr Vincent Schlegel :: University of Adelaide

                  Media...
                  Arguably the most famous problem in discrete mathematics, the Four Colour Theorem was first conjectured in 1852 by South African mathematician Francis Guthrie. For 124 years, it defied many attempts to prove and disprove it. I will talk briefly about some of the rich history of this result, including some of the graph-theoretic techniques used in the 1976 Appel-Haken proof.
                  The Banach-Tarski Paradox
                  11:10 Mon 30 Jul, 2012 :: G.07 Engineering Mathematics :: Mr William Crawford :: University of Adelaide

                  Media...
                  The Banach-Tarski Paradox is one of the most counter intuitive results in set theory. It states that a ball can be cut up into a finite number of pieces, which using just rotations and translations can be reassembled into two identical copies of the original ball. This contradicts our naive belief that cutting, rotating and translating objects in Euclidean space should preserve volume. However the construction of the "cutting" is heavily dependent on the axiom of choice, and the resultant pieces are non-measurable, i.e. no consistent notion of volume can be assigned to them. A stronger form of the theorem states that any two bounded subsets of R^3 with non-empty interior are equidecomposable, that is one can be disassembled and reassembled into the other. I'll be going through a brief proof of the theorem (and in doing so further alienate the pure mathematicians in the room from everybody else).
                  The motivic logarithm and its realisations
                  13:10 Fri 3 Aug, 2012 :: Engineering North 218 :: Dr James Borger :: Australian National University

                  When a complex manifold is defined by polynomial equations, its cohomology groups inherit extra structure. This was discovered by Hodge in the 1920s and 30s. When the defining polynomials have rational coefficients, there is some additional, arithmetic structure on the cohomology. This was discovered by Grothendieck and others in the 1960s. But here the situation is still quite mysterious because each cohomology group has infinitely many different arithmetic structures and while they are not directly comparable, they share many properties---with each other and with the Hodge structure. All written accounts of this that I'm aware of treat arbitrary varieties. They are beautifully abstract and non-explicit. In this talk, I'll take the opposite approach and try to give a flavour of the subject by working out a perhaps the simplest nontrivial example, the cohomology of C* relative to a subset of two points, in beautifully concrete and explicit detail. Here the common motif is the logarithm. In Hodge theory, it is realised as the complex logarithm; in the crystalline theory, it's as the p-adic logarithm; and in the etale theory, it's as Kummer theory. I'll assume you have some familiarity with usual, singular cohomology of topological spaces, but I won't assume that you know anything about these non-topological cohomology theories.
                  AFL Tipping isn't all about numbers and stats...or is it.....
                  12:10 Mon 6 Aug, 2012 :: B.21 Ingkarni Wardli :: Ms Jessica Tan :: University of Adelaide

                  Media...
                  The result of an AFL game is always unpredictable - we all know that. Hence why we discuss the weekend's upsets and the local tipping competition as part of the "water-cooler and weekend" conversation on a Monday morning. Different people use various weird and wonderful techniques or criteria to predict the winning team. With readily available data, I will investigate and compare various strategies and define a measure of the hardness of a round (full acknowledgements will be made in my presentation). Hopefully this will help me for next year's tipping competition...
                  The importance of being fractal
                  13:10 Tue 7 Aug, 2012 :: 7.15 Ingkarni Wardli :: Prof Tony Roberts :: School of Mathematical Sciences

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                  Euclid's geometry describes the world around us in terms of points, lines and planes. For two thousand years these have formed the limited repertoire of basic geometric objects with which to describe the universe. Fractals immeasurably enhance this world-view by providing a description of much around us that is rough and fragmented---of objects that have structure on many sizes.
                  Hodge numbers and cohomology of complex algebraic varieties
                  13:10 Fri 10 Aug, 2012 :: Engineering North 218 :: Prof Gus Lehrer :: University of Sydney

                  Let $X$ be a complex algebraic variety defined over the ring $\mathfrak{O}$ of integers in a number field $K$ and let $\Gamma$ be a group of $\mathfrak{O}$-automorphisms of $X$. I shall discuss how the counting of rational points over reductions mod $p$ of $X$, and an analysis of the Hodge structure of the cohomology of $X$, may be used to determine the cohomology as a $\Gamma$-module. This will include some joint work with Alex Dimca and with Mark Kisin, and some classical unsolved problems.
                  Drawing of Viscous Threads with Temperature-dependent Viscosity
                  14:10 Fri 10 Aug, 2012 :: Engineering North N218 :: Dr Jonathan Wylie :: City University of Hong Kong

                  The drawing of viscous threads is important in a wide range of industrial applications and is a primary manufacturing process in the optical fiber and textile industries. Most of the materials used in these processes have viscosities that vary extremely strongly with temperature. We investigate the role played by viscous heating in the drawing of viscous threads. Usually, the effects of viscous heating and inertia are neglected because the parameters that characterize them are typically very small. However, by performing a detailed theoretical analysis we surprisingly show that even very small amounts of viscous heating can lead to a runaway phenomena. On the other hand, inertia prevents runaway, and the interplay between viscous heating and inertia results in very complicated dynamics for the system. Even more surprisingly, in the absence of viscous heating, we find that a new type of instability can occur when a thread is heated by a radiative heat source. By analyzing an asymptotic limit of the Navier-Stokes equation we provide a theory that describes the nature of this instability and explains the seemingly counterintuitive behavior.
                  Air-cooled binary Rankine cycle performance with varying ambient temperature
                  12:10 Mon 13 Aug, 2012 :: B.21 Ingkarni Wardli :: Ms Josephine Varney :: University of Adelaide

                  Media...
                  Next month, I have to give a presentation in Reno, Nevada to a group of geologists, engineers and geophysicists. So, for this talk, I am going to ask you to pretend you know very little about maths (and perhaps a lot about geology) and give me some feedback on my proposed talk. The presentation itself, is about the effect of air-cooling on geothermal power plant performance. Air-cooling is necessary for geothermal plays in dry areas, and ambient air temperature significantly affects the power output of air-cooled geothermal power plants. Hence, a method for determining the effect of ambient air temperature on geothermal power plants is presented. Using the ambient air temperature distribution from Leigh Creek, South Australia, this analysis shows that an optimally designed plant produces 6% more energy annually than a plant designed using the mean ambient temperature.
                  Differential topology 101
                  13:10 Fri 17 Aug, 2012 :: Engineering North 218 :: Dr Nicholas Buchdahl :: University of Adelaide

                  Much of my recent research been directed at a problem in the theory of compact complex surfaces---trying to fill in a gap in the Enriques-Kodaira classification. Attempting to classify some collection of mathematical objects is a very common activity for pure mathematicians, and there are many well-known examples of successful classification schemes; for example, the classification of finite simple groups, and the classification of simply connected topological 4-manifolds. The aim of this talk will be to illustrate how techniques from differential geometry can be used to classify compact surfaces. The level of the talk will be very elementary, and the material is all very well known, but it is sometimes instructive to look back over simple cases of a general problem with the benefit of experience to gain greater insight into the more general and difficult cases.
                  Dealing with some maths
                  12:10 Mon 20 Aug, 2012 :: B.21 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide

                  Media...
                  A group marched on a checkered path,
                  Bold but split in parts.
                  They turned and all were lost,
                  Save five regal hearts.
                  Noncommutative geometry and conformal geometry
                  13:10 Fri 24 Aug, 2012 :: Engineering North 218 :: Dr Hang Wang :: Tsinghua University

                  In this talk, we shall use noncommutative geometry to obtain an index theorem in conformal geometry. This index theorem follows from an explicit and geometric computation of the Connes-Chern character of the spectral triple in conformal geometry, which was introduced recently by Connes and Moscovici. This (twisted) spectral triple encodes the geometry of the group of conformal diffeomorphisms on a spin manifold. The crux of of this construction is the conformal invariance of the Dirac operator. As a result, the Connes-Chern character is intimately related to the CM cocycle of an equivariant Dirac spectral triple. We compute this equivariant CM cocycle by heat kernel techniques. On the way we obtain a new heat kernel proof of the equivariant index theorem for Dirac operators. (Joint work with Raphael Ponge.)
                  Star Wars Vs The Lord of the Rings: A Survival Analysis
                  12:10 Mon 27 Aug, 2012 :: B.21 Ingkarni Wardli :: Mr Christopher Davies :: University of Adelaide

                  Media...
                  Ever wondered whether you are more likely to die in the Galactic Empire or Middle Earth? Well this is the postgraduate seminar for you! I'll be attempting to answer this question using survival analysis, the statistical method of choice for investigating time to event data. Spoiler Warning: This talk will contain references to the deaths of characters in the above movie sagas.
                  Boundary-layer transition and separation over asymmetrically textured spherical surfaces
                  12:30 Mon 27 Aug, 2012 :: B.21 Ingkarni Wardli :: Mr Adam Tunney :: University of Adelaide

                  Media...
                  The game of cricket is unique among ball sports by the ignorant exploitation of \thetitle in the practice of swing bowling, often referred to as a "mysterious art". I will talk a bit about the Magnus effect exploited in inferior sports, the properties of a cricket ball that allow swing bowling, and the explanation of three modes of swing (conventional, contrast and reverse). Following that there will be some discussion on how I plan to use mathematics to turn this "art" into science.
                  Holomorphic flexibility properties of compact complex surfaces
                  13:10 Fri 31 Aug, 2012 :: Engineering North 218 :: A/Prof Finnur Larusson :: University of Adelaide

                  I will describe recent joint work with Franc Forstneric (arXiv, July 2012). We introduce a new property, called the stratified Oka property, which fits into a hierarchy of anti-hyperbolicity properties that includes the Oka property. We show that stratified Oka manifolds are strongly dominable by affine spaces. It follows that Kummer surfaces are strongly dominable. We determine which minimal surfaces of class VII are Oka (assuming the global spherical shell conjecture). We deduce that the Oka property and several other anti-hyperbolicity properties are in general not closed in families of compact complex manifolds. I will summarise what is known about how the Oka property fits into the Enriques-Kodaira classification of surfaces.
                  Wave propagation in disordered media
                  15:10 Fri 31 Aug, 2012 :: B.21 Ingkarni Wardli :: Dr Luke Bennetts :: The University of Adelaide

                  Media...
                  Problems involving wave propagation through systems composed of arrays of scattering sources embedded in some background medium will be considered. For example, in a fluids setting, the background medium is the open ocean surface and the scatterers are floating bodies, such as wave energy devices. Waves propagate in very different ways if the system is structured or disordered. If the disorder is random the problem is to determine the `effective' wave propagation properties by considering the ensemble average over all possible realisations of the system. I will talk about semi-analytical (i.e. low numerical cost) approaches to determining the effective properties.
                  Principal Component Analysis (PCA)
                  12:30 Mon 3 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr Lyron Winderbaum :: University of Adelaide

                  Media...
                  Principal Component Analysis (PCA) has become something of a buzzword recently in a number of disciplines including the gene expression and facial recognition. It is a classical, and fundamentally simple, concept that has been around since the early 1900's, its recent popularity largely due to the need for dimension reduction techniques in analyzing high dimensional data that has become more common in the last decade, and the availability of computing power to implement this. I will explain the concept, prove a result, and give a couple of examples. The talk should be accessible to all disciplines as it (should?) only assume first year linear algebra, the concept of a random variable, and covariance.
                  Examples of counterexamples
                  13:10 Tue 4 Sep, 2012 :: 7.15 Ingkarni Wardli :: Dr Pedram Hekmati :: School of Mathematical Sciences

                  Media...
                  This aims to be an example of an exemplary talk on examples of celebrated counterexamples in mathematics. A famous example, for example, is Euler's counterexample to Fermat's conjecture in number theory.
                  Classification of a family of symmetric graphs with complete quotients
                  13:10 Fri 7 Sep, 2012 :: Engineering North 218 :: A/Prof Sanming Zhou :: University of Melbourne

                  A finite graph is called symmetric if its automorphism group is transitive on the set of arcs (ordered pairs of adjacent vertices) of the graph. This is to say that all arcs have the same status in the graph. I will talk about recent results on the classification of a family of symmetric graphs with complete quotients. The most interesting graphs arising from this classification are defined in terms of Hermitian unitals (which are specific block designs), and they admit unitary groups as groups of automorphisms. I will also talk about applications of our results in constructing large symmetric graphs of given degree and diameter. This talk contains joint work with M. Giulietti, S. Marcugini and F. Pambianco.
                  Knot Theory
                  12:10 Mon 10 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr Konrad Pilch :: University of Adelaide

                  Media...
                  The ancient Chinese used it, the Celts had this skill in spades, it was a big skill of seafarers and pirates, and even now we need it if only to be able to wear shoes! This talk will be about Knot Theory. Knot theory has a colourful and interesting past and I will touch on the why, the what and the when of knots in mathematics. I shall also discuss the major problems concerning knots including the different methods of classification of knots, the unresolved questions about knots, and why have they even been studied. It will be a thorough immersion that will leave you knotted!
                  The Wonderful World of Interval Arithmetic
                  12:30 Mon 10 Sep, 2012 :: B.21 Ingkarni Wardli :: Ms Mingmei Teo :: University of Adelaide

                  Media...
                  There are many situations where we round off answers or give approximations to solutions to equations. Are we happy to do so or are there ways we can overcome this problem? What about providing intervals in which the true solution lies? An example of this is when Archimedes was able to contain \pi by taking a circle between inscribed and circumscribed polygons and take an increasing number of sides of the polygons. In this talk, I will explain a variety of things to do with interval arithmetic. These range from why interval arithmetic is useful to us, some basics of interval arithmetic and also some interesting and cool properties of intervals. I will also discuss briefly how I use it in my project.
                  Geometric quantisation in the noncompact setting
                  13:10 Fri 14 Sep, 2012 :: Engineering North 218 :: Dr Peter Hochs :: Leibniz University, Hannover

                  Traditionally, the geometric quantisation of an action by a compact Lie group on a compact symplectic manifold is defined as the equivariant index of a certain Dirac operator. This index is a well-defined formal difference of finite-dimensional representations, since the Dirac operator is elliptic and the manifold and the group in question are compact. From a mathematical and physical point of view however, it is very desirable to extend geometric quantisation to noncompact groups and manifolds. Defining a suitable index is much harder in the noncompact setting, but several interesting results in this direction have been obtained. I will review the difficulties connected to noncompact geometric quantisation, and some of the solutions that have been proposed so far, mainly in connection to the "quantisation commutes with reduction" principle. (An introduction to this principle will be given in my talk at the Colloquium on the same day.)
                  Krylov Subspace Methods or: How I Learned to Stop Worrying and Love GMRes
                  12:10 Mon 17 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr David Wilke :: University of Adelaide

                  Media...
                  Many problems within applied mathematics require the solution of a linear system of equations. For instance, models of arterial umbilical blood flow are obtained through a finite element approximation, resulting in a linear, n x n system. For small systems the solution is (almost) trivial, but what happens when n is large? Say, n ~ 10^6? In this case matrix inversion is expensive (read: completely impractical) and we seek approximate solutions in a reasonable time. In this talk I will discuss the basic theory underlying Krylov subspace methods; a class of non-stationary iterative methods which are currently the methods-of-choice for large, sparse, linear systems. In particular I will focus on the method of Generalised Minimum RESiduals (GMRes), which is of the most popular for nonsymmetric systems. It is hoped that through this presentation I will convince you that a) solving linear systems is not necessarily trivial, and that b) my lack of any tangible results is not (entirely) a result of my own incompetence.
                  Introduction to pairings in cryptography
                  13:10 Fri 21 Sep, 2012 :: Napier 209 :: Dr Naomi Benger :: University of Adelaide

                  From cryptanalysis to a powerful tool which made identity based cryptography possible, pairings have a range of applications in cryptography. I will present basic background (algebraic geometry) needed to understand pairings, hard problems associated with pairings and protocols which use pairings.
                  The advection-diffusion-reaction equation on the surface of the sphere
                  12:10 Mon 24 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr Kale Davies :: University of Adelaide

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                  We aim to solve the advection-diffusion-reaction equation on the surface of a sphere. In order to do this we will be required to utilise spherical harmonics, a set of solutions to Laplace's equation in spherical coordinates. Upon solving the equations, we aim to find a set of parameters that cause a localised concentration to be maintained in the flow, referred to as a hotspot. In this talk I will discuss the techniques that are required to numerically solve this problem and the issues that occur/how to deal with these issues when searching for hotspot solutions.
                  Electrokinetics of concentrated suspensions of spherical particles
                  15:10 Fri 28 Sep, 2012 :: B.21 Ingkarni Wardli :: Dr Bronwyn Bradshaw-Hajek :: University of South Australia

                  Electrokinetic techniques are used to gather specific information about concentrated dispersions such as electronic inks, mineral processing slurries, pharmaceutical products and biological fluids (e.g. blood). But, like most experimental techniques, intermediate quantities are measured, and consequently the method relies explicitly on theoretical modelling to extract the quantities of experimental interest. A self-consistent cell-model theory of electrokinetics can be used to determine the electrical conductivity of a dense suspension of spherical colloidal particles, and thereby determine the quantities of interest (such as the particle surface potential). The numerical predictions of this model compare well with published experimental results. High frequency asymptotic analysis of the cell-model leads to some interesting conclusions.
                  Turbulent flows, semtex, and rainbows
                  12:10 Mon 8 Oct, 2012 :: B.21 Ingkarni Wardli :: Ms Sophie Calabretto :: University of Adelaide

                  Media...
                  The analysis of turbulence in transient flows has applications across a broad range of fields. We use the flow of fluid in a toroidal container as a paradigm for studying the complex dynamics due to this turbulence. To explore the dynamics of our system, we exploit the numerical capabilities of semtex; a quadrilateral spectral element DNS code. Rainbows result.
                  Rescaling the coalescent
                  12:30 Mon 8 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr Adam Rohrlach :: University of Adelaide

                  Media...
                  Recently I gave a short talk about how researchers use mathematics to estimate the time since a species' most recent common ancestor. I also pointed out why this generally doesn't work when a population hasn't had a constant population size. Then I quickly changed the subject. In this talk I aim to reintroduce the Coalescent Model, show how it works in general, and finally how researcher's deal with varying a population size.
                  Probability, what can it tell us about health?
                  13:10 Tue 9 Oct, 2012 :: 7.15 Ingkarni Wardli :: Prof Nigel Bean :: School of Mathematical Sciences

                  Media...
                  Clinical trials are the way in which modern medical systems test whether individual treatments are worthwhile. Sophisticated statistics is used to try and make the conclusions from clinical trials as meaningful as possible. What can a very simple probability model then tell us about the worth of multiple treatments? What might the implications of this be for the whole health system?

                  This talk is based on research currently being conducted with a physician at a major Adelaide hospital. It requires no health knowledge and was not tested on animals. All you need is an enquiring and open mind.
                  Optimal Experimental Design: What Is It?
                  12:10 Mon 15 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr David Price :: University of Adelaide

                  Media...
                  Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion. That answers the question, right? But what do I mean by 'optimal', and which 'statistical criterion' should you use? In this talk I will answer all these questions, and provide an overly simple example to demonstrate how optimal design works. I will then give a brief explanation of how I will use this methodology, and what chickens have to do with it.
                  Supermanifolds and the moduli space of instantons
                  13:10 Fri 19 Oct, 2012 :: Engineering North 218 :: Prof Ugo Bruzzo :: International School for Advanced Studies (SISSA), Trieste

                  I will give an example of an application of supermanifold theory to physics, i.e., how to "superize" the moduli space of instantons on a 4-fold and use it to give a description of the BRST transformations, to compute the "supermeasure" of the moduli space, and the Nekrasov partition function.
                  Multi-scale models of evolutionary epidemiology: where is HIV going?
                  14:00 Fri 19 Oct, 2012 :: Napier 205 :: Dr Lorenzo Pellis :: The University of Warwick

                  An important component of pathogen evolution at the population level is evolution within hosts, which can alter the composition of genotypes available for transmission as infection progresses. I will present a deterministic multi-scale model, linking the within-host competition dynamics with the transmission dynamics at a population level. I will take HIV as an example of how this framework can help clarify the conflicting evolutionary pressure an infectious disease might be subject to.
                  AD Model Builder and the estimation of lobster abundance
                  12:10 Mon 22 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr John Feenstra :: University of Adelaide

                  Media...
                  Determining how many millions of lobsters reside in our waters and how it changes over time is a central aim of lobster stock assessment. ADMB is powerful optimisation software to model and solve complex non-linear problems using automatic differentiation and plays a major role in SA and worldwide in fisheries stock assessment analyses. In this talk I will provide a brief description of an example modelling problem, key features and use of ADMB.
                  Mathematics in Popular Culture: the Good, the Bad and the Ugly
                  12:30 Mon 22 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr Patrick Korbel :: University of Adelaide

                  Media...
                  A slightly unusual (for this School at least) and hopefully entertaining look at representations of mathematics and mathematicians in popular culture. Do these representations affect people's perceptions of mathematics and its mysterious practitioners? What examples of positive and negative representations are there? Should we care and should it affect our enjoyment those texts? All these questions and many more will remain hopelessly unanswered as we try to cover examples such as Numb3rs, Mean Girls, A Beautiful Mind, Good Will Hunting, 21, The Simpsons and Futurama. Feel free to come prepared with your own examples of egregious crimes against mathematics or refreshing beacons of hope.
                  Epidemic models in socially structured populations: when are simple models too simple?
                  14:00 Thu 25 Oct, 2012 :: 5.56 Ingkarni Wardli :: Dr Lorenzo Pellis :: The University of Warwick

                  Both age and household structure are recognised as important heterogeneities affecting epidemic spread of infectious pathogens, and many models exist nowadays that include either or both forms of heterogeneity. However, different models may fit aggregate epidemic data equally well and nevertheless lead to different predictions of public health interest. I will here present an overview of stochastic epidemic models with increasing complexity in their social structure, focusing in particular on households models. For these models, I will present recent results about the definition and computation of the basic reproduction number R0 and its relationship with other threshold parameters. Finally, I will use these results to compare models with no, either or both age and household structure, with the aim of quantifying the conditions under which each form of heterogeneity is relevant and therefore providing some criteria that can be used to guide model design for real-time predictions.
                  Epidemic models in socially structured populations: when are simple models too simple?
                  14:00 Thu 25 Oct, 2012 :: 5.56 Ingkarni Wardli :: Dr Lorenzo Pellis :: The University of Warwick

                  Both age and household structure are recognised as important heterogeneities affecting epidemic spread of infectious pathogens, and many models exist nowadays that include either or both forms of heterogeneity. However, different models may fit aggregate epidemic data equally well and nevertheless lead to different predictions of public health interest. I will here present an overview of stochastic epidemic models with increasing complexity in their social structure, focusing in particular on households models. For these models, I will present recent results about the definition and computation of the basic reproduction number R0 and its relationship with other threshold parameters. Finally, I will use these results to compare models with no, either or both age and household structure, with the aim of quantifying the conditions under which each form of heterogeneity is relevant and therefore providing some criteria that can be used to guide model design for real-time predictions.
                  The space of cubic rational maps
                  13:10 Fri 26 Oct, 2012 :: Engineering North 218 :: Mr Alexander Hanysz :: University of Adelaide

                  For each natural number d, the space of rational maps of degree d on the Riemann sphere has the structure of a complex manifold. The topology of these manifolds has been extensively studied. The recent development of Oka theory raises some new and interesting questions about their complex structure. We apply geometric invariant theory to the degree 3 case, studying a double action of the Mobius group on the space of cubic rational maps. We show that the categorical quotient is C, and that the space of cubic rational maps enjoys the holomorphic flexibility properties of strong dominability and C-connectedness.
                  Thin-film flow in helically-wound channels with small torsion
                  15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide

                  The study of flow in open helically-wound channels has application to many natural and industrial flows. We will consider laminar flow down helically-wound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steady-state flow that is independent of position along the axis of the channel, the flow solution may be determined in the two-dimensional cross section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier-Stokes equations. This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particle-laden thin-film flow in spiral channels will also be discussed.
                  Thin-film flow in helically-wound channels with small torsion
                  15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide

                  The study of flow in open helically-wound channels has application to many natural and industrial flows. We will consider laminar flow down helically-wound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steady-state flow that is independent of position along the axis of the channel, the flow solution may be determined in the two-dimensional cross section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier-Stokes equations. This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particle-laden thin-film flow in spiral channels will also be discussed.
                  Fair and Loathing in State Parliament
                  12:10 Mon 29 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr Casey Briggs :: University of Adelaide

                  Media...
                  The South Australian electoral system has a history of bias, malapportionment and perceived unfairness. These days, it is typical of most systems across Australia, except with one major difference - a specific legislated criterion designed to force the system to be 'fair'. In reality, fairness is a hard concept to define, and an even harder concept to enforce. In this talk I will briefly take you through the history of South Australian electoral reform, the current state of affairs and my proposed research. There will be very little in the way of rigorous mathematics. No knowledge of politics is assumed, but an understanding of the process of voting would be useful.
                  Interaction of double-stranded DNA inside single-walled carbon nanotubes
                  12:10 Mon 5 Nov, 2012 :: B.21 Ingkarni Wardli :: Mr Mansoor Alshehri :: University of Adelaide

                  Media...
                  Here we investigate the interaction of deoxyribonucleic acid (DNA) inside single walled carbon nanotubes (SWCNTs). Using classical applied mathematical modeling, we derive explicit analytical expressions for the encapsulation of DNA inside single-walled carbon nanotubes. We adopt the 6-12 Lennard-Jones potential function together with the continuous approach to determine the preferred minimum energy position of the dsDNA molecule inside a single-walled carbon nanotube, so as to predict its location with reference to the cross- section of the carbon nanotube. An analytical expression is obtained in terms of hypergeometric functions, which provides a computationally rapid procedure to determine critical numerical values.
                  Spatiotemporally Autoregressive Partially Linear Models with Application to the Housing Price Indexes of the United States
                  12:10 Mon 12 Nov, 2012 :: B.21 Ingkarni Wardli :: Ms Dawlah Alsulami :: University of Adelaide

                  Media...
                  We propose a Spatiotemporal Autoregressive Partially Linear Regression ( STARPLR) model for data observed irregularly over space and regularly in time. The model is capable of catching possible non linearity and nonstationarity in space by coefficients to depend on locations. We suggest two-step procedure to estimate both the coefficients and the unknown function, which is readily implemented and can be computed even for large spatio-temoral data sets. As an illustration, we apply our model to analyze the 51 States' House Price Indexes (HPIs) in USA.
                  Dynamics of microbial populations from a copper sulphide leaching heap
                  12:30 Mon 12 Nov, 2012 :: B.21 Ingkarni Wardli :: Ms Susana Soto Rojo :: University of Adelaide

                  Media...
                  We are interested in the dynamics of the microbial population from a copper sulphide bioleaching heap. The composition of the microbial consortium is closely related to the kinetics of the oxidation processes that lead to copper recovery. Using a non-linear model, which considers the effect of substrate depletion and incorporates spatial dependence, we analyse adjacent strips correlation, patterns of microbial succession, relevance of pertinent physic-chemical parameters and the implications of the absence of barriers between the three lifts of the heap. We also explore how the dynamics of the microbial community relate to the mineral composition of the individual strips of the bioleaching pile.
                  Twisted analytic torsion and adiabatic limits
                  13:10 Wed 5 Dec, 2012 :: Ingkarni Wardli B17 :: Mr Ryan Mickler :: University of Adelaide

                  We review Mathai-Wu's recent extension of Ray-Singer analytic torsion to supercomplexes. We explore some new results relating these two torsions, and how we can apply the adiabatic spectral sequence due to Forman and Farber's analytic deformation theory to compute some spectral invariants of the complexes involved, answering some questions that were posed in Mathai-Wu's paper.
                  Variation of Hodge structure for generalized complex manifolds
                  13:10 Fri 7 Dec, 2012 :: Ingkarni Wardli B20 :: Dr David Baraglia :: University of Adelaide

                  Generalized complex geometry combines complex and symplectic geometry into a single framework, incorporating also holomorphic Poisson and bi-Hermitian structures. The Dolbeault complex naturally extends to the generalized complex setting giving rise to Hodge structures in twisted cohomology. We consider the variations of Hodge structure and period mappings that arise from families of generalized complex manifolds. As an application we prove a local Torelli theorem for generalized Calabi-Yau manifolds.
                  Hyperplane arrangements and tropicalization of linear spaces
                  10:10 Mon 17 Dec, 2012 :: Ingkarni Wardli B17 :: Dr Graham Denham :: University of Western Ontario

                  I will give an introduction to a sequence of ideas in tropical geometry, the tropicalization of linear spaces. In the beginning, a construction due to De Concini and Procesi (wonderful models, 1995) gave a combinatorially explicit description of various iterated blowups of projective spaces along (proper transforms of) linear subspaces. A decade later, Tevelev's notion of tropical compactifications led to, in particular, a new view of the wonderful models and their intersection theory in terms of the theory of toric varieties (via work of Feichtner-Sturmfels, Feichtner-Yuzvinsky, Ardila-Klivans, and others). Recently, these ideas have played a role in Huh and Katz's proof of a long-standing conjecture in combinatorics.
                  Stably Cayley groups over fields of characteristic 0
                  11:10 Mon 17 Dec, 2012 :: Ingkarni Wardli B17 :: Dr Nicole Lemire :: University of Western Ontario

                  A linear algebraic group is called a Cayley group if it is equivariantly birationally isomorphic to its Lie algebra. It is stably Cayley if the product of the group and some torus is Cayley. Cayley gave the first examples of Cayley groups with his Cayley map back in 1846. Over an algebraically closed field of characteristic 0, Cayley and stably Cayley simple groups were classified by Lemire, Popov and Reichstein in 2006. In recent joint work with Blunk, Borovoi, Kunyavskii and Reichstein, we classify the simple stably Cayley groups over an arbitrary field of characteristic 0.
                  Recent results on holomorphic extension of functions on unbounded domains in C^n
                  11:10 Fri 21 Dec, 2012 :: Ingkarni Wardli B19 :: Prof Roman Dwilewicz :: Missouri University of Science and Technology

                  In the talk there will be given a short review of holomorphic extension problems starting with the famous Hartogs theorem (1906) up to recent results on global holomorphic extensions for unbounded domains, obtained together with Al Boggess (Arizona State Univ.) and Zbigniew Slodkowski (Univ. Illinois at Chicago). There is an interesting geometry behind the extension problem for unbounded domains, namely (in some cases) it depends on the position of a complex variety in the closure of the domain. The extension problem appeared non-trivial and the work is in progress. However the talk will be illustrated by many figures and pictures and should be accessible also to graduate students.
                  Conformally Fedosov manifolds
                  12:10 Fri 8 Mar, 2013 :: Ingkarni Wardli B19 :: Prof Michael Eastwood :: Australian National University

                  Symplectic and projective structures may be compatibly combined. The resulting structure closely resembles conformal geometry and a manifold endowed with such a structure is called conformally Fedosov. This talk will present the basic theory of conformally Fedosov geometry and, in particular, construct a Cartan connection for them. This is joint work with Jan Slovak.
                  Twistor space for rolling bodies
                  12:10 Fri 15 Mar, 2013 :: Ingkarni Wardli B19 :: Prof Pawel Nurowski :: University of Warsaw

                  We consider a configuration space of two solids rolling on each other without slipping or twisting, and identify it with an open subset U of R^5, equipped with a generic distribution D of 2-planes. We will discuss symmetry properties of the pair (U,D) and will mention that, in the case of the two solids being balls, when changing the ratio of their radii, the dimension of the group of local symmetries unexpectedly jumps from 6 to 14. This occurs for only one such ratio, and in such case the local group of symmetries of the pair (U,D) is maximal. It is maximal not only among the balls with various radii, but more generally among all (U,D)s corresponding to configuration spaces of two solids rolling on each other without slipping or twisting. This maximal group is isomorphic to the split real form of the exceptional Lie group G2. In the remaining part of the talk we argue how to identify the space U from the pair (U,D) defined above with the bundle T of totally null real 2-planes over a 4-manifold equipped with a split signature metric. We call T the twistor bundle for rolling bodies. We show that the rolling distribution D, can be naturally identified with an appropriately defined twistor distribution on T. We use this formulation of the rolling system to find more surfaces which, when rigidly rolling on each other without slipping or twisting, have the local group of symmetries isomorphic to the exceptional group G2.
                  Modular forms: a rough guide
                  12:10 Mon 18 Mar, 2013 :: B.19 Ingkarni Wardli :: Damien Warman :: University of Adelaide

                  Media...
                  I recently found the need to learn a little about what I had naively believed to be an abstruse branch of number theory, but which turns out to be a ubiquitous and intriguing theory. I'll introduce some of the geometry underlying the elementary theory of modular functions and modular forms. We'll look at some pictures and play with sage, time permitting.
                  Einstein's special relativity beyond the speed of light
                  14:10 Mon 18 Mar, 2013 :: 7.15 Ingkarni Wardli :: Prof. Jim Hill :: School of Mathematical Sciences

                  Media...
                  We derive extended Lorentz transformations between inertial frames for relative velocities greater than the speed of light, and which are complementary to the Lorentz transformation giving rise to the Einstein special theory of relativity. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions.
                  On the chromatic number of a random hypergraph
                  13:10 Fri 22 Mar, 2013 :: Ingkarni Wardli B21 :: Dr Catherine Greenhill :: University of New South Wales

                  A hypergraph is a set of vertices and a set of hyperedges, where each hyperedge is a subset of vertices. A hypergraph is r-uniform if every hyperedge contains r vertices. A colouring of a hypergraph is an assignment of colours to vertices such that no hyperedge is monochromatic. When the colours are drawn from the set {1,..,k}, this defines a k-colouring. We consider the problem of k-colouring a random r-uniform hypergraph with n vertices and cn edges, where k, r and c are constants and n tends to infinity. In this setting, Achlioptas and Naor showed that for the case of r = 2, the chromatic number of a random graph must have one of two easily computable values as n tends to infinity. I will describe some joint work with Martin Dyer (Leeds) and Alan Frieze (Carnegie Mellon), in which we generalised this result to random uniform hypergraphs. The argument uses the second moment method, and applies a general theorem for performing Laplace summation over a lattice. So the proof contains something for everyone, with elements from combinatorics, analysis and algebra.
                  What would happen if geothermal energy was used to preheat the feedwater for a traditional steam power plant?
                  12:10 Mon 25 Mar, 2013 :: B.19 Ingkarni Wardli :: Jo Varney :: University of Adelaide

                  Media...
                  In our effort to determine the most effective way to use geothermal energy this is a left field, yet enticing, idea. Would this produce more 'extra' power than a geothermal plant on its own? Would there be sufficient benefit to interest traditional power generators? We investigated retro-fitting two different geothermal preheating options to a 500MW supercritical steam power plant. We then compared the 'extra-power' produced using geothermal preheating, to the power produced by using geothermal energy on its own. We think the results are interesting and promising, but come along and judge for yourself.
                  Gauge groupoid cocycles and Cheeger-Simons differential characters
                  13:10 Fri 5 Apr, 2013 :: Ingkarni Wardli B20 :: Prof Jouko Mickelsson :: Royal Institute of Technology, Stockholm

                  Groups of gauge transformations in quantum field theory are typically extended by a 2-cocycle with values in a certain abelian group due to chiral symmetry breaking. For these extensions there exist a global explicit construction since the 1980's. I shall study the higher group cocycles following a recent paper by F. Wagemann and C. Wockel, but extending to the transformation groupoid setting (motivated by QFT) and discussing potential obstructions in the construction due to a nonvanishing of low dimensional homology groups of the gauge group. The resolution of the obstruction is obtained by an application of the Cheeger-Simons differential characters.
                  Kronecker-Weber Theorem
                  12:10 Mon 8 Apr, 2013 :: B.19 Ingkarni Wardli :: Konrad Pilch :: University of Adelaide

                  Media...
                  The Kronecker-Weber Theorem has a rich and inspiring history. Much like Fermat's Last Theorem, it can be expressed in a very simple way. Its many proofs often utilise heavy machinery and those who claim it can be solved using elementary means, have quite frankly redefined the meaning of elementary. It has inspired David Hilbert and many other mathematicians leading to a great amount of fantastic work in the area. In this talk, I will discuss this theorem, a 'fairly' simple proof of it as well as discuss how it is relevant to my work and the works of others.
                  The Mathematics of Secrets
                  14:10 Mon 8 Apr, 2013 :: 210 Napier Building :: Dr Naomi Benger :: School of Mathematical Sciences

                  Media...
                  One very important application of number theory is the implementation of public key cryptosystems that we use today. I will introduce elementary number theory, Fermat's theorem and use these to explain how ElGamal encryption and digital signatures work.
                  M-theory and higher gauge theory
                  13:10 Fri 12 Apr, 2013 :: Ingkarni Wardli B20 :: Dr Christian Saemann :: Heriot-Watt University

                  I will review my recent work on integrability of M-brane configurations and the description of M-brane models in higher gauge theory. In particular, I will discuss categorified analogues of instantons and present superconformal equations of motion for the non-abelian tensor multiplet in six dimensions. The latter are derived from considering non-abelian gerbes on certain twistor spaces.
                  What in the world is a chebfun?
                  12:10 Mon 15 Apr, 2013 :: B.19 Ingkarni Wardli :: Hayden Tronnolone :: University of Adelaide

                  Media...
                  Good question. Many functions encountered in practice can be well-approximated by a linear combination of Chebyshev polynomials, which then allows the use of some powerful numerical techniques. I will give a very brief overview of the theory behind some of these methods, demonstrate how they may be implemented using the MATLAB package known as Chebfun, and answer the question posed in the title along the way. No knowledge of approximation theory or MATLAB is required, however, you will need to accept the transliteration "Chebyshev".
                  Conformal Killing spinors in Riemannian and Lorentzian geometry
                  12:10 Fri 19 Apr, 2013 :: Ingkarni Wardli B19 :: Prof Helga Baum :: Humboldt University

                  Conformal Killing spinors are the solutions of the conformally covariant twistor equation on spinors. Special cases are parallel and Killing spinors, the latter appear as eigenspinors of the Dirac operator on compact Riemannian manifolds of positive scalar curvature for the smallest possible positive eigenvalue. In the talk I will discuss geometric properties of manifolds admitting (conformal) Killing spinors. In particular, I will explain a local classification of the special geometric structures admitting conformal Killing spinors without zeros in the Riemannian as well as in the Lorentzian setting.
                  The boundary conditions for macroscale modelling of a discrete diffusion system with periodic diffusivity
                  12:10 Mon 29 Apr, 2013 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide

                  Media...
                  Many mathematical and engineering problems have a multiscale nature. There are a vast of theories supporting multiscale modelling on infinite domain, such as homogenization theory and centre manifold theory. To date, there are little consideration of the correct boundary conditions to be used at the edge of macroscale model. In this seminar, I will present how to derive macroscale boundary conditions for the diffusion system.
                  An Oka principle for equivariant isomorphisms
                  12:10 Fri 3 May, 2013 :: Ingkarni Wardli B19 :: A/Prof Finnur Larusson :: University of Adelaide

                  I will discuss new joint work with Frank Kutzschebauch (Bern) and Gerald Schwarz (Brandeis). Let $G$ be a reductive complex Lie group acting holomorphically on Stein manifolds $X$ and $Y$, which are locally $G$-biholomorphic over a common categorical quotient $Q$. When is there a global $G$-biholomorphism $X\to Y$? In a situation that we describe, with some justification, as generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that $X$ and $Y$ are $G$-biholomorphic if $X$ is $K$-contractible, where $K$ is a maximal compact subgroup of $G$, or if there is a $G$-diffeomorphism $X\to Y$ over $Q$, which is holomorphic when restricted to each fibre of the quotient map $X\to Q$. When $G$ is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of $G$-biholomorphisms from $X$ to $Y$ over $Q$. This sheaf can be badly singular, even in simply defined examples. Our work is in part motivated by the linearisation problem for actions on $\C^n$. It follows from one of our main results that a holomorphic $G$-action on $\C^n$, which is locally $G$-biholomorphic over a common quotient to a generic linear action, is linearisable.
                  Filtering Theory in Modelling the Electricity Market
                  12:10 Mon 6 May, 2013 :: B.19 Ingkarni Wardli :: Ahmed Hamada :: University of Adelaide

                  Media...
                  In mathematical finance, as in many other fields where applied mathematics is a powerful tool, we assume that a model is good enough when it captures different sources of randomness affecting the quantity of interests, which in this case is the electricity prices. The power market is very different from other markets in terms of the randomness sources that can be observed in the prices feature and evolution. We start from suggesting a new model that simulates the electricity prices, this new model is constructed by adding a periodicity term, a jumps terms and a positives mean reverting term. The later term is driven by a non-observable Markov process. So in order to prices some financial product, we have to use some of the filtering theory to deal with the non-observable process, these techniques are gaining very much of interest from practitioners and researchers in the field of financial mathematics.
                  Diffeological spaces and differentiable stacks
                  12:10 Fri 10 May, 2013 :: Ingkarni Wardli B19 :: Dr David Roberts :: University of Adelaide

                  The category of finite-dimensional smooth manifolds gives rise to interesting structures outside of itself, two examples being mapping spaces and classifying spaces. Diffeological spaces are a notion of generalised smooth space which form a cartesian closed category, so all fibre products and all mapping spaces of smooth manifolds exist as diffeological spaces. Differentiable stacks are a further generalisation that can also deal with moduli spaces (including classifying spaces) for objects with automorphisms. This talk will give an introduction to this circle of ideas.
                  Colour
                  12:10 Mon 13 May, 2013 :: B.19 Ingkarni Wardli :: Lyron Winderbaum :: University of Adelaide

                  Media...
                  Colour is a powerful tool in presenting data, but it can be tricky to choose just the right colours to represent your data honestly - do the colours used in your heatmap overemphasise the differences between particular values over others? does your choice of colours overemphasize one when they should be represented as equal? etc. All these questions are fundamentally based in how we perceive colour. There has been alot of research into how we perceive colour in the past century, and some interesting results. I will explain how a `standard observer' was found empirically and used to develop an absolute reference standard for colour in 1931. How although the common Red-Green-Blue representation of colour is useful and intuitive, distances between colours in this space do not reflect our perception of difference between colours and how alternative, perceptually focused colourspaces where introduced in 1976. I will go on to explain how these results can be used to provide simple mechanisms by which to choose colours that satisfy particular properties such as being equally different from each other, or being linearly more different in sequence, or maintaining such properties when transferred to greyscale, or for a colourblind person.
                  Crystallographic groups I: the classical theory
                  12:10 Fri 17 May, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide

                  A discrete isometry group acting properly discontinuously on the n-dimensional Euclidean space with compact quotient is called a crystallographic group. This name reflects the fact that in dimension n=3 their compact fundamental domains resemble a space-filling crystal pattern. For higher dimensions, Hilbert posed his famous 18th problem: "Is there in n-dimensional Euclidean space only a finite number of essentially different kinds of groups of motions with a [compact] fundamental region?" This problem was solved by Bieberbach when he proved that in every dimension n there exists only a finite number of isomorphic crystallographic groups and also gave a description of these groups. From the perspective of differential geometry these results are of major importance, as crystallographic groups are precisely the fundamental groups of compact flat Riemannian orbifolds. The quotient is even a manifold if the fundamental group is required to be torsion-free, in which case it is called a Bieberbach group. Moreover, for a flat manifold the fundamental group completely determines the holonomy group. In this talk I will discuss the properties of crystallographic groups, study examples in dimension n=2 and n=3, and present the three Bieberbach theorems on the structure of crystallographic groups.
                  Pulsatile Flow
                  12:10 Mon 20 May, 2013 :: B.19 Ingkarni Wardli :: David Wilke :: University of Adelaide

                  Media...
                  Blood flow within the human arterial system is inherently unsteady as a consequence of the pulsations of the heart. The unsteady nature of the flow gives rise to a number of important flow features which may be critical in understanding pathologies of the cardiovascular system. For example, it is believed that large oscillations in wall shear stress may enhance the effects of artherosclerosis, among other pathologies. In this talk I will present some of the basic concepts of pulsatile flow and follow the analysis first performed by J.R. Womersley in his seminal 1955 paper.
                  Coincidences
                  14:10 Mon 20 May, 2013 :: 7.15 Ingkarni Wardli :: A/Prof. Robb Muirhead :: School of Mathematical Sciences

                  Media...
                  This is a lighthearted (some would say content-free) talk about coincidences, those surprising concurrences of events that are often perceived as meaningfully related, with no apparent causal connection. Time permitting, it will touch on topics like:
                  Patterns in data and the dangers of looking for patterns, unspecified ahead of time, and trying to "explain" them; e.g. post hoc subgroup analyses, cancer clusters, conspiracy theories ...
                  Matching problems; e.g. the birthday problem and extensions
                  People who win a lottery more than once -- how surprised should we really be? What's the question we should be asking?
                  When you become familiar with a new word, and see it again soon afterwards, how surprised should you be?
                  Caution: This is a shortened version of a talk that was originally prepared for a group of non-mathematicians and non-statisticians, so it's mostly non-technical. It probably does not contain anything you don't already know -- it will be an amazing coincidence if it does!
                  Crystallographic groups II: generalisations
                  12:10 Fri 24 May, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide

                  The theory of crystallographic groups acting cocompactly on Euclidean space can be extended and generalised in many different ways. For example, instead of studying discrete groups of Euclidean isometries, one can consider groups of isometries for indefinite inner products. These are the fundamental groups of compact flat pseudo-Riemannian manifolds. Still more generally, one might study group of affine transformation on n-space that are not required to preserve any bilinear form. Also, the condition of cocompactness can be dropped. In this talk, I will present some of the results obtained for these generalisations, and also discuss some of my own work on flat homogeneous pseudo-Riemannian spaces.
                  Multiscale modelling couples patches of wave-like simulations
                  12:10 Mon 27 May, 2013 :: B.19 Ingkarni Wardli :: Meng Cao :: University of Adelaide

                  Media...
                  A multiscale model is proposed to significantly reduce the expensive numerical simulations of complicated waves over large spatial domains. The multiscale model is built from given microscale simulations of complicated physical processes such as sea ice or turbulent shallow water. Our long term aim is to enable macroscale simulations obtained by coupling small patches of simulations together over large physical distances. This initial work explores the coupling of patch simulations of wave-like pdes. With the line of development being to water waves we discuss the dynamics of two complementary fields called the 'depth' h and 'velocity' u. A staggered grid is used for the microscale simulation of the depth h and velocity u. We introduce a macroscale staggered grid to couple the microscale patches. Linear or quadratic interpolation provides boundary conditions on the field in each patch. Linear analysis of the whole coupled multiscale system establishes that the resultant macroscale dynamics is appropriate. Numerical simulations support the linear analysis. This multiscale method should empower the feasible computation of large scale simulations of wave-like dynamics with complicated underlying physics.
                  A strong Oka principle for proper immersions of finitely connected planar domains into CxC*
                  12:10 Fri 31 May, 2013 :: Ingkarni Wardli B19 :: Dr Tyson Ritter :: University of Adelaide

                  Gromov, in his seminal 1989 paper on the Oka principle, proved that every continuous map from a Stein manifold into an elliptic manifold is homotopic to a holomorphic map. In previous work we showed that, given a continuous map from X to the elliptic manifold CxC*, where X is a finitely connected planar domain without isolated boundary points, a stronger Oka property holds whereby the map is homotopic to a proper holomorphic embedding. If the planar domain is additionally permitted to have isolated boundary points the problem becomes more difficult, and it is not yet clear whether a strong Oka property for embeddings into CxC* continues to hold. We will discuss recent results showing that every continuous map from a finitely connected planar domain into CxC* is homotopic to a proper immersion that, in most cases, identifies at most finitely many pairs of distinct points. This is joint work with Finnur Larusson.
                  Markov decision processes and interval Markov chains: what is the connection?
                  12:10 Mon 3 Jun, 2013 :: B.19 Ingkarni Wardli :: Mingmei Teo :: University of Adelaide

                  Media...
                  Markov decision processes are a way to model processes which involve some sort of decision making and interval Markov chains are a way to incorporate uncertainty in the transition probability matrix. How are these two concepts related? In this talk, I will give an overview of these concepts and discuss how they relate to each other.
                  A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces
                  12:10 Fri 7 Jun, 2013 :: Ingkarni Wardli B19 :: Prof Thierry Coulhon :: Australian National University

                  On doubling metric measure spaces endowed with a Dirichlet form and satisfying the Davies-Gaffney estimate, we show some characterisations of pointwise upper bounds of the heat kernel in terms of one-parameter weighted inequalities which correspond respectively to the Nash inequality and to a Gagliardo-Nirenberg type inequality when the volume growth is polynomial. This yields a new and simpler proof of the well-known equivalence between classical heat kernel upper bounds and the relative Faber-Krahn inequalities. We are also able to treat more general pointwise estimates where the heat kernel rate of decay is not necessarily governed by the volume growth. This is a joint work with Salahaddine Boutayeb and Adam Sikora.
                  Birational geometry of M_g
                  12:10 Fri 21 Jun, 2013 :: Ingkarni Wardli B19 :: Dr Jarod Alper :: Australian National University

                  In 1969, Deligne and Mumford introduced a beautiful compactification of the moduli space of smooth curves which has proved extremely influential in geometry, topology and physics. Using recent advances in higher dimensional geometry and the minimal model program, we study the birational geometry of M_g. In particular, in an effort to understand the canonical model of M_g, we study the log canonical models as well as the associated divisorial contractions and flips by interpreting these models as moduli spaces of particular singular curves.
                  IGA/AMSI Workshop: Representation theory and operator algebras
                  10:00 Mon 1 Jul, 2013 :: 7.15 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University

                  Media...
                  This interdisciplinary workshop will be about aspects of representation theory (in the sense of Harish-Chandra), aspects of noncommutative geometry (in the sense of Alain Connes) and aspects of operator K-theory (in the sense of Gennadi Kasparov). It features the renowned speaker, Professor Nigel Higson (Penn State University) http://www.iga.adelaide.edu.au/workshops/WorkshopJuly2013/ All are welcome.
                  K-homology and the quantization commutes with reduction problem
                  12:10 Fri 5 Jul, 2013 :: 7.15 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University

                  The quantization commutes with reduction problem for Hamiltonian actions of compact Lie groups was solved by Meinrenken in the mid-1990s using geometric techniques, and solved again shortly afterwards by Tian and Zhang using analytic methods. In this talk I shall outline some of the close links that exist between the problem, the two solutions, and the geometric and analytic versions of K-homology theory that are studied in noncommutative geometry. I shall try to make the case for K-homology as a useful conceptual framework for the solutions and (at least some of) their various generalizations.
                  The search for the exotic - subfactors and conformal field theory
                  13:10 Fri 26 Jul, 2013 :: Engineering-Maths 212 :: Prof David E. Evans :: Cardiff University

                  Subfactor theory provides a framework for studying modular invariant partition functions in conformal field theory, and candidates for exotic modular tensor categories. I will describe work with Terry Gannon on the search for exotic theories beyond those from symmetries based on loop groups, Wess-Zumino-Witten models and finite groups.
                  Fire-Atmosphere Models
                  12:10 Mon 29 Jul, 2013 :: B.19 Ingkarni Wardli :: Mika Peace :: University of Adelaide

                  Media...
                  Fire behaviour models are increasingly being used to assist in planning and operational decisions for bush fires and fuel reduction burns. Rate of spread (ROS) of the fire front is a key output of such models. The ROS value is typically calculated from a formula which has been derived from empirical data, using very simple meteorological inputs. We have used a coupled fire-atmosphere model to simulate real bushfire events. The results show that complex interactions between a fire and the atmosphere can have a significant influence on fire spread, thus highlighting the limitations of a model that uses simple meteorological inputs.
                  Subfactors and twisted equivariant K-theory
                  12:10 Fri 2 Aug, 2013 :: Ingkarni Wardli B19 :: Prof David E. Evans :: Cardiff University

                  The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFTs associated to loop groups as twisted equivariant K-theory. In joint work with Terry Gannon, we build on their work to express K-theoretically the structures of full CFT. In particular, the modular invariant partition functions (which essentially parametrise the possible full CFTs) have a rich interpretation within von Neumann algebras (subfactors), which has led to the developments of structures of full CFT such as the full system (fusion ring of defect lines), nimrep (cylindrical partition function), alpha-induction etc.
                  An Overview of Mathematics in the Australian Curriculum
                  12:10 Mon 5 Aug, 2013 :: B.19 Ingkarni Wardli :: Patrick Korbel :: University of Adelaide

                  Media...
                  I will be doing an overview of mathematics in the new Australian Curriculum from Foundation (Reception) to Year 12 for those not familiar with new curriculum.
                  Four hats, three prisoners, two colours and a jailer
                  12:35 Mon 5 Aug, 2013 :: B.19 Ingkarni Wardli :: Kale Davies :: University of Adelaide

                  Media...
                  It was a dark and stormy night. Theodore Jailer sat alone in his office scrawling notes on a piece of paper, muttering to himself in frustration. Suddenly he stops, his eyes widen in excitement and a smile spreads across his face. No, not a smile, but a grimace, for you see, evil was afoot! For Jailer, who was the jailer at a local prison had devised a nefarious scheme in order to execute all of the prisoners once and for all. Can his evil plans be thwarted in time? Stay tuned to find out!
                  Symplectic Lie groups
                  12:10 Fri 9 Aug, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide

                  A "symplectic Lie group" is a Lie group G with a symplectic form such that G acts by symplectic transformations on itself. Such a G cannot be semisimple, so the research focuses on solvable symplectic Lie groups. In the compact case, a classification of these groups is known. In many cases, a solvable symplectic Lie group G is a cotangent bundle of a flat Lie group H. Then H is a Lagrange subgroup of G, meaning its Lie algebra h is isotropic in the Lie algebra g of G. The existence of Lagrange subalgebras or ideals in g is an important question which relates to many problems in the general structure theory of symplectic Lie groups. In my talk, I will give a brief overview of the known results in this field, ranging from the 1970s to a very recent structure theory.
                  What is Tight Clustering?
                  12:10 Mon 12 Aug, 2013 :: B.19 Ingkarni Wardli :: Chris Davies :: University of Adelaide

                  Media...
                  Most clustering methods partition the observations in such a way that those in the same cluster are more similar to each other than they are to observations in different clusters. However, in some situations you might not want to assign all observations into clusters. That is, you might prefer to consider some subjects to have characteristics so dissimilar from others that they are not assigned to any cluster. In this seminar I will describe an algorithm that can be used to assign some observations into tight and stable clusters, while leaving some observations unassigned.
                  Eigenvalue Magic Tricks
                  14:10 Mon 12 Aug, 2013 :: 7.15 Ingkarni Wardli :: Dr David Butler :: Maths Learning Centre

                  Media...
                  Eigenvalues are awesome, but students rarely get the chance to see just how supremely awesome they are. In this talk I will tell you some awesome truths about eigenvalues that you do not get to see in first year, and show you their proofs, which happen to contain some of the most clever magic tricks in the whole of maths.
                  A survey of non-abelian cohomology
                  12:10 Fri 16 Aug, 2013 :: Ingkarni Wardli B19 :: Dr Danny Stevenson :: University of Adelaide

                  If G is a topological group, not necessarily abelian, then the set H^1(M,G) has a natural interpretation in terms of principal G-bundles on the space M. In this talk I will describe higher degree analogs of both the set H^1(M,G) and the notion of a principal bundle (the latter is closely connected to the subject of bundle gerbes). I will explain, following work of Joyal, Jardine and many others, how the language of abstract homotopy theory gives a very convenient framework for discussing these ideas.
                  Privacy-Preserving Computation: Not just for secretive millionaires*
                  12:10 Mon 19 Aug, 2013 :: B.19 Ingkarni Wardli :: Wilko Henecka :: University of Adelaide

                  Media...
                  PPC enables parties to share information while preserving their data privacy. I will introduce the concept, show a common ingredient and illustrate its use in an example. *See Yao's Millionaires Problem.
                  The Einstein equations with torsion, reduction and duality
                  12:10 Fri 23 Aug, 2013 :: Ingkarni Wardli B19 :: Dr David Baraglia :: University of Adelaide

                  We consider the Einstein equations for connections with skew torsion. After some general remarks we look at these equations on principal G-bundles, making contact with string structures and heterotic string theory in the process. When G is a torus the equations are shown to possess a symmetry not shared by the usual Einstein equations - T-duality. This is joint work with Pedram Hekmati.
                  Group meeting
                  15:10 Fri 23 Aug, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Barry Cox, Professor Tony Roberts & Stephen Wade :: University of Adelaide

                  Talk: Dr Barry Cox - 'Conformation space of seven-member rings'. Work in progress discussion: Professor Tony Roberts - Macroscale PDEs emerge from microscale dynamics with quantified errors Stephen Wade - Trapped waves in flow past a trench
                  The Lowenheim-Skolem theorem
                  12:10 Mon 26 Aug, 2013 :: B.19 Ingkarni Wardli :: William Crawford :: University of Adelaide

                  Media...
                  For those of us who didn't do an undergrad course in logic, the foundations of set theory are pretty daunting. I will give a run down of some of the basics and then talk about a lesser known, but interesting result; the Lowenheim-Skolem theorem. One of the consequences of the theorem is that a set can be countable in one model of set theory, while being uncountable in another.
                  Quadratic Forms in Statistics: Evaluating Contributions of Individual Variables
                  11:10 Tue 27 Aug, 2013 :: Ingkarni Wardli Level 5 Room 5.57 :: A/Prof Inge Koch :: University of Adelaide

                  Geometry of moduli spaces
                  12:10 Fri 30 Aug, 2013 :: Ingkarni Wardli B19 :: Prof Georg Schumacher :: University of Marburg

                  We discuss the concept of moduli spaces in complex geometry. The main examples are moduli of compact Riemann surfaces, moduli of compact projective varieties and moduli of holomorphic vector bundles, whose points correspond to isomorphism classes of the given objects. Moduli spaces carry a natural topology, whereas a complex structure that reflects the variation of the structure in a family exists in general only under extra conditions. In a similar way, a natural hermitian metric (Weil-Petersson metric) on moduli spaces that induces a symplectic structure can be constructed from the variation of distinguished metrics on the fibers. In this way, various questions concerning the underlying symplectic structure, the curvature of the Weil-Petersson metric, hyperbolicity of moduli spaces, and construction of positive/ample line bundles on compactified moduli spaces can be answered.
                  Medical Decision Analysis
                  12:10 Mon 2 Sep, 2013 :: B.19 Ingkarni Wardli :: Eka Baker :: University of Adelaide

                  Doctors make life changing decisions every day based on clinical trial data. However, this data is often obtained from studies on healthy individuals or on patients with only the disease that a treatment is targeting. Outside of these studies, many patients will have other conditions that may affect the predicted benefit of receiving a certain treatment. I will talk about what clinical trials are, how to measure the benefit of treatments, and how having multiple conditions (comorbidities) will affect the benefit of treatments.
                  What are fusion categories?
                  12:10 Fri 6 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Scott Morrison :: Australian National University

                  Fusion categories are a common generalization of finite groups and quantum groups at roots of unity. I'll explain a little of their structure, mention their applications (to topological field theory and quantum computing), and then explore the ways in which they are in general similar to, or different from, the 'classical' cases. We've only just started exploring, and don't yet know what the exotic examples we've discovered signify about the landscape ahead.
                  Thin-film flow in helical channels
                  12:10 Mon 9 Sep, 2013 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide

                  Media...
                  Spiral particle separators are used in the mineral processing industry to refine ores. A slurry, formed by mixing crushed ore with a fluid, is run down a helical channel and at the end of the channel, the particles end up sorted in different sections of the channel. Design of such devices is largely experimentally based, and mathematical modelling of flow in helical channels is relatively limited. In this talk, I will outline some of the work that I have been doing on thin-film flow in helical channels.
                  K-theory and solid state physics
                  12:10 Fri 13 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Keith Hannabuss :: Balliol College, Oxford

                  More than 50 years ago Dyson showed that there is a nine-fold classification of random matrix models, the classes of which are each associated with Riemannian symmetric spaces. More recently it was realised that a related argument enables one to classify the insulating properties of fermionic systems (with the addition of an extra class to give 10 in all), and can be described using K-theory. In this talk I shall give a survey of the ideas, and a brief outline of work with Guo Chuan Thiang.
                  Group meeting
                  15:10 Fri 13 Sep, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Sanjeeva Balasuriya and Dr Michael Chen :: University of Adelaide

                  Talks: Nonautonomous control of invariant manifolds - Dr Sanjeeva Balasuriya :: Interface problems in viscous flow - Dr Michael Chen
                  The logarithmic singularities of the Green functions of the conformal powers of the Laplacian
                  11:10 Mon 16 Sep, 2013 :: Ingkarni Wardli B20 :: Prof Raphael Ponge :: Seoul National University

                  Green functions play an important role in conformal geometry. In this talk, we shall explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators are the Yamabe and Paneitz operators, as well as the conformal fractional powers of the Laplacian arising from scattering theory for Poincare-Einstein metrics. The results are formulated in terms of Weyl conformal invariants defined via the ambient metric of Fefferman-Graham.
                  Noncommutative geometry and conformal geometry
                  13:10 Mon 16 Sep, 2013 :: Ingkarni Wardli B20 :: Prof Raphael Ponge :: Seoul National University

                  In this talk we shall report on a program of using the recent framework of twisted spectral triples to study conformal geometry from a noncommutative geometric perspective. One result is a local index formula in conformal geometry taking into account the action of the group of conformal diffeomorphisms. Another result is a version of Vafa-Witten's inequality for twisted spectral triples. Geometric applications include a version of Vafa-Witten's inequality in conformal geometry. There are also noncommutative versions for spectral triples over noncommutative tori and duals of discrete cocompact subgroups of semisimple Lie groups satisfying the Baum-Connes conjecture. (This is joint work with Hang Wang.)
                  How to see in many dimensions
                  14:10 Mon 16 Sep, 2013 :: 7.15 Ingkarni Wardli :: Prof. Michael Murray :: School of Mathematical Sciences

                  Media...
                  The human brain has evolved to be able to think intuitively in three dimensions. Unfortunately the real world is at least four and maybe 10, 11 or 26 dimensional. In this talk I will show how mathematics can be used to develop your ability to think in more than three dimensions.
                  Random Wanderings on a Sphere...
                  11:10 Tue 17 Sep, 2013 :: Ingkarni Wardli Level 5 Room 5.57 :: A/Prof Robb Muirhead :: University of Adelaide

                  This will be a short talk (about 30 minutes) about the following problem. (Even if I tell you all I know about it, it won't take very long!) Imagine the earth is a unit sphere in 3-dimensions. You're standing at a fixed point, which we may as well take to be the North Pole. Suddenly you get moved to another point on the sphere by a random (uniform) orthogonal transormation. Where are you now? You're not at a point which is uniformly distributed on the surface of the sphere (so, since most of the earth's surface is water, you're probably drowning). But then you get moved again by the same orthogonal transformation. Where are you now? And what happens to your location it this happens repeatedly? I have only a partial answwer to this question, for 2 and 3 transformations. (There's nothing special about 3 dimensions here--results hold for all dimensions which are at least 3.) I don't know of any statistical application for this! This work was motivated by a talk I heard, given by Tom Marzetta (Bell Labs) at a conference at MIT. Although I know virtually nothing about signal processing, I gather Marzetta was trying to encode signals using powers of ranfom orthogonal matrices. After carrying out simulations, I think he decided it wasn't a good idea.
                  Conformal geometry in four variables and a special geometry in five
                  12:10 Fri 20 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Dennis The :: Australian National University

                  Starting with a split signature 4-dimensional conformal manifold, one can build a 5-dimensional bundle over it equipped with a 2-plane distribution. Generically, this is a (2,3,5)-distribution in the sense of Cartan's five variables paper, an aspect that was recently pursued by Daniel An and Pawel Nurowski (finding new examples concerning the geometry of rolling bodies where the (2,3,5)-distribution has G2-symmetry). I shall explain how to understand some elementary aspects of this "twistor construction" from the perspective of parabolic geometry. This is joint work with Michael Eastwood and Katja Sagerschnig.
                  Controlling disease, one household at a time.
                  12:10 Mon 23 Sep, 2013 :: B.19 Ingkarni Wardli :: Michael Lydeamore :: University of Adelaide

                  Pandemics and Epidemics have always caused significant disruption to society. Attempting to model each individual in any reasonable sized population is unfeasible at best, but we can get surprisingly good results just by looking at a single household in a population. In this talk, I'll try to guide you through the logic I've discovered this year, and present some of the key results we've obtained so far, as well as provide a brief indication of what's to come.
                  The irrational line on the torus
                  12:35 Mon 23 Sep, 2013 :: B.19 Ingkarni Wardli :: Kelli Francis-Staite :: University of Adelaide

                  The torus is very common example of a surface in R^3, but it's a lot more interesting than just a donut! I will introduce some standard mathematical descriptions of the torus, a bit of number theory, and finally what the irrational line on the torus is. Why is this interesting? Well despite donuts being yummy to eat, the irrational line on the torus gives a range of pathological counter-examples. In Differential Geometry, it is an example of a manifold that is a subset of another manifold, but not a submanifold. In Lie theory, it is an example of a subgroup of a Lie group which is not a Lie subgroup. If that wasn't enough of a mouthful, I may also provide some sweet incentives to come along! Does anyone know the location of a good donut store?
                  A mathematician walks into a bar.....
                  12:10 Mon 30 Sep, 2013 :: B.19 Ingkarni Wardli :: Ben Rohrlach :: University of Adelaide

                  Media...
                  Man is by his very nature, inquisitive. Our need to know has been the reason we've always evolved as a species. From discovering fire, to exploring the galaxy with those Vulcan guys in that documentary I saw, knowing the answer to a question has always driven human kind. Clearly then, I had to ask something. Something that by it's very nature is a thing. A thing that, specifically, I had to know. That thing that I had to know was this: Do mathematicians get stupider the more they drink? Is this effect more pronounced than for normal (Gaussian) people? At the quiz night that AUMS just ran I managed to talk two tables into letting me record some key drinking statistics. I'll be using those statistics to introduce some different statistical tests commonly seen in most analyses you'll see in other fields. Oh, and I'll answer those questions I mentioned earlier too, hopefully. Let's do this thing.
                  Exact Fefferman-Graham metrics
                  12:10 Fri 11 Oct, 2013 :: Ingkarni Wardli B19 :: Prof Pawel Nurowski :: University of Warsaw

                  Modelling the South Australian garfish population slice by slice.
                  12:10 Mon 14 Oct, 2013 :: B.19 Ingkarni Wardli :: John Feenstra :: University of Adelaide

                  Media...
                  In this talk I will provide a taste of how South Australian garfish populations are modelled. The role and importance of garfish 'slices' will be explained and how these help produce important reporting quantities of yearly recruitment, legal-size biomass, and exploitation rate within a framework of an age and length based population model.
                  Lost in Space: Point Pattern Matching and Astrometry
                  12:35 Mon 14 Oct, 2013 :: B.19 Ingkarni Wardli :: Annie Conway :: University of Adelaide

                  Astrometry is the field of research that concerns the positions of objects in space. This can be useful for satellite tracking where we would like to know accurate positions of satellites at given times. Telescopes give us some idea of the position, but unfortunately they are not very precise. However, if a photograph of a satellite has stars in the background, we can use that information to refine our estimate of the location of the image, since the positions of stars are known to high accuracy and are readily available in star catalogues. But there are billions of stars in the sky so first we would need to determine which ones we're actually looking at. In this talk I will give a brief introduction to astrometry and walk through a point pattern matching algorithm for identifying stars in a photograph.
                  How the leopard got his spots
                  14:10 Mon 14 Oct, 2013 :: 7.15 Ingkarni Wardli :: Dr Ed Green :: School of Mathematical Sciences

                  Media...
                  Patterns are everywhere in nature, whether they be the spots and stripes on animals' coats, or the intricate arrangement of different cell types in a tissue. But how do these patterns arise? Whilst every cell contains a plan of the organism in its genes, the cells need to organise themselves so that each knows what it should do to achieve this plan. Mathematics can help biologists explore how different types of signals might be used to control the patterning process. In this talk, I will introduce two simple mathematical theories of biological pattern formation: Turing patterns where, surprisingly, the essential ingredient for producing the pattern is diffusion, which usually tends to make things more uniform; and the Keller-Segel model, which provides a simple mechanism for the formation of multicellular structures from isolated single cells. These mathematical models can be used to explain how tissues develop, and why there are many spotted animals with a stripy tail, but no stripy animals with a spotted tail.
                  Geodesic completeness of compact pp-waves
                  12:10 Fri 18 Oct, 2013 :: Ingkarni Wardli B19 :: Dr Thomas Leistner :: University of Adelaide

                  A semi-Riemannian manifold is geodesically complete (or for short, complete) if all its maximal geodesics are defined on the real line. Whereas for Riemannian metrics the compactness of the manifold implies completeness, there are compact Lorentzian manifolds that are not complete (e.g. the Clifton-Pohl torus). Several rather strong conditions have been found in the literature under which a compact Lorentzian manifold is complete, including being homogeneous (Marsden) or of constant curvature (Carriere, Klingler), or admitting a timelike Killing vector field (Romero, Sanchez). We will consider pp-waves, which are Lorentzian manifold with a parallel null vector field and a highly degenerate curvature tensor, but which do not satisfy any of the above conditions. We will show that a compact pp-wave is universally covered by a vector space, determine the metric on the universal cover and consequently show that they are geodesically complete.
                  Model Misspecification due to Site Specific Rate Heterogeneity: how is tree inference affected?
                  12:10 Mon 21 Oct, 2013 :: B.19 Ingkarni Wardli :: Stephen Crotty :: University of Adelaide

                  Media...
                  In this talk I'll answer none of the questions you ever had about phylogenetics, but hopefully some you didn't. I'll be giving this presentation at a phylogenetics conference in 3 weeks, so sorry it is a little light on background. You've been warned! Phlyogeneticists have long recognised that different sites in a DNA sequence can experience different rates of nucleotide substitution, and many models have been developed to accommodate this rate heterogeneity. But what happens when a single site exhibits rate heterogeneity along different branches of an evolutionary tree? In this talk I'll introduce the notion of Site Specific Rate Heterogeneity (SSRH) and investigate a simple case, looking at the impact of SSRH on inference via maximum parsimony, neighbour joining and maximum likelihood.
                  Equivalence of P-values - not what you expect
                  11:10 Tue 22 Oct, 2013 :: Ingkarni Wardli Level 5 Room 5.57 :: Dr Jono Tuke :: University of Adelaide

                  Localised index and L^2-Lefschetz fixed point formula
                  12:10 Fri 25 Oct, 2013 :: Ingkarni Wardli B19 :: Dr Hang Wang :: University of Adelaide

                  In this talk we introduce a class of localised indices for the Dirac type operators on a complete Riemannian manifold, where a discrete group acts properly, co-compactly and isometrically. These localised indices, generalising the L^2-index of Atiyah, are obtained by taking Hattori-Stallings traces of the higher index for the Dirac type operators. We shall talk about some motivation and applications for working on localised indices. The talk is related to joint work with Bai-Ling Wang.
                  Group meeting
                  15:10 Fri 25 Oct, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Ben Binder and Mr David Wilke :: University of Adelaide

                  Dr Ben Binder :: 'An inverse approach for solutions to free-surface flow problems' :: Abstract: Surface water waves are familiar to most people, for example, the wave pattern generated at the stern of a ship. The boundary or interface between the air and water is called the free-surface. When determining a solution to a free-surface flow problem it is commonplace for the forcing (eg. shape of ship or waterbed topography) that creates the surface waves to be prescribed, with the free-surface coming as part of the solution. Alternatively, one can choose to prescribe the shape of the free-surface and find the forcing inversely. In this talk I will discuss my ongoing work using an inverse approach to discover new types of solutions to free-surface flow problems in two and three dimensions, and how the predictions of the method might be verified with experiments. :: Mr David Wilke:: 'A Computational Fluid Dynamic Study of Blood Flow Within the Coiled Umbilical Arteries':: Abstract: The umbilical cord is the lifeline of the fetus throughout gestation. In a normal pregnancy it facilitates the supply of oxygen and nutrients from the placenta via a single vein, in addition to the return of deoxygenated blood from the developing embryo or fetus via two umbilical arteries. Despite the major role it plays in the growth of the fetus, pathologies of the umbilical cord are poorly understood. In particular, variations in the cord geometry, which typically forms a helical arrangement, have been correlated with adverse outcomes in pregnancy. Cords exhibiting either abnormally low or high levels of coiling have been associated with pathological results including growth-restriction and fetal demise. Despite this, the methodology currently employed by clinicians to characterise umbilical pathologies can misdiagnose cords and is prone to error. In this talk a computational model of blood flow within rigid three-dimensional structures representative of the umbilical arteries will be presented. This study determined that the current characterization was unable to differentiate between cords which exhibited clinically distinguishable flow properties, including the cord pressure drop, which provides a measure of the loading on the fetal heart.
                  Modelling and optimisation of group dose-response challenge experiments
                  12:10 Mon 28 Oct, 2013 :: B.19 Ingkarni Wardli :: David Price :: University of Adelaide

                  Media...
                  An important component of scientific research is the 'experiment'. Effective design of these experiments is important and, accordingly, has received significant attention under the heading 'optimal experimental design'. However, until recently, little work has been done on optimal experimental design for experiments where the underlying process can be modelled by a Markov chain. In this talk, I will discuss some of the work that has been done in the field of optimal experimental design for Markov Chains, and some of the work that I have done in applying this theory to dose-response challenge experiments for the bacteria Campylobacter jejuni in chickens.
                  Interaction of double-stranded DNA inside single-walled carbon nanotubes
                  12:35 Mon 28 Oct, 2013 :: B.19 Ingkarni Wardli :: Mansoor Alshehri :: University of Adelaide

                  Media...
                  Here we investigate the interaction of deoxyribonucleic acid (DNA) inside single walled carbon nanotubes (SWCNTs). Using classical applied mathematical modeling, we derive explicit analytical expressions for the encapsulation of DNA inside single-walled carbon nanotubes. We adopt the 6-12 Lennard-Jones potential function together with the continuous approach to determine the preferred minimum energy position of the dsDNA molecule inside a single-walled carbon nanotube, so as to predict its location with reference to the cross- section of the carbon nanotube. An analytical expression is obtained in terms of hypergeometric functions, which provides a computationally rapid procedure to determine critical numerical values.
                  IGA Lectures on Finsler geometry
                  13:30 Thu 31 Oct, 2013 :: Ingkarni Wardli 7.15 :: Prof Robert Bryant :: Duke University

                  Media...
                  13:30 Refreshments. 14:00 Lecture 1: The origins of Finsler geometry in the calculus of variations. 15:00 Lecture 2: Finsler manifolds of constant flag curvature.
                  Recent developments in special holonomy manifolds
                  12:10 Fri 1 Nov, 2013 :: Ingkarni Wardli 7.15 :: Prof Robert Bryant :: Duke University

                  One of the big classification results in differential geometry from the past century has been the classification of the possible holonomies of affine manifolds, with the major first step having been taken by Marcel Berger in his 1954 thesis. However, Berger's classification was only partial, and, in the past 20 years, an extensive research effort has been expended to complete this classification and extend it in a number of ways. In this talk, after recounting the major parts of the history of the subject, I will discuss some of the recent results and surprising new examples discovered as a by-product of research into Finsler geometry. If time permits, I will also discuss some of the open problems in the subject.
                  Braids and entropy
                  10:10 Fri 8 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Burglind Joricke :: Australian National University

                  This talk will be a brief introduction to some aspects of braid theory and to entropy, to provide background for the speaker's talk at 12:10 pm the same day.
                  Braids, conformal module and entropy
                  12:10 Fri 8 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Burglind Joricke :: Australian National University

                  I will discuss two invariants of conjugacy classes of braids. The first invariant is the conformal module which implicitly occurred already in a paper of Gorin and Lin in connection with their interest in Hilbert's 13th problem. The second is a popular dynamical invariant, the entropy. It appeared in connection with Thurston's theory of surface homeomorphisms. It turns out that these invariants are related: They are inversely proportional. In a preparatory talk (at 10:10 am) I will give a brief introduction to some aspects of braid theory and to entropy.
                  Developing Multiscale Methodologies for Computational Fluid Mechanics
                  12:10 Mon 11 Nov, 2013 :: B.19 Ingkarni Wardli :: Hammad Alotaibi :: University of Adelaide

                  Media...
                  Recently the development of multiscale methods is one of the most fertile research areas in mathematics, physics, engineering and computer science. The need for multiscale modeling comes usually from the fact that the available macroscale models are not accurate enough, and the microscale models are not efficient enough. By combining both viewpoints, one hopes to arrive at a reasonable compromise between accuracy and efficiency. In this seminar I will give an overview of the recent efforts on developing multiscale methods such as patch dynamics scheme which is used to address an important class of time dependent multiscale problems.
                  Euler and Lagrange solutions of the three-body problem and beyond
                  12:10 Fri 15 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Pawel Nurowski :: Centre for Theoretical Physics, Polish Academy of Sciences

                  All at sea with spectral analysis
                  11:10 Tue 19 Nov, 2013 :: Ingkarni Wardli Level 5 Room 5.56 :: A/Prof Andrew Metcalfe :: The University of Adelaide

                  The steady state response of a single degree of freedom damped linear stystem to a sinusoidal input is a sinusoidal function at the same frequency, but generally with a different amplitude and a phase shift. The analogous result for a random stationary input can be described in terms of input and response spectra and a transfer function description of the linear system. The practical use of this result is that the parameters of a linear system can be estimated from the input and response spectra, and the response spectrum can be predicted if the transfer function and input spectrum are known. I shall demonstrate these results with data from a small ship in the North Sea. The results from the sea trial raise the issue of non-linearity, and second order amplitude response functons are obtained using auto-regressive estimators. The possibility of using wavelets rather than spectra is consedred in the context of single degree of freedom linear systems. Everybody welcome to attend. Please not a change of venue - we will be in room 5.56
                  A gentle introduction to bubble evolution in Hele-Shaw flows
                  15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT

                  A Hele-Shaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a Hele-Shaw cell that is otherwise filled with viscous fluid, we can observe a bubble of air growing in size. The process is highly unstable, and the bubble boundary expands in an uneven fashion, leading to striking fingering patterns (look up Hele-Shaw cell or Saffman-Taylor instability on YouTube). From a mathematical perspective, modelling these Hele-Shaw flows is interesting because the governing equations are sufficiently ``simple'' that a considerable amount of analytical progress is possible. Indeed, there is no other context in which (genuinely) two-dimensional moving boundary problems are so tractable. More generally, Hele-Shaw flows are important as they serve as prototypes for more complicated (and important) physical processes such as crystal growth and diffusion limited aggregation. I will give an introduction to some of the main ideas and summarise some of my present research in this area.
                  Buoyancy driven exchange flows in the nearshore regions of lakes and reservoirs
                  15:10 Mon 2 Dec, 2013 :: 5.58 (Ingkarni Wardli) :: Professor John Patterson :: University of Sydney

                  Natural convection is the flow driven by differences in density, and is ubiquitous in nature and industry. It is the source of most environmental flows, and is the basis for almost all industrial heat exchange processes. It operates on both massive and micro scales. It is usually considered as a flow driven by temperature gradients, but could equally be from a gradient in any density determining property - salinity is one obvious example. It also depends on gravity; so magnetohydrodynamics becomes relevant as well. One particular interesting and environmentally relevant flow is the exchange flow in the nearshore regions of lakes and reservoirs. This occurs because of the effects of a decreasing depth approaching the shore resulting laterally unequal heat loss and heat gain during the diurnal cooling and heating cycle. This presentation will discuss some of the results obtained by the Natural Convection Group at Sydney University in analytical, numerical and experimental investigations of this mechanism, and the implications for lake water quality.
                  Reductive group actions and some problems concerning their quotients
                  12:10 Fri 17 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Gerald Schwarz :: Brandeis University

                  Media...
                  We will gently introduce the concept of a complex reductive group and the notion of the quotient Z of a complex vector space V on which our complex reductive group G acts linearly. There is the quotient mapping p from V to Z. The quotient is an affine variety with a stratification coming from the group action. Let f be an automorphism of Z. We consider the following questions (and give some answers). 1) Does f preserve the stratification of Z, i.e., does it permute the strata? 2) Is there a lift F of f? This means that F maps V to V and p(F(v))=f(p(v)) for all v in V. 3) Can we arrange that F is equivariant? We show that 1) is almost always true, that 2) is true in a lot of cases and that a twisted version of 3) then holds.
                  The density property for complex manifolds: a strong form of holomorphic flexibility
                  12:10 Fri 24 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Frank Kutzschebauch :: University of Bern

                  Compared with the real differentiable case, complex manifolds in general are more rigid, their groups of holomorphic diffeomorphisms are rather small (in general trivial). A long known exception to this behavior is affine n-space C^n for n at least 2. Its group of holomorphic diffeomorphisms is infinite dimensional. In the late 1980s Andersen and Lempert proved a remarkable theorem which stated in its generalized version due to Forstneric and Rosay that any local holomorphic phase flow given on a Runge subset of C^n can be locally uniformly approximated by a global holomorphic diffeomorphism. The main ingredient in the proof was formalized by Varolin and called the density property: The Lie algebra generated by complete holomorphic vector fields is dense in the Lie algebra of all holomorphic vector fields. In these manifolds a similar local to global approximation of Andersen-Lempert type holds. It is a precise way of saying that the group of holomorphic diffeomorphisms is large. In the talk we will explain how this notion is related to other more recent flexibility notions in complex geometry, in particular to the notion of a Oka-Forstneric manifold. We will give examples of manifolds with the density property and sketch applications of the density property. If time permits we will explain criteria for the density property developed by Kaliman and the speaker.
                  Holomorphic null curves and the conformal Calabi-Yau problem
                  12:10 Tue 28 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Franc Forstneric :: University of Ljubljana

                  Media...
                  I shall describe how methods of complex analysis can be used to give new results on the conformal Calabi-Yau problem concerning the existence of bounded metrically complete minimal surfaces in real Euclidean 3-space R^3. We shall see in particular that every bordered Riemann surface admits a proper complete holomorphic immersion into the ball of C^2, and a proper complete embedding as a holomorphic null curve into the ball of C^3. Since the real and the imaginary parts of a holomorphic null curve in C^3 are conformally immersed minimal surfaces in R^3, we obtain a bounded complete conformal minimal immersion of any bordered Riemann surface into R^3. The main advantage of our methods, when compared to the existing ones in the literature, is that we do not need to change the conformal type of the Riemann surface. (Joint work with A. Alarcon, University of Granada.)
                  Integrability of infinite-dimensional Lie algebras and Lie algebroids
                  12:10 Fri 7 Feb, 2014 :: Ingkarni Wardli B20 :: Christoph Wockel :: Hamburg University

                  Lie's Third Theorem states that each finite-dimensional Lie algebra is the Lie algebra of a Lie group (we also say "integrates to a Lie group"). The corresponding statement for infinite-dimensional Lie algebras or Lie algebroids is false and we will explain geometrically why this is the case. The underlying pattern is that of integration of central extensions of Lie algebras and Lie algebroids. This also occurs in other contexts, and we will explain some aspects of string group models in these terms. In the end we will sketch how the non-integrability of Lie algebras and Lie algebroids can be overcome by passing to higher categorical objects (such as smooth stacks) and give a panoramic (but still conjectural) perspective on the precise relation of the various integrability problems.
                  Hormander's estimate, some generalizations and new applications
                  12:10 Mon 17 Feb, 2014 :: Ingkarni Wardli B20 :: Prof Zbigniew Blocki :: Jagiellonian University

                  Lars Hormander proved his estimate for the d-bar equation in 1965. It is one the most important results in several complex variables (SCV). New applications have emerged recently, outside of SCV. We will present three of them: the Ohsawa-Takegoshi extension theorem with optimal constant, the one-dimensional Suita Conjecture, and Nazarov's approach to the Bourgain-Milman inequality from convex analysis.
                  The structuring role of chaotic stirring on pelagic ecosystems
                  11:10 Fri 28 Feb, 2014 :: B19 Ingkarni Wardli :: Dr Francesco d'Ovidio :: Universite Pierre et Marie Curie (Paris VI)

                  The open ocean upper layer is characterized by a complex transport dynamics occuring over different spatiotemporal scales. At the scale of 10-100 km - which covers the so called mesoscale and part of the submesoscale - in situ and remote sensing observations detect strong variability in physical and biogeochemical fields like sea surface temperature, salinity, and chlorophyll concentration. The calculation of Lyapunov exponent and other nonlinear diagnostics applied to the surface currents have allowed to show that an important part of this tracer variability is due to chaotic stirring. Here I will extend this analysis to marine ecosystems. For primary producers, I will show that stable and unstable manifolds of hyperbolic points embedded in the surface velocity field are able to structure the phytoplanktonic community in fluid dynamical niches of dominant types, where competition can locally occur during bloom events. By using data from tagged whales, frigatebirds, and elephant seals, I will also show that chaotic stirring affects the behaviour of higher trophic levels. In perspective, these relations between transport structures and marine ecosystems can be the base for a biodiversity index constructued from satellite information, and therefore able to monitor key aspects of the marine biodiversity and its temporal variability at the global scale.
                  Geometric quantisation in the noncompact setting
                  12:10 Fri 7 Mar, 2014 :: Ingkarni Wardli B20 :: Peter Hochs :: University of Adelaide

                  Geometric quantisation is a way to construct quantum mechanical phase spaces (Hilbert spaces) from classical mechanical phase spaces (symplectic manifolds). In the presence of a group action, the quantisation commutes with reduction principle states that geometric quantisation should be compatible with the ways the group action can be used to simplify (reduce) the classical and quantum phase spaces. This has deep consequences for the link between symplectic geometry and representation theory. The quantisation commutes with reduction principle has been given explicit meaning, and been proved, in cases where the symplectic manifold and the group acting on it are compact. There have also been results where just the group, or the orbit space of the action, is assumed to be compact. These are important and difficult, but it is somewhat frustrating that they do not even apply to the simplest example from the physics point of view: a free particle in Rn. This talk is about a joint result with Mathai Varghese where the group, manifold and orbit space may all be noncompact.
                  The phase of the scattering operator from the geometry of certain infinite dimensional Lie groups
                  12:10 Fri 14 Mar, 2014 :: Ingkarni Wardli B20 :: Jouko Mickelsson :: University of Helsinki

                  This talk is about some work on the phase of the time evolution operator in QED and QCD, related to the geometry of certain infinite-dimensional groups (essentially modelled by PSDO's).
                  Dynamical systems approach to fluid-plasma turbulence
                  15:10 Fri 14 Mar, 2014 :: 5.58 Ingkarni Wardli :: Professor Abraham Chian

                  Sun-Earth system is a complex, electrodynamically coupled system dominated by multiscale interactions. The complex behavior of the space environment is indicative of a state driven far from equilibrium whereby instabilities, nonlinear waves, and turbulence play key roles in the system dynamics. First, we review the fundamental concepts of nonlinear dynamics in fluids and plasmas and discuss their relevance to the study of the Sun-Earth relation. Next, we show how Lagrangian coherent structures identify the transport barriers of plasma turbulence modeled by 3-D solar convective dynamo. Finally, we show how Lagrangian coherent structures can be detected in the solar photospheric turbulence using satellite observations.
                  What Technical Performance Measures are Critical to Evaluate Geothermal Developments?
                  12:10 Mon 17 Mar, 2014 :: B.19 Ingkarni Wardli :: Jo Varney :: University of Adelaide

                  Media...
                  Josephine Varney, Nigel Bean and Betina Bendall. When geologists, geophysicists and engineers study geothermal developments, each group has their own set of technical performance measures. While these performance measures tell each group something important about the geothermal development, there is often difficulty in translating these technical performance measures into financial performance measures for investors. In this paper, we argue that brine effectiveness is the best, simple financial performance measure for a geothermal investor. This is because it is a good, yet simple indicator of ROI (return on investment); and importantly, links well production to power plant production, hence describes the geothermal development in a holistic sense.
                  Embed to homogenise heterogeneous wave equation.
                  12:35 Mon 17 Mar, 2014 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide

                  Media...
                  Consider materials with complicated microstructure: we want to model their large scale dynamics by equations with effective, `average' coefficients. I will show an example of heterogeneous wave equation in 1D. If Centre manifold theory is applied to model the original heterogeneous wave equation directly, we will get a trivial model. I embed the wave equation into a family of more complex wave problems and I show the equivalence of the two sets of solutions.
                  Viscoelastic fluids: mathematical challenges in determining their relaxation spectra
                  15:10 Mon 17 Mar, 2014 :: 5.58 Ingkarni Wardli :: Professor Russell Davies :: Cardiff University

                  Determining the relaxation spectrum of a viscoelastic fluid is a crucial step before a linear or nonlinear constitutive model can be applied. Information about the relaxation spectrum is obtained from simple flow experiments such as creep or oscillatory shear. However, the determination process involves the solution of one or more highly ill-posed inverse problems. The availability of only discrete data, the presence of noise in the data, as well as incomplete data, collectively make the problem very hard to solve. In this talk I will illustrate the mathematical challenges inherent in determining relaxation spectra, and also introduce the method of wavelet regularization which enables the representation of a continuous relaxation spectrum by a set of hyperbolic scaling functions.
                  Is it possible to beat the lottery system?
                  12:10 Mon 24 Mar, 2014 :: B.19 Ingkarni Wardli :: Michael Lydeamore :: University of Adelaide

                  Media...
                  Every week millions of people around the country buy tickets for a round of the lottery. Known as the "lotto", the chances of winning the big prize are less than 1 in 8 million, yet every week people will purchase a ticket. What if there was a smart way of betting which would increase your odds? A few weeks ago an article came across my desk with those very words: "Using this scheme you will win more". In this talk, we'll test those claims. Looking first at a basic counting argument, and then later moving the hard work over to a computer we'll find out if this betting scheme (and many others similar to it) will actually win you more or if just like playing in a casino, you'll still go bankrupt with probability 1.
                  Moduli spaces of contact instantons
                  12:10 Fri 28 Mar, 2014 :: Ingkarni Wardli B20 :: David Baraglia :: University of Adelaide

                  In dimensions greater than four there are several notions of higher Yang-Mills instantons. This talk concerns one such case, contact instantons, defined for 5-dimensional contact manifolds. The geometry transverse to the Reeb foliation turns out to be important in understanding the moduli space. For example, we show the dimension of the moduli space is the index of a transverse elliptic complex. This is joint work with Pedram Hekmati.
                  Scattering theory and noncommutative geometry
                  01:10 Mon 31 Mar, 2014 :: Ingkarni Wardli B20 :: Alan Carey :: Australian National University

                  Aircraft flight dynamics and stability
                  12:10 Mon 31 Mar, 2014 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide

                  Media...
                  In general, a stable plane is safer, more efficient and more comfortable than an unstable plane, however there are many design features that affect stability. In this talk I will discuss the dynamics of fixed wing aircraft in flight, with particular emphasis on stability. I will discuss some basic stability considerations, and how they influence aircraft design as well as some interesting modes of instability, and how they may be managed. Hopefully this talk will help to explain why planes to look the way they do.
                  The limits of proof
                  14:10 Wed 2 Apr, 2014 :: Hughes Lecture Room 322 :: Assoc. Prof. Finnur Larusson :: School of Mathematical Sciences

                  Media...
                  The job of the mathematician is to discover new truths about mathematical objects and their relationships. Such truths are established by proving them. This raises a fundamental question. Can every mathematical truth be proved (by a sufficiently clever being) or are there truths that will forever lie beyond the reach of proof? Mathematics can be turned on itself to investigate this question. In this talk, we will see that under certain assumptions about proofs, there are truths that cannot be proved. You must decide for yourself whether you think these assumptions are valid!
                  Semiclassical restriction estimates
                  12:10 Fri 4 Apr, 2014 :: Ingkarni Wardli B20 :: Melissa Tacy :: University of Adelaide

                  Eigenfunctions of Hamiltonians arise naturally in the theory of quantum mechanics as stationary states of quantum systems. Their eigenvalues have an interpretation as the square root of E, where E is the energy of the system. We wish to better understand the high energy limit which defines the boundary between quantum and classical mechanics. In this talk I will focus on results regarding the restriction of eigenfunctions to lower dimensional subspaces, in particular to hypersurfaces. A convenient way to study such problems is to reframe them as problems in semiclassical analysis.
                  The Dynamics of Falling
                  12:10 Mon 7 Apr, 2014 :: B.19 Ingkarni Wardli :: Lyron Winderbaum :: University of Adelaide

                  Media...
                  As most of you know I am addicted to climbing. So I thought I might talk abit about some math related to climbing, ropes, tension, and to be entirely honest, mostly statics -- not dynamics, but the title was catchy. I'll explain a little about climbing, and the different ways in which you can go about protecting yourself from a fall by using ropes. This involves some interesting formulae for friction that most of you probably haven't seen before, and even some trig for the geometry enthusiast, but be warned -- it delves into the realms of physics. I even uncovered a few unexpected and somewhat anti-intuitive results that might interest you.
                  T-Duality and its Generalizations
                  12:10 Fri 11 Apr, 2014 :: Ingkarni Wardli B20 :: Jarah Evslin :: Theoretical Physics Center for Science Facilities, CAS

                  Given a manifold M with a torus action and a choice of integral 3-cocycle H, T-duality yields another manifold with a torus action and integral 3-cocyle. It induces a number of surprising automorphisms between structures on these manifolds. In this talk I will review T-duality and describe some work on two generalizations which are realized in string theory: NS5-branes and heterotic strings. These respectively correspond to non-closed 3-classes H and to principal bundles fibered over M.
                  CARRYING CAPACITY FOR FINFISH AQUACULTURE IN SPENCER GULF: RAPID ASSESSMENT USING HYDRODYNAMIC AND NEAR-FIELD, SEMI - ANALYTIC SOLUTIONS
                  15:10 Fri 11 Apr, 2014 :: 5.58 Ingkarni Wardli :: Associate Professor John Middleton :: SARDI Aquatic Sciences and University of Adelaide

                  Aquaculture farming involves daily feeding of finfish and a subsequent excretion of nutrients into Spencer Gulf. Typically, finfish farming is done in six or so 50m diameter cages and over 600m X 600m lease sites. To help regulate the industry, it is desired that the finfish feed rates and the associated nutrient flux into the ocean are determined such that the maximum nutrient concentration c does not exceed a prescribed value (say cP) for ecosystem health. The prescribed value cP is determined by guidelines from the E.P.A. The concept is known as carrying capacity since limiting the feed rates limits the biomass of the farmed finfish. Here, we model the concentrations that arise from a constant input flux (F) of nutrients in a source region (the cage or lease) using the (depth-averaged) two dimensional, advection diffusion equation for constant and sinusoidal (tides) currents. Application of the divergence theorem to this equation results in a new scale estimate of the maximum flux F (and thus feed rate) that is given by F= cP /T* (1) where cP is the maximum allowed concentration and T* is a new time scale of “flushing” that involves both advection and diffusion. The scale estimate (1) is then shown to compare favourably with mathematically exact solutions of the advection diffusion equation that are obtained using Green’s functions and Fourier transforms. The maximum nutrient flux and associated feed rates are then estimated everywhere in Spencer Gulf through the development and validation of a hydrodynamic model. The model provides seasonal averages of the mean currents U and horizontal diffusivities KS that are needed to estimate T*. The diffusivities are estimated from a shear dispersal model of the tides which are very large in the gulf. The estimates have been provided to PIRSA Fisheries and Aquaculture to assist in the sustainable expansion of finfish aquaculture.
                  Bayesian Indirect Inference
                  12:10 Mon 14 Apr, 2014 :: B.19 Ingkarni Wardli :: Brock Hermans :: University of Adelaide

                  Media...
                  Bayesian likelihood-free methods saw the resurgence of Bayesian statistics through the use of computer sampling techniques. Since the resurgence, attention has focused on so-called 'summary statistics', that is, ways of summarising data that allow for accurate inference to be performed. However, it is not uncommon to find data sets in which the summary statistic approach is not sufficient. In this talk, I will be summarising some of the likelihood-free methods most commonly used (don't worry if you've never seen any Bayesian analysis before), as well as looking at Bayesian Indirect Likelihood, a new way of implementing Bayesian analysis which combines new inference methods with some of the older computational algorithms.
                  A generalised Kac-Peterson cocycle
                  11:10 Thu 17 Apr, 2014 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide

                  The Kac-Peterson cocycle appears in the study of highest weight modules of infinite dimensional Lie algebras and determines a central extension. The vanishing of its cohomology class is tied to the existence of a cubic Dirac operator whose square is a quadratic Casimir element. I will introduce a closely related Lie algebra cocycle that comes about when constructing spin representations and gives rise to a Banach Lie group with a highly nontrivial topology. I will also explain how to make sense of the cubic Dirac operator in this setting and discuss its relation to twisted K-theory. This is joint work with Jouko Mickelsson.
                  Outlier removal using the Bayesian information criterion for group-based trajectory modelling
                  12:10 Mon 28 Apr, 2014 :: B.19 Ingkarni Wardli :: Chris Davies :: University of Adelaide

                  Media...
                  Attributes measured longitudinally can be used to define discrete paths of measurements, or trajectories, for each individual in a given population. Group-based trajectory modelling methods can be used to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Existing methods generally allocate every individual trajectory into one of the estimated groups. However this does not allow for the possibility that some individuals may be following trajectories so different from the rest of the population that they should not be included in a group-based trajectory model. This results in these outlying trajectories being treated as though they belong to one of the groups, distorting the estimated trajectory groups and any subsequent analyses that use them. We have developed an algorithm for removing outlying trajectories based on the maximum change in Bayesian information criterion (BIC) due to removing a single trajectory. As well as deciding which trajectory to remove, the number of groups in the model can also change. The decision to remove an outlying trajectory is made by comparing the log-likelihood contributions of the observations to those of simulated samples from the estimated group-based trajectory model. In this talk the algorithm will be detailed and an application of its use will be demonstrated.
                  Night thoughts of an inveterate tile pusher
                  12:35 Mon 28 Apr, 2014 :: B.19 Ingkarni Wardli :: Damien Warman :: University of Adelaide

                  Media...
                  Wow. Much double. So partition. OEIS. Very code.
                  Lefschetz fixed point theorem and beyond
                  12:10 Fri 2 May, 2014 :: Ingkarni Wardli B20 :: Hang Wang :: University of Adelaide

                  A Lefschetz number associated to a continuous map on a closed manifold is a topological invariant determined by the geometric information near the neighbourhood of fixed point set of the map. After an introduction of the Lefschetz fixed point theorem, we shall use the Dirac-dual Dirac method to derive the Lefschetz number on K-theory level. The method concerns the comparison of the Dirac operator on the manifold and the Dirac operator on some submanifold. This method can be generalised to several interesting situations when the manifold is not necessarily compact.
                  The Mandelbrot Set
                  12:10 Mon 5 May, 2014 :: B.19 Ingkarni Wardli :: David Bowman :: University of Adelaide

                  Media...
                  The Mandelbrot set is an icon of modern mathematics, an image which fires the popular imagination when accompanied by the words 'chaos' and 'fractal'. However, few could give even a vague definition of this mysterious set and fewer still know the mathematical meaning behind it. In this talk we will be looking at the role that the Mandelbrot set plays in complex dynamics, the study of iterated complex valued functions. We shall discuss attracting and repelling cycles and how they are related to the different components of the Mandelbrot set.
                  A geometric model for odd differential K-theory
                  12:10 Fri 9 May, 2014 :: Ingkarni Wardli B20 :: Raymond Vozzo :: University of Adelaide

                  Odd K-theory has the interesting property that-unlike even K-theory-it admits an infinite number of inequivalent differential refinements. In this talk I will give a description of odd differential K-theory using infinite rank bundles and explain why it is the correct differential refinement. This is joint work with Michael Murray, Pedram Hekmati and Vincent Schlegel.
                  Ice floe collisions in the Marginal Ice Zone
                  12:10 Mon 12 May, 2014 :: B.19 Ingkarni Wardli :: Lucas Yiew :: University of Adelaide

                  Media...
                  In an era of climate change, it is becoming increasingly important to model the dynamics of sea-ice cover in the polar regions. The Marginal Ice Zone represents a vast region of ice cover strongly influenced by the effects of ocean waves. As ocean waves penetrate this region, wave energy is progressively dispersed through energy dissipative mechanisms such as collisions between ice floes (discrete chunks of ice). In this talk I will discuss the mathematical models required to build a collision model, and the validation of these models with experimental results.
                  Parrondo's Paradox
                  12:10 Mon 19 May, 2014 :: B.19 Ingkarni Wardli :: Peter Ballard :: University of Adelaide

                  Media...
                  Parrondo's Paradox refers to two games with a curious property: Play Game A, and you will lose money. Play Game B, and you will lose money. Randomly switch between Games A and B, and you will win money. What's going on here? I will look at the maths behind Parrondo's Paradox, and offer an explanation.
                  Multiple Sclerosis and linear stability analysis
                  12:35 Mon 19 May, 2014 :: B.19 Ingkarni Wardli :: Saber Dini :: University of Adelaide

                  Media...
                  Multiple sclerosis (MS), is an inflammatory disease in which the immune system of the body attacks the myelin sheaths around axons in the brain and damages, or in other words, demyelinates the axons. Demyelination process can lead to scarring as well as a broad spectrum of signs and symptoms. Brain of vertebrates has a mechanism to restore the demyelination or Remyelinate the damaged area. Remyelination in the brain is accomplished by glial cells (servers of neurons). Glial cells should accumulate in the damaged areas of the brain to start the repairing process and this accumulation can be viewed as instability. Therefore, spatiotemporal linear stability analysis can be undertaken on the issue to investigate quantitative aspects of the remyelination process.
                  Maths and sea ice
                  13:10 Mon 19 May, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. Luke Bennetts :: School of Mathematical Sciences

                  Media...
                  Anyone that hasn't been cryogenically frozen for the last decade will be aware that sea ice is diminishing rapidly. Less people are aware of the impacts this is having on the global climate. I'll present examples to show how maths is helping to understand sea ice and predict its fate, followed by a short movie.
                  World Is Fukt, or, Why our system for elections doesn't reflect the will of the people, but micro parties like it Just The Way It Is.
                  12:10 Mon 2 Jun, 2014 :: B.19 Ingkarni Wardli :: Casey Briggs :: University of Adelaide

                  Media...
                  Results of elections for upper houses in Australia are notoriously difficult to predict, largely because of the quirky voting counting system used. In this seminar I will explain how the system works and why voters have low control over the outcome. I will then demonstrate using a senate calculator the sensitivity of these elections, including how small changes in votes can lead to dramatically different outcomes.
                  Oka properties of groups of holomorphic and algebraic automorphisms of complex affine space
                  12:10 Fri 6 Jun, 2014 :: Ingkarni Wardli B20 :: Finnur Larusson :: University of Adelaide

                  I will discuss new joint work with Franc Forstneric. The group of holomorphic automorphisms of complex affine space C^n, n>1, is huge. It is not an infinite-dimensional manifold in any recognised sense. Still, our work shows that in some ways it behaves like a finite-dimensional Oka manifold.
                  Group meeting
                  15:10 Fri 6 Jun, 2014 :: 5.58 Ingkarni Wardli :: Meng Cao and Trent Mattner :: University of Adelaide

                  Meng Cao:: Multiscale modelling couples patches of nonlinear wave-like simulations :: Abstract: The multiscale gap-tooth scheme is built from given microscale simulations of complicated physical processes to empower macroscale simulations. By coupling small patches of simulations over unsimulated physical gaps, large savings in computational time are possible. So far the gap-tooth scheme has been developed for dissipative systems, but wave systems are also of great interest. This article develops the gap-tooth scheme to the case of nonlinear microscale simulations of wave-like systems. Classic macroscale interpolation provides a generic coupling between patches that achieves arbitrarily high order consistency between the multiscale scheme and the underlying microscale dynamics. Eigen-analysis indicates that the resultant gap-tooth scheme empowers feasible computation of large scale simulations of wave-like dynamics with complicated underlying physics. As an pilot study, we implement numerical simulations of dam-breaking waves by the gap-tooth scheme. Comparison between a gap-tooth simulation, a microscale simulation over the whole domain, and some published experimental data on dam breaking, demonstrates that the gap-tooth scheme feasibly computes large scale wave-like dynamics with computational savings. Trent Mattner :: Coupled atmosphere-fire simulations of the Canberra 2003 bushfires using WRF-Sfire :: Abstract: The Canberra fires of January 18, 2003 are notorious for the extreme fire behaviour and fire-atmosphere-topography interactions that occurred, including lee-slope fire channelling, pyrocumulonimbus development and tornado formation. In this talk, I will discuss coupled fire-weather simulations of the Canberra fires using WRF-SFire. In these simulations, a fire-behaviour model is used to dynamically predict the evolution of the fire front according to local atmospheric and topographic conditions, as well as the associated heat and moisture fluxes to the atmosphere. It is found that the predicted fire front and heat flux is not too bad, bearing in mind the complexity of the problem and the severe modelling assumptions made. However, the predicted moisture flux is too low, which has some impact on atmospheric dynamics.
                  The p-Minkowski problem
                  12:10 Fri 13 Jun, 2014 :: Ingkarni Wardli B20 :: Xu-Jia Wang :: Australian National University

                  The p-Minkowski problem is an extension of the classical Minkowski problem. It concerns the existence, uniqueness, and regularity of closed convex hypersurfaces with prescribed Gauss curvature. The Minkowski problem has been studied by many people in the last century and has been completely resolved. The p-Minkowski problem involves more applications. In this talk we will review the development of the study of the p-Minkowski problem and discuss some recent works on the problem.​
                  Not nots, knots.
                  12:10 Mon 16 Jun, 2014 :: B.19 Ingkarni Wardli :: Luke Keating-Hughes :: University of Adelaide

                  Media...
                  Although knot theory does not ordinarily arise in classical mathematics, the study of knots themselves proves to be very intricate and is certainly an area with promise for new developments. Ultimately, the study of knots boils down to problems of classification and when two knots are seen to be 'equivalent'. In this seminar we will first talk about some basic definitions and properties of knots, then move on to calculating the knot polynomial - a powerful invariant on knots.
                  Complexifications, Realifications, Real forms and Complex Structures
                  12:10 Mon 23 Jun, 2014 :: B.19 Ingkarni Wardli :: Kelli Francis-Staite :: University of Adelaide

                  Media...
                  Italian mathematicians Niccolò Fontana Tartaglia and Gerolamo Cardano introduced complex numbers to solve polynomial equations such as x^2+1=0. Solving a standard real differential equation often uses complex eigenvalues and eigenfunctions. In both cases, the solution space is expanded to include the complex numbers, solved, and then translated back to the real case. My talk aims to explain the process of complexification and related concepts. It will give vocabulary and some basic results about this important process. And it will contain cute cat pictures.
                  Jacques Hadamard: A useful Frenchman
                  12:10 Mon 30 Jun, 2014 :: B.19 Ingkarni Wardli :: Stephen Crotty :: University of Adelaide

                  Media...
                  In this talk we will learn* very little about Jacques Hadamard. We will then learn* a little more than very little about Hadamard Matrices. Finally, we will learn* nothing at all about how they can be helpful in a phylogenetic framework, other than the fact that they can be helpful in a phylogenetic framework. * In the loosest possible sense
                  The Bismut-Chern character as dimension reduction functor and its twisting
                  12:10 Fri 4 Jul, 2014 :: Ingkarni Wardli B20 :: Fei Han :: National University of Singapore

                  The Bismut-Chern character is a loop space refinement of the Chern character. It plays an essential role in the interpretation of the Atiyah-Singer index theorem from the point of view of loop space. In this talk, I will first briefly review the construction of the Bismut-Chern character and show how it can be viewed as a dimension reduction functor in the Stolz-Teichner program on supersymmetric quantum field theories. I will then introduce the construction of the twisted Bismut-Chern character, which represents our joint work with Varghese Mathai.
                  Higher-Dimensional Geometry
                  12:10 Mon 28 Jul, 2014 :: B.19 Ingkarni Wardli :: Ashley Gibson :: University of Adelaide

                  Media...
                  Since the first millennium BC, geometers have been fascinated by convex regular polytopes. The two- and three-dimensional cases are well-known, with the latter being named after the Greek philosopher Plato. Much less attention has been paid to the higher-dimensional cases, so this seminar will investigate the existence of convex regular polytopes in four or more dimensions. It will also cover the existence of higher-dimensional versions of the cross product, which most people are only familiar with in three dimensions.
                  All's Fair in Love and Statistics
                  12:35 Mon 28 Jul, 2014 :: B.19 Ingkarni Wardli :: Annie Conway :: University of Adelaide

                  Media...
                  Earlier this year Wired.com published an article about a "math genius" who found true love after scraping and analysing data from a dating site. In this talk I will be investigating the actual mathematics that he used, in particular methods for clustering categorical data, and whether or not the approach was successful.
                  Estimates for eigenfunctions of the Laplacian on compact Riemannian manifolds
                  12:10 Fri 1 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Hassell :: Australian National University

                  I am interested in estimates on eigenfunctions, accurate in the high-eigenvalue limit. I will discuss estimates on the size (as measured by L^p norms) of eigenfunctions, on the whole Riemannian manifold, at the boundary, or at an interior hypersurface. The link between high-eigenvalue estimates, geometry, and the dynamics of geodesic flow will be emphasized.
                  Modelling the mean-field behaviour of cellular automata
                  12:10 Mon 4 Aug, 2014 :: B.19 Ingkarni Wardli :: Kale Davies :: University of Adelaide

                  Media...
                  Cellular automata (CA) are lattice-based models in which agents fill the lattice sites and behave according to some specified rule. CA are particularly useful when modelling cell behaviour and as such many people consider CA model in which agents undergo motility and proliferation type events. We are particularly interested in predicting the average behaviour of these models. In this talk I will show how a system of differential equations can be derived for the system and discuss the difficulties that arise in even the seemingly simple case of a CA with motility and proliferation.
                  Hydrodynamics and rheology of self-propelled colloids
                  15:10 Fri 8 Aug, 2014 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide

                  The sub-cellular world has many components in common with soft condensed matter systems (polymers, colloids and liquid crystals). But it has novel properties, not present in traditional complex fluids, arising from a rich spectrum of non-equilibrium behavior: flocking, chemotaxis and bioconvection. The talk is divided into two parts. In the first half, we will (get an idea on how to) derive a hydrodynamic model for self-propelled particles of an arbitrary shape from first principles, in a sufficiently dilute suspension limit, moving in a 3-dimensional space inside a viscous solvent. The model is then restricted to particles with ellipsoidal geometry to quantify the interplay of the long-range excluded volume and the short-range self-propulsion effects. The expression for the constitutive stresses, relating the kinetic theory with the momentum transport equations, are derived using a combination of the virtual work principle (for extra elastic stresses) and symmetry arguments (for active stresses). The second half of the talk will highlight on my current numerical expertise. In particular we will exploit a specific class of spectral basis functions together with RK4 time-stepping to determine the dynamical phases/structures as well as phase-transitions of these ellipsoidal clusters. We will also discuss on how to define the order (or orientation) of these clusters and understand the other rheological quantities.
                  Approximate dynamic programming: An introduction
                  12:10 Mon 11 Aug, 2014 :: B.19 Ingkarni Wardli :: Mingmei Teo :: University of Adelaide

                  Media...
                  In this talk, I'll attempt to give insights into what is dynamic programming and a common method used to solve dynamic programming problems. Then, we'll explore some issues with this method and introduce the idea of approximate dynamic programming. Finally, I'll very briefly describe why I'm interested in approximate dynamic programming.
                  The Dirichlet problem for the prescribed Ricci curvature equation
                  12:10 Fri 15 Aug, 2014 :: Ingkarni Wardli B20 :: Artem Pulemotov :: University of Queensland

                  We will discuss the following question: is it possible to find a Riemannian metric whose Ricci curvature is equal to a given tensor on a manifold M? To answer this question, one must analyze a weakly elliptic second-order geometric PDE. In the first part of the talk, we will review the history of the subject and state several classical theorems. After that, our focus will be on new results concerning the case where M has nonempty boundary.
                  Frequentist vs. Bayesian.
                  12:10 Mon 18 Aug, 2014 :: B.19 Ingkarni Wardli :: David Price :: University of Adelaide

                  Media...
                  Abstract: There are two frameworks in which we can do statistical analyses. Choosing one framework over the other can be* as controversial as choosing between team Jacob and... that other guy. In this talk, I aim to give a very very simple explanation of the main difference between frequentist and Bayesian methods. I'll probably flip a coin and show you a video too. * to people who really care.
                  Quasimodes that do not Equidistribute
                  13:10 Tue 19 Aug, 2014 :: Ingkarni Wardli B17 :: Shimon Brooks :: Bar-Ilan University

                  The QUE Conjecture of Rudnick-Sarnak asserts that eigenfunctions of the Laplacian on Riemannian manifolds of negative curvature should equidistribute in the large eigenvalue limit. For a number of reasons, it is expected that this property may be related to the (conjectured) small multiplicities in the spectrum. One way to study this relationship is to ask about equidistribution for "quasimodes"-or approximate eigenfunctions- in place of highly-degenerate eigenspaces. We will discuss the case of surfaces of constant negative curvature; in particular, we will explain how to construct some examples of sufficiently weak quasimodes that do not satisfy QUE, and show how they fit into the larger theory.
                  T-duality and the chiral de Rham complex
                  12:10 Fri 22 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Linshaw :: University of Denver

                  The chiral de Rham complex of Malikov, Schechtman, and Vaintrob is a sheaf of vertex algebras that exists on any smooth manifold M. It has a square-zero differential D, and contains the algebra of differential forms on M as a subcomplex. In this talk, I'll give an introduction to vertex algebras and sketch this construction. Finally, I'll discuss a notion of T-duality in this setting. This is based on joint work in progress with V. Mathai.
                  Spherical T-duality
                  01:10 Mon 25 Aug, 2014 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide

                  I will talk on a new variant of T-duality, called spherical T-duality, which relates pairs of the form (P,H) consisting of a principal SU(2)-bundle P --> M and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c_2(P). This is precisely true when M is compact oriented and dim(M) is at most 4. When M is higher dimensional, not all pairs (P,H) admit spherical T-duals and even when they exist, the spherical T-duals are not always unique. We will try and explain this phenomenon. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when dim(M) is at most 7, also their integral twisted cohomologies and, when dim(M) is at most 4, even their 7-twisted K-theories. While the complete physical relevance of spherical T-duality is still being explored, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications. This is joint work with Peter Bouwknegt and Jarah Evslin.
                  Software and protocol verification using Alloy
                  12:10 Mon 25 Aug, 2014 :: B.19 Ingkarni Wardli :: Dinesha Ranathunga :: University of Adelaide

                  Media...
                  Reliable software isn't achieved by trial and error. It requires tools to support verification. Alloy is a tool based on set theory that allows expression of a logic-based model of software or a protocol, and hence allows checking of this model. In this talk, I will cover its key concepts, language syntax and analysis features.
                  Mathematics: a castle in the sky?
                  14:10 Mon 25 Aug, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. David Roberts :: School of Mathematical Sciences

                  Media...
                  At university you are exposed to more rigorous mathematics than at school, exemplified by definitions such as those of real numbers individually or as a whole. However, what does mathematics ultimately rest on? Definitions depend on things defined earlier, and this process must stop at some point. Mathematicians expended a lot of energy in the late 19th and early 20th centuries trying to pin down the absolutely fundamental ideas of mathematics, with unexpected results. The results of these efforts are called foundations and are still an area of active research today. This talk will explain what foundations are, some of the historical setting in which they arose, and several of the various systems on which mathematics can be built -- and why most of the mathematics you will do only uses a tiny portion of it!
                  Ideal membership on singular varieties by means of residue currents
                  12:10 Fri 29 Aug, 2014 :: Ingkarni Wardli B20 :: Richard Larkang :: University of Adelaide

                  On a complex manifold X, one can consider the following ideal membership problem: Does a holomorphic function on X belong to a given ideal of holomorphic functions on X? Residue currents give a way of expressing analytically this essentially algebraic problem. I will discuss some basic cases of this, why such an analytic description might be useful, and finish by discussing a generalization of this to singular varieties.
                  Neural Development of the Visual System: a laminar approach
                  15:10 Fri 29 Aug, 2014 :: This talk will now be given as a School Colloquium :: Dr Andrew Oster :: Eastern Washington University

                  In this talk, we will introduce the architecture of the visual system in higher order primates and cats. Through activity-dependent plasticity mechanisms, the left and right eye streams segregate in the cortex in a stripe-like manner, resulting in a pattern called an ocular dominance map. We introduce a mathematical model to study how such a neural wiring pattern emerges. We go on to consider the joint development of the ocular dominance map with another feature of the visual system, the cytochrome oxidase blobs, which appear in the center of the ocular dominance stripes. Since cortex is in fact comprised of layers, we introduce a simple laminar model and perform a stability analysis of the wiring pattern. This intricate biological structure (ocular dominance stripes with 'blobs' periodically distributed in their centers) can be understood as occurring due to two Turing instabilities combined with the leading-order dynamics of the system.
                  Testing Statistical Association between Genetic Pathways and Disease Susceptibility
                  12:10 Mon 1 Sep, 2014 :: B.19 Ingkarni Wardli :: Andy Pfieffer :: University of Adelaide

                  Media...
                  A major research area is the identification of genetic pathways associated with various diseases. However, a detailed comparison of methods that have been designed to ascertain the association between pathways and diseases has not been performed. I will give the necessary biological background behind Genome-Wide Association Studies (GWAS), and explain the shortfalls in traditional GWAS methodologies. I will then explore various methods that use information about genetic pathways in GWAS, and explain the challenges in comparing these methods.
                  Modelling biological gel mechanics
                  12:10 Mon 8 Sep, 2014 :: B.19 Ingkarni Wardli :: James Reoch :: University of Adelaide

                  Media...
                  The behaviour of gels such as collagen is the result of complex interactions between mechanical and chemical forces. In this talk, I will outline the modelling approaches we are looking at in order to incorporate the influence of cell behaviour alongside chemical potentials, and the various circumstances which lead to gel swelling and contraction.
                  ⌊ n!/e ⌉
                  14:10 Tue 9 Sep, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. David Butler :: Maths Learning Centre

                  Media...
                  What is this formula? Why does it use those strangely mismatched brackets, and why does it use both factorial and the number e? What is it supposed to calculate? And why would someone love it so much that they put it on a t-shirt? In this seminar you will find out the answers to all of these questions, and also find out what derangements have to do with Taylor's theorem.
                  The FKMM invariant in low dimension
                  12:10 Fri 12 Sep, 2014 :: Ingkarni Wardli B20 :: Kiyonori Gomi (Shinshu University)

                  On a space with involutive action, the natural notion of vector bundles is equivariant vector bundles. But, there is an important variant called `Real' vector bundles in the sense of Atiyah, and, its cousin, `symplectic' or `Quaternionic' vector bundles in the sense of Dupont. The FKMM invariant is an invariant of `symplectic' vector bundles originally introduced by Furuta, Kametani, Matsue and Minami. The subject of my talk is recent development of this invariant in my joint work with Giuseppe De Nittis: The classifications of `symplectic' vector bundles in low dimension and the descriptions of some Z/2-invariants by using the FKMM invariant.
                  Translating solitons for mean curvature flow
                  12:10 Fri 19 Sep, 2014 :: Ingkarni Wardli B20 :: Julie Clutterbuck :: Monash University

                  Mean curvature flow gives a deformation of a submanifold in the direction of its mean curvature vector. Singularities may arise, and can be modelled by special solutions of the flow. I will describe the special solutions that move by only a translation under the flow, and give some explicit constructions of such surfaces. This is based on joint work with Oliver Schnuerer and Felix Schulze.
                  A Random Walk Through Discrete State Markov Chain Theory
                  12:10 Mon 22 Sep, 2014 :: B.19 Ingkarni Wardli :: James Walker :: University of Adelaide

                  Media...
                  This talk will go through the basics of Markov chain theory; including how to construct a continuous-time Markov chain (CTMC), how to adapt a Markov chain to include non-memoryless distributions, how to simulate CTMC's and some key results.
                  Inferring absolute population and recruitment of southern rock lobster using only catch and effort data
                  12:35 Mon 22 Sep, 2014 :: B.19 Ingkarni Wardli :: John Feenstra :: University of Adelaide

                  Media...
                  Abundance estimates from a data-limited version of catch survey analysis are compared to those from a novel one-parameter deterministic method. Bias of both methods is explored using simulation testing based on a more complex data-rich stock assessment population dynamics fishery operating model, exploring the impact of both varying levels of observation error in data as well as model process error. Recruitment was consistently better estimated than legal size population, the latter most sensitive to increasing observation errors. A hybrid of the data-limited methods is proposed as the most robust approach. A more statistically conventional error-in-variables approach may also be touched upon if enough time.
                  Spectral asymptotics on random Sierpinski gaskets
                  12:10 Fri 26 Sep, 2014 :: Ingkarni Wardli B20 :: Uta Freiberg :: Universitaet Stuttgart

                  Self similar fractals are often used in modeling porous media. Hence, defining a Laplacian and a Brownian motion on such sets describes transport through such materials. However, the assumption of strict self similarity could be too restricting. So, we present several models of random fractals which could be used instead. After recalling the classical approaches of random homogenous and recursive random fractals, we show how to interpolate between these two model classes with the help of so called V-variable fractals. This concept (developed by Barnsley, Hutchinson & Stenflo) allows the definition of new families of random fractals, hereby the parameter V describes the degree of `variability' of the realizations. We discuss how the degree of variability influences the geometric, analytic and stochastic properties of these sets. - These results have been obtained with Ben Hambly (University of Oxford) and John Hutchinson (ANU Canberra).
                  To Complex Analysis... and beyond!
                  12:10 Mon 29 Sep, 2014 :: B.19 Ingkarni Wardli :: Brett Chenoweth :: University of Adelaide

                  Media...
                  In the undergraduate complex analysis course students learn about complex valued functions on domains in C (the complex plane). Several interesting and surprising results come about from this study. In my talk I will introduce a more general setting where complex analysis can be done, namely Riemann surfaces (complex manifolds of dimension 1). I will then prove that all non-compact Riemann surfaces are Stein; which loosely speaking means that their function theory is similar to that of C.
                  A Hybrid Markov Model for Disease Dynamics
                  12:35 Mon 29 Sep, 2014 :: B.19 Ingkarni Wardli :: Nicolas Rebuli :: University of Adelaide

                  Media...
                  Modelling the spread of infectious diseases is fundamental to protecting ourselves from potentially devastating epidemics. Among other factors, two key indicators for the severity of an epidemic are the size of the epidemic and the time until the last infectious individual is removed. To estimate the distribution of the size and duration of an epidemic (within a realistic population) an epidemiologist will typically use Monte Carlo simulations of an appropriate Markov process. However, the number of states in the simplest Markov epidemic model, the SIR model, is quadratic in the population size and so Monte Carlo simulations are computationally expensive. In this talk I will discuss two methods for approximating the SIR Markov process and I will demonstrate the approximation error by comparing probability distributions and estimates of the distributions of the final size and duration of an SIR epidemic.
                  Exploration vs. Exploitation with Partially Observable Gaussian Autoregressive Arms
                  15:00 Mon 29 Sep, 2014 :: Engineering North N132 :: Julia Kuhn :: The University of Queensland & The University of Amsterdam

                  Media...
                  We consider a restless bandit problem with Gaussian autoregressive arms, where the state of an arm is only observed when it is played and the state-dependent reward is collected. Since arms are only partially observable, a good decision policy needs to account for the fact that information about the state of an arm becomes more and more obsolete while the arm is not being played. Thus, the decision maker faces a tradeoff between exploiting those arms that are believed to be currently the most rewarding (i.e. those with the largest conditional mean), and exploring arms with a high conditional variance. Moreover, one would like the decision policy to remain tractable despite the infinite state space and also in systems with many arms. A policy that gives some priority to exploration is the Whittle index policy, for which we establish structural properties. These motivate a parametric index policy that is computationally much simpler than the Whittle index but can still outperform the myopic policy. Furthermore, we examine the many-arm behavior of the system under the parametric policy, identifying equations describing its asymptotic dynamics. Based on these insights we provide a simple heuristic algorithm to evaluate the performance of index policies; the latter is used to optimize the parametric index.
                  Topology, geometry, and moduli spaces
                  12:10 Fri 10 Oct, 2014 :: Ingkarni Wardli B20 :: Nick Buchdahl :: University of Adelaide

                  In recent years, moduli spaces of one kind or another have been shown to be of great utility, this quite apart from their inherent interest. Many of their applications involve their topology, but as we all know, understanding of topological structures is often facilitated through the use of geometric methods, and some of these moduli spaces carry geometric structures that are considerable interest in their own right. In this talk, I will describe some of the background and the ideas in this general context, focusing on questions that I have been considering lately together with my colleague Georg Schumacher from Marburg in Germany, who was visiting us recently.
                  The Mathematics behind Simultaneous Localisation and Mapping
                  12:10 Mon 13 Oct, 2014 :: B.19 Ingkarni Wardli :: David Skene :: University of Adelaide

                  Media...
                  Simultaneous localisation and mapping (or SLAM) is a process where individual images of an environment are taken and compared against one another. This comparison allows a map of the environment and changes in the location the images were taken to be determined. This presentation discusses the relevance of SLAM in making a motorised platform autonomous, the process of a SLAM algorithm, and the all important mathematics that makes a SLAM algorithm work. The resulting algorithm is then tested against using a real world motorised platform.
                  Optimally Chosen Quadratic Forms for Partitioning Multivariate Data
                  13:10 Tue 14 Oct, 2014 :: Ingkarni Wardli 715 Conference Room :: Assoc. Prof. Inge Koch :: School of Mathematical Sciences

                  Media...
                  Quadratic forms are commonly used in linear algebra. For d-dimensional vectors they have a matrix representation, Q(x) = x'Ax, for some symmetric matrix A. In statistics quadratic forms are defined for d-dimensional random vectors, and one of the best-known quadratic forms is the Mahalanobis distance of two random vectors. In this talk we want to partition a quadratic form Q(X) = X'MX, where X is a random vector, and M a symmetric matrix, that is, we want to find a d-dimensional random vector W such that Q(X) = W'W. This problem has many solutions. We are interested in a solution or partition W of X such that pairs of corresponding variables (X_j, W_j) are highly correlated and such that W is simpler than the given X. We will consider some natural candidates for W which turn out to be suboptimal in the sense of the above constraints, and we will then exhibit the optimal solution. Solutions of this type are useful in the well-known T-square statistic. We will see in examples what these solutions look like.
                  Compact pseudo-Riemannian solvmanifolds
                  12:10 Fri 17 Oct, 2014 :: Ingkarni Wardli B20 :: Wolfgang Globke :: University of Adelaide

                  A compact solvmanifold M is a quotient of a solvable Lie group G by a cocompact closed subgroup H. A pseudo-Riemannian metric on M is induced by an H-invariant symmetric 2-tensor on G. In this talk I will describe some foundations and results of my ongoing work with Oliver Baues on the nature of this 2-tensor and what it can imply for the subgroup H.
                  Geometric singular perturbation theory and canard theory to study travelling waves in: 1) a model for tumor invasion; and 2) a model for wound healing angiogenesis.
                  15:10 Fri 17 Oct, 2014 :: EM 218 Engineering & Mathematics Building :: Dr Petrus (Peter) van Heijster :: QUT

                  In this talk, I will present results on the existence of smooth and shock-like travelling wave solutions for two advection-reaction-diffusion models. The first model describes malignant tumour (i.e. skin cancer) invasion, while the second one is a model for wound healing angiogenesis. Numerical solutions indicate that both smooth and shock-fronted travelling wave solutions exist for these two models. I will verify the existence of both type of these solutions using techniques from geometric singular perturbation theory and canard theory. Moreover, I will provide numerical results on the stability of the waves and the actual observed wave speeds. This is joint work with K. Harley, G. Pettet, R. Marangell and M. Wechselberger.
                  The Serre-Grothendieck theorem by geometric means
                  12:10 Fri 24 Oct, 2014 :: Ingkarni Wardli B20 :: David Roberts :: University of Adelaide

                  The Serre-Grothendieck theorem implies that every torsion integral 3rd cohomology class on a finite CW-complex is the invariant of some projective bundle. It was originally proved in a letter by Serre, used homotopical methods, most notably a Postnikov decomposition of a certain classifying space with divisible homotopy groups. In this talk I will outline, using work of the algebraic geometer Offer Gabber, a proof for compact smooth manifolds using geometric means and a little K-theory.
                  What happens when you eat pizza?: the science and mathematics behind digestion
                  14:10 Mon 27 Oct, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. Sarthok Sircar :: School of Mathematical Sciences

                  Media...
                  Our stomach is an inferno with acidic juices that are strong enough to bore a hole through our hands. Ever wondered why the stomach does not digest itself ? The answer lies in an interesting defence mechanism along the stomach lining which also aids in digestion of food. In this talk I will present this mechanism and briefly present the physics, chemistry, biology and (off course !) the mathematics to describe this system. The talk may also answer your queries regarding heart-burn especially when you eat a lot of free-food !!
                  Happiness and social information flow: Computational social science through data.
                  15:10 Fri 7 Nov, 2014 :: EM G06 (Engineering & Maths Bldg) :: Dr Lewis Mitchell :: University of Adelaide

                  The recent explosion in big data coming from online social networks has led to an increasing interest in bringing quantitative methods to bear on questions in social science. A recent high-profile example is the study of emotional contagion, which has led to significant challenges and controversy. This talk will focus on two issues related to emotional contagion, namely remote-sensing of population-level wellbeing and the problem of information flow across a social network. We discuss some of the challenges in working with massive online data sets, and present a simple tool for measuring large-scale happiness from such data. By combining over 10 million geolocated messages collected from Twitter with traditional census data we uncover geographies of happiness at the scale of states and cities, and discuss how these patterns may be related to traditional wellbeing measures and public health outcomes. Using tools from information theory we also study information flow between individuals and how this may relate to the concept of predictability for human behaviour.
                  Happiness and social information flow: Computational social science through data.
                  15:10 Fri 7 Nov, 2014 :: EM G06 (Engineering & Maths Bldg) :: Dr Lewis Mitchell :: University of Adelaide

                  The recent explosion in big data coming from online social networks has led to an increasing interest in bringing quantitative methods to bear on questions in social science. A recent high-profile example is the study of emotional contagion, which has led to significant challenges and controversy. This talk will focus on two issues related to emotional contagion, namely remote-sensing of population-level wellbeing and the problem of information flow across a social network. We discuss some of the challenges in working with massive online data sets, and present a simple tool for measuring large-scale happiness from such data. By combining over 10 million geolocated messages collected from Twitter with traditional census data we uncover geographies of happiness at the scale of states and cities, and discuss how these patterns may be related to traditional wellbeing measures and public health outcomes. Using tools from information theory we also study information flow between individuals and how this may relate to the concept of predictability for human behaviour.
                  Extending holomorphic maps from Stein manifolds into affine toric varieties
                  12:10 Fri 14 Nov, 2014 :: Ingkarni Wardli B20 :: Richard Larkang :: University of Adelaide

                  One way of defining so-called Oka manifolds is by saying that they satisfy the following interpolation property (IP): Y satisfies the IP if any holomorphic map from a closed submanifold S of a Stein manifold X into Y which has a continuous extension to X also has a holomorphic extension. An ostensibly weaker property is the convex interpolation property (CIP), where S is assumed to be a contractible submanifold of X = C^n. By a deep theorem of Forstneric, these (and several other) properties are in fact equivalent. I will discuss a joint work with Finnur Larusson, where we consider the interpolation property when the target Y is a singular affine toric variety. We show that all affine toric varieties satisfy an interpolation property stronger than CIP, but that only in very special situations do they satisfy the full IP.
                  Modelling segregation distortion in multi-parent crosses
                  15:00 Mon 17 Nov, 2014 :: 5.57 Ingkarni Wardli :: Rohan Shah (joint work with B. Emma Huang and Colin R. Cavanagh) :: The University of Queensland

                  Construction of high-density genetic maps has been made feasible by low-cost high-throughput genotyping technology; however, the process is still complicated by biological, statistical and computational issues. A major challenge is the presence of segregation distortion, which can be caused by selection, difference in fitness, or suppression of recombination due to introgressed segments from other species. Alien introgressions are common in major crop species, where they have often been used to introduce beneficial genes from wild relatives. Segregation distortion causes problems at many stages of the map construction process, including assignment to linkage groups and estimation of recombination fractions. This can result in incorrect ordering and estimation of map distances. While discarding markers will improve the resulting map, it may result in the loss of genomic regions under selection or containing beneficial genes (in the case of introgression). To correct for segregation distortion we model it explicitly in the estimation of recombination fractions. Previously proposed methods introduce additional parameters to model the distortion, with a corresponding increase in computing requirements. This poses difficulties for large, densely genotyped experimental populations. We propose a method imposing minimal additional computational burden which is suitable for high-density map construction in large multi-parent crosses. We demonstrate its use modelling the known Sr36 introgression in wheat for an eight-parent complex cross.
                  Topology Tomography with Spatial Dependencies
                  15:00 Tue 25 Nov, 2014 :: Engineering North N132 :: Darryl Veitch :: The University of Melbourne

                  Media...
                  There has been quite a lot of tomography inference work on measurement networks with a tree topology. Here observations are made, at the leaves of the tree, of `probes' sent down from the root and copied at each branch point. Inference can be performed based on loss or delay information carried by probes, and used in order to recover loss parameters, delay parameters, or the topology, of the tree. In all of these a strong assumption of spatial independence between links in the tree has been made in prior work. I will describe recent work on topology inference, based on loss measurement, which breaks that assumption. In particular I will introduce a new model class for loss with non trivial spatial dependence, the `Jump Independent Models', which are well motivated, and prove that within this class the topology is identifiable.
                  Fractal substitution tilings
                  11:10 Wed 17 Dec, 2014 :: Ingkarni Wardli B17 :: Mike Whittaker :: University of Wollongong

                  Starting with a substitution tiling, I will demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles typically have fractal boundary. As an application, we construct an odd spectral triple on a C*-algebra associated with an aperiodic substitution tiling. No knowledge of tilings, C*-algebras, or spectral triples will be assumed. This is joint work with Natalie Frank, Michael Mampusti, and Sam Webster.
                  Factorisations of Distributive Laws
                  12:10 Fri 19 Dec, 2014 :: Ingkarni Wardli B20 :: Paul Slevin :: University of Glasgow

                  Recently, distributive laws have been used by Boehm and Stefan to construct new examples of duplicial (paracyclic) objects, and hence cyclic homology theories. The paradigmatic example of such a theory is the cyclic homology HC(A) of an associative algebra A. It was observed by Kustermans, Murphy, and Tuset that the functor HC can be twisted by automorphisms of A. It turns out that this twisting procedure can be applied to any duplicial object defined by a distributive law. I will begin by defining duplicial objects and cyclic homology, as well as discussing some categorical concepts, then describe the construction of Boehm and Stefan. I will then define the category of factorisations of a distributive law and explain how this acts on their construction, and give some examples, making explicit how the action of this category generalises the twisting of an associative algebra.
                  Nonlinear analysis over infinite dimensional spaces and its applications
                  12:10 Fri 6 Feb, 2015 :: Ingkarni Wardli B20 :: Tsuyoshi Kato :: Kyoto University

                  In this talk we develop moduli theory of holomorphic curves over infinite dimensional manifolds consisted by sequences of almost Kaehler manifolds. Under the assumption of high symmetry, we verify that many mechanisms of the standard moduli theory over closed symplectic manifolds also work over these infinite dimensional spaces. As an application, we study deformation theory of discrete groups acting on trees. There is a canonical way, up to conjugacy to embed such groups into the automorphism group over the infinite projective space. We verify that for some class of Hamiltonian functions, the deformed groups must be always asymptotically infinite.
                  Boundary behaviour of Hitchin and hypo flows with left-invariant initial data
                  12:10 Fri 27 Feb, 2015 :: Ingkarni Wardli B20 :: Vicente Cortes :: University of Hamburg

                  Hitchin and hypo flows constitute a system of first order pdes for the construction of Ricci-flat Riemannian mertrics of special holonomy in dimensions 6, 7 and 8. Assuming that the initial geometric structure is left-invariant, we study whether the resulting Ricci-flat manifolds can be extended in a natural way to complete Ricci-flat manifolds. This talk is based on joint work with Florin Belgun, Marco Freibert and Oliver Goertsches, see arXiv:1405.1866 (math.DG).
                  Predicting pressure drops in pipelines due to pump trip events
                  12:10 Mon 2 Mar, 2015 :: Napier LG29 :: David Arnold :: University of Adelaide

                  Media...
                  Sunwater is a Queensland company that designs, builds and manages large-scale water infrastructure such as dams, weirs and pipelines. In this talk, I will discuss one of the aspects that is crucial in the design stage of long pipelines, the pipelines ability to withstand large pressure disturbances caused by pump trip events. A pump trip is a sudden, unplanned shutdown of a pump, which causes potentially destructive pressure waves to propagate through the pipe network. Accurate simulation of such events is time consuming and costly, so rules of thumb and intuition are used during initial planning and design of a pipeline project. I will discuss some simple mathematical models for pump trip events, show some results, and discuss how they could be used in the initial design process.
                  Tannaka duality for stacks
                  12:10 Fri 6 Mar, 2015 :: Ingkarni Wardli B20 :: Jack Hall :: Australian National University

                  Traditionally, Tannaka duality is used to reconstruct a group from its representations. I will describe a reformulation of this duality for stacks, which is due to Lurie, and briefly touch on some applications.
                  On the analyticity of CR-diffeomorphisms
                  12:10 Fri 13 Mar, 2015 :: Engineering North N132 :: Ilya Kossivskiy :: University of Vienna

                  One of the fundamental objects in several complex variables is CR-mappings. CR-mappings naturally occur in complex analysis as boundary values of mappings between domains, and as restrictions of holomorphic mappings onto real submanifolds. It was already observed by Cartan that smooth CR-diffeomorphisms between CR-submanifolds in C^N tend to be very regular, i.e., they are restrictions of holomorphic maps. However, in general smooth CR-mappings form a more restrictive class of mappings. Thus, since the inception of CR-geometry, the following general question has been of fundamental importance for the field: Are CR-equivalent real-analytic CR-structures also equivalent holomorphically? In joint work with Lamel, we answer this question in the negative, in any positive CR-dimension and CR-codimension. Our construction is based on a recent dynamical technique in CR-geometry, developed in my earlier work with Shafikov.
                  Cricket and Maths
                  12:10 Mon 16 Mar, 2015 :: Napier LG29 :: Peter Ballard :: University of Adelaide

                  Media...
                  Each game of international cricket has a scorecard. You don't need to know much maths to go through these scorecards and extract simple information, such as batting and bowling averages. However there is also the opportunity to use some more advanced maths. I will be using a bit of optimisation, probability and statistics to try to answer the questions: Which was the most dominant team ever? What scores are most likely? And are some players unlucky?
                  Singular Pfaffian systems in dimension 6
                  12:10 Fri 20 Mar, 2015 :: Napier 144 :: Pawel Nurowski :: Center for Theoretical Physics, Polish Academy of Sciences

                  We consider a pair of rank 3 distributions in dimension 6 with some remarkable properties. They define an analog of the celebrated nearly-Kahler structure on the 6 sphere, with the exceptional simple Lie group G2 as a group of symmetries. In our case the metric associated with the structure is pseudo-Riemannian, of split signature. The 6 manifold has a 5-dimensional boundary with interesting induced geometry. This structure on the boundary has no analog in the Riemannian case.
                  The Mathematics behind the Ingkarni Wardli Quincunx
                  12:10 Mon 23 Mar, 2015 :: Napier LG29 :: Andrew Pfeiffer :: University of Adelaide

                  The quincunx is a fun machine on the ground floor of Ingkarni Wardli. Hopefully you've had a chance to play with it at some point. Perhaps you were waiting for your coffee, or just procrastinating. However, you may have no idea what I'm talking about. If so, read on. To operate the quincunx, you turn a handle and push balls into a sea of needles. The needles then pseudo-randomly direct each ball into one of eight bins. On the quincunx, there is a page of instructions that makes some mathematical claims. For example, it claims that the balls should look roughly like a normal distribution. In this talk, I will discuss some of the mathematics behind the quincunx. I will also seek to make the claims of the quincunx more precise.
                  Higher homogeneous bundles
                  12:10 Fri 27 Mar, 2015 :: Napier 144 :: David Roberts :: University of Adelaide

                  Historically, homogeneous bundles were among the first examples of principal bundles. This talk will cover a general method that gives rise to many homogeneous principal 2-bundles.
                  Dynamic programming and optimal scoring rates in cricket
                  12:10 Mon 30 Mar, 2015 :: Napier LG29 :: Mingmei Teo :: University of Adelaide

                  Media...
                  With the cricket world cup having reached it's exciting conclusion and many world cup batting records being re-written at this world cup, we look back to the year 1987 where batting occurred at a more sedate pace and totals of 300+ were a rarity. In this talk, I'll discuss how dynamic programming has been applied to one-day cricket to determine optimal scoring rates and I'll also attempt to give a brief introduction into what is dynamic programming and a common method used to solve dynamic programming problems.
                  How do we quantify the filamentous growth in yeast colony?
                  12:10 Mon 30 Mar, 2015 :: Ingkarni Wardli 715 Conference Room :: Dr. Benjamin Binder :: School of Mathematical Sciences

                  Media...
                  In this talk we will develop a systematic method to measure the spatial patterning of colony morphology. A hybrid modelling approach of the growth process will also be discussed.
                  Topological matter and its K-theory
                  11:10 Thu 2 Apr, 2015 :: Ingkarni Wardli B18 :: Guo Chuan Thiang :: University of Adelaide

                  The notion of fundamental particles, as well as phases of condensed matter, evolves as new mathematical tools become available to the physicist. I will explain how K-theory provides a powerful language for describing quantum mechanical symmetries, homotopies of their realisations, and topological insulators. Real K-theory is crucial in this framework, and its rich structure is still being explored both physically and mathematically.
                  Higher rank discrete Nahm equations for SU(N) monopoles in hyperbolic space
                  11:10 Wed 8 Apr, 2015 :: Engineering & Maths EM213 :: Joseph Chan :: University of Melbourne

                  Braam and Austin in 1990, proved that SU(2) magnetic monopoles in hyperbolic space H^3 are the same as solutions of the discrete Nahm equations. I apply equivariant K-theory to the ADHM construction of instantons/holomorphic bundles to extend the Braam-Austin result from SU(2) to SU(N). During its evolution, the matrices of the higher rank discrete Nahm equations jump in dimensions and this behaviour has not been observed in discrete evolution equations before. A secondary result is that the monopole field at the boundary of H^3 determines the monopole.
                  Groups acting on trees
                  12:10 Fri 10 Apr, 2015 :: Napier 144 :: Anitha Thillaisundaram :: Heinrich Heine University of Duesseldorf

                  From a geometric point of view, branch groups are groups acting spherically transitively on a spherically homogeneous rooted tree. The applications of branch groups reach out to analysis, geometry, combinatorics, and probability. The early construction of branch groups were the Grigorchuk group and the Gupta-Sidki p-groups. Among its many claims to fame, the Grigorchuk group was the first example of a group of intermediate growth (i.e. neither polynomial nor exponential). Here we consider a generalisation of the family of Grigorchuk-Gupta-Sidki groups, and we examine the restricted occurrence of their maximal subgroups.
                  IGA Workshop on Symmetries and Spinors: Interactions Between Geometry and Physics
                  09:30 Mon 13 Apr, 2015 :: Conference Room 7.15 on Level 7 of the Ingkarni Wardli building :: J. Figueroa-O'Farrill (University of Edinburgh), M. Zabzine (Uppsala University), et al

                  Media...
                  The interplay between physics and geometry has lead to stunning advances and enriched the internal structure of each field. This is vividly exemplified in the theory of supergravity, which is a supersymmetric extension of Einstein's relativity theory to the small scales governed by the laws of quantum physics. Sophisticated mathematics is being employed for finding solutions to the generalised Einstein equations and in return, they provide a rich source for new exotic geometries. This workshop brings together world-leading scientists from both, geometry and mathematical physics, as well as young researchers and students, to meet and learn about each others work.
                  Minimal Surfaces and their Application to Soap Films
                  12:10 Mon 13 Apr, 2015 :: Napier LG29 :: Jonathon Pantelis :: University of Adelaide

                  Media...
                  We all have some idea about what a surface is. We can classify surfaces depending on a range of properties or characteristics. Discussed in this seminar are Minimal Surfaces, a particular class of surface. We will find out what it means for a surface to be minimal and take a look at what these things look like. We will also see how to create them, and also how they relate to soap films.
                  A Model to Represent the Propagation of a Wave Over a Bovine Oocyte
                  12:10 Mon 20 Apr, 2015 :: Napier LG29 :: Amelia Thomas :: University of Adelaide

                  Media...
                  When the fertilization of egg cells is studied experimentally, generally the cumulus cells surrounding the egg are removed, for easier visualization of the egg itself. However, interesting phenomena are observed in the cumulus cells if they are left intact. In this talk I will present some models that can be used to describe the travelling wavelike movement of the cumulus cells away from the egg cell which occurs post-fertilisation.
                  Group Meeting
                  15:10 Fri 24 Apr, 2015 :: N218 Engineering North :: Dr Ben Binder :: University of Adelaide

                  Talk (Dr Ben Binder): How do we quantify the filamentous growth in a yeast colony? Abstract: In this talk we will develop a systematic method to measure the spatial patterning of yeast colony morphology. The methods are applicable to other physical systems with circular spatial domains, for example, batch mixing fluid devices. A hybrid modelling approach of the yeast growth process will also be discussed. After the seminar, Ben will start a group discussion by sharing some information and experiences on attracting honours/PhD students to the group.
                  Did the Legend of Zelda unfold in our Solar System?
                  12:10 Mon 27 Apr, 2015 :: Napier LG29 :: Adam Rohrlach :: University of Adelaide

                  Media...
                  Well, obviously not. We can see the other planets, and they're not terribly conducive to Elven based life. Still, I aim to exhaustively explore the topic, all the while avoiding conventional logic and reasoning. Clearly, one could roll out any number of 'telescope' based proofs, and 'video game characters aren't really real, even after a million wishes' arguments, but I want to tackle this hotly debated issue using physics (the ugly cousin of actual mathematics). Armed with a remedial understanding of year 12 physics, from the acclaimed 2000 South Australian syllabus, I can think of no one better qualified, or possibly willing, to give this talk.
                  Identifying the Missing Aspects of the ANSI/ISA Best Practices for Security Policy
                  12:10 Mon 27 Apr, 2015 :: Napier LG29 :: Dinesha Ranathunga :: University of Adelaide

                  Media...
                  Firewall configuration is a critical activity but it is often conducted manually, which often result in inaccurate, unreliable configurations that leave networks vulnerable to cyber attack. Firewall misconfigurations can have severe consequences in the context of critical infrastructure plants. Internal networks within these plants interconnect valuable industrial control equipment which often control safety critical processes. Security breaches here can result in disruption of critical services, cause severe environmental damage and at worse, loss of human lives. Automation can make designing firewall configurations less tedious and their deployment more reliable and increasingly cost-effective. In this talk I will discuss of our efforts to arrive at a high-level security policy description based on the ANSI/ISA standard, suitable for automation. In doing do, we identify the missing aspects of the existing best practices and propose solutions. We then apply the corrected best practice specifications to real SCADA firewall configurations and evaluate their usefulness in describing SCADA policies accurately.
                  Spherical T-duality: the non-principal case
                  12:10 Fri 1 May, 2015 :: Napier 144 :: Mathai Varghese :: University of Adelaide

                  Spherical T-duality is related to M-theory and was introduced in recent joint work with Bouwknegt and Evslin. I will begin by briefly reviewing the case of principal SU(2)-bundles with degree 7 flux, and then focus on the non-principal case for most of the talk, ending with the relation to SUGRA/M-theory.
                  A Collision Algorithm for Sea Ice
                  12:10 Mon 4 May, 2015 :: Napier LG29 :: Lucas Yiew :: University of Adelaide

                  Media...
                  The wave-induced collisions between sea ice are highly complex and nonlinear, and involves a multitude of subprocesses. Several collision models do exist, however, to date, none of these models have been successfully integrated into sea-ice forecasting models. A key component of a collision model is the development of an appropriate collision algorithm. In this seminar I will present a time-stepping, event-driven algorithm to detect, analyse and implement the pre- and post-collision processes.
                  Indefinite spectral triples and foliations of spacetime
                  12:10 Fri 8 May, 2015 :: Napier 144 :: Koen van den Dungen :: Australian National University

                  Motivated by Dirac operators on Lorentzian manifolds, we propose a new framework to deal with non-symmetric and non-elliptic operators in noncommutative geometry. We provide a definition for indefinite spectral triples, which correspond bijectively with certain pairs of spectral triples. Next, we will show how a special case of indefinite spectral triples can be constructed from a family of spectral triples. In particular, this construction provides a convenient setting to study the Dirac operator on a spacetime with a foliation by spacelike hypersurfaces. This talk is based on joint work with Adam Rennie (arXiv:1503.06916).
                  Medical Decision Making
                  12:10 Mon 11 May, 2015 :: Napier LG29 :: Eka Baker :: University of Adelaide

                  Media...
                  Practicing physicians make treatment decisions based on clinical trial data every day. This data is based on trials primarily conducted on healthy volunteers, or on those with only the disease in question. In reality, patients do have existing conditions that can affect the benefits and risks associated with receiving these treatments. In this talk, I will explain how we modified an already existing Markov model to show the progression of treatment of a single condition over time. I will then explain how we adapted this to a different condition, and then created a combined model, which demonstrated how both diseases and treatments progressed on the same patient over their lifetime.
                  The twistor equation on Lorentzian Spin^c manifolds
                  12:10 Fri 15 May, 2015 :: Napier 144 :: Andree Lischewski :: University of Adelaide

                  In this talk I consider a conformally covariant spinor field equation, called the twistor equation, which can be formulated on any Lorentzian Spin^c manifold. Its solutions have become of importance in the study of supersymmetric field theories in recent years and were named "charged conformal Killing spinors". After a short review of conformal Spin^c geometry in Lorentzian signature, I will briefly discuss the emergence of charged conformal Killing spinors in supergravity. I will then focus on special geometric structures related to the twistor equation and use charged conformal Killing spinors in order to establish a link between conformal and CR geometry.
                  An Engineer-Mathematician Duality Approach to Finite Element Methods
                  12:10 Mon 18 May, 2015 :: Napier LG29 :: Jordan Belperio :: University of Adelaide

                  Media...
                  The finite element method has been a prominently used numerical technique for engineers solving solid mechanics, electro-magnetic and heat transfer problems for over 30 years. More recently the finite element method has been used to solve fluid mechanics problems, a field where finite difference methods are more commonly used. In this talk, I will introduce the basic mathematics behind the finite element method, the similarity between the finite element method and finite difference method and comparing how engineers and mathematicians use finite element methods. I will then demonstrate two solutions to the wave equation using the finite element method.
                  Big things are weird
                  12:10 Mon 25 May, 2015 :: Napier LG29 :: Luke Keating-Hughes :: University of Adelaide

                  Media...
                  The pyramids of Giza, the depths of the Mariana trench, the massive Einstein Cross Quasar; all of these things are big and weird. Big weird things aren't just apparent in the physical world though, they appear in mathematics too! In this talk I will try to motivate a mathematical big thing and then show that it is weird. In particular, we will introduce the necessary topology and homotopy theory in order to show that although all finite dimensional spheres are (almost canonically) non-contractible spaces - an infinite dimensional sphere IS contractible! This result's significance will then be explained in the context of Kuiper's Theorem if time permits.
                  People smugglers and statistics
                  12:10 Mon 25 May, 2015 :: Ingkarni Wardli 715 Conference Room :: Prof. Patty Solomon :: School of Mathematical Sciences

                  Media...
                  In 2012 the Commonwealth Chief Scientist asked for my advice on the statistics being used in people smuggling prosecutions. Many defendants come from poor fishing villages in Indonesia, where births are not routinely recorded and the age of the defendant is not known. However mandatory jail sentences apply in Australia for individuals convicted of people smuggling which do not apply to children less than 18 years old - so assessing the age of each defendant is very important. Following an Australian Human Rights Commission inquiry into the treatment of individuals suspected of people smuggling, the Attorney-General's department sought advice from the Chief Scientist, which is where I come in. I'll present the methods used by the prosecution and defence, which are both wrong, and introduce the prosecutor's fallacy.
                  Monodromy of the Hitchin system and components of representation varieties
                  12:10 Fri 29 May, 2015 :: Napier 144 :: David Baraglia :: University of Adelaide

                  Representations of the fundamental group of a compact Riemann surface into a reductive Lie group form a moduli space, called a representation variety. An outstanding problem in topology is to determine the number of components of these varieties. Through a deep result known as non-abelian Hodge theory, representation varieties are homeomorphic to moduli spaces of certain holomorphic objects called Higgs bundles. In this talk I will describe recent joint work with L. Schaposnik computing the monodromy of the Hitchin fibration for Higgs bundle moduli spaces. Our results give a new unified proof of the number of components of several representation varieties.
                  Group Meeting
                  15:10 Fri 29 May, 2015 :: EM 213 :: Dr Judy Bunder :: University of Adelaide

                  Talk : Patch dynamics for efficient exascale simulations Abstract Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must be developed which minimise the transfer of data. Patch dynamics is a computational macroscale modelling scheme which provides a coarse macroscale solution of a problem defined on a fine microscale by dividing the domain into many nonoverlapping, coupled patches. Patch dynamics is readily adaptable to massive parallelisation as each processor core can evaluate the dynamics on one, or a few, patches. However, patch coupling conditions interpolate across the unevaluated parts of the domain between patches and require almost continuous data transfer. We propose a modified patch dynamics scheme which minimises data transfer by only reevaluating the patch coupling conditions at `mesoscale' time scales which are significantly larger than the microscale time of the microscale problem. We analyse and quantify the error arising from patch dynamics with mesoscale temporal coupling.
                  Hillary Clinton was liberal. Hillary Clinton is liberal.
                  12:10 Mon 1 Jun, 2015 :: Napier LG29 :: Brock Hermans :: University of Adelaide

                  Media...
                  Didn't enjoy last weeks talk? Thought it was a bit too complicated in some areas? Too much pure maths? Well even if your answer is no you should still come along to mine. I will be talking about the most uniting, agreeable area of our lives; politics. By using rudimentary statistics I'll be looking at three things. One, a method for poll aggression as a tool to predict elections (using Bayesian statistics). Two, why the polls were so wrong in the U.K. election recently. And three, what claims (if any) can we make about the current 2016 U.S. presidential race. In one of the most exciting talks of the year so far, I'll be looking at 'Shy Torries', 'Freedom loving-libertarians' and answering the question "is Hilary Clinton the most liberal (that means left wing in America) candidate in the race?".
                  Some approaches toward a stronger Jacobian conjecture
                  12:10 Fri 5 Jun, 2015 :: Napier 144 :: Tuyen Truong :: University of Adelaide

                  The Jacobian conjecture states that if a polynomial self-map of C^n has invertible Jacobian, then the map has a polynomial inverse. Is it true, false or simply undecidable? In this talk I will propose a conjecture concerning general square matrices with complex coefficients, whose validity implies the Jacobian conjecture. The conjecture is checked in various cases, in particular it is true for generic matrices. Also, a heuristic argument is provided explaining why the conjecture (and thus, also the Jacobian conjecture) should be true.
                  Instantons and Geometric Representation Theory
                  12:10 Thu 23 Jul, 2015 :: Engineering and Maths EM212 :: Professor Richard Szabo :: Heriot-Watt University

                  We give an overview of the various approaches to studying supersymmetric quiver gauge theories on ALE spaces, and their conjectural connections to two-dimensional conformal field theory via AGT-type dualities. From a mathematical perspective, this is formulated as a relationship between the equivariant cohomology of certain moduli spaces of sheaves on stacks and the representation theory of infinite-dimensional Lie algebras. We introduce an orbifold compactification of the minimal resolution of the A-type toric singularity in four dimensions, and then construct a moduli space of framed sheaves which is conjecturally isomorphic to a Nakajima quiver variety. We apply this construction to derive relations between the equivariant cohomology of these moduli spaces and the representation theory of the affine Lie algebra of type A.
                  Dirac operators and Hamiltonian loop group action
                  12:10 Fri 24 Jul, 2015 :: Engineering and Maths EM212 :: Yanli Song :: University of Toronto

                  A definition to the geometric quantization for compact Hamiltonian G-spaces is given by Bott, defined as the index of the Spinc-Dirac operator on the manifold. In this talk, I will explain how to generalize this idea to the Hamiltonian LG-spaces. Instead of quantizing infinite-dimensional manifolds directly, we use its equivalent finite-dimensional model, the quasi-Hamiltonian G-spaces. By constructing twisted spinor bundle and twisted pre-quantum bundle on the quasi-Hamiltonian G-space, we define a Dirac operator whose index are given by positive energy representation of loop groups. A key role in the construction will be played by the algebraic cubic Dirac operator for loop algebra. If time permitted, I will also explain how to prove the quantization commutes with reduction theorem for Hamiltonian LG-spaces under this framework.
                  Workshop on Geometric Quantisation
                  10:10 Mon 27 Jul, 2015 :: Level 7 conference room Ingkarni Wardli :: Michele Vergne, Weiping Zhang, Eckhard Meinrenken, Nigel Higson and many others

                  Media...
                  Geometric quantisation has been an increasingly active area since before the 1980s, with links to physics, symplectic geometry, representation theory, index theory, and differential geometry and geometric analysis in general. In addition to its relevance as a field on its own, it acts as a focal point for the interaction between all of these areas, which has yielded far-reaching and powerful results. This workshop features a large number of international speakers, who are all well-known for their work in (differential) geometry, representation theory and/or geometric analysis. This is a great opportunity for anyone interested in these areas to meet and learn from some of the top mathematicians in the world. Students are especially welcome. Registration is free.
                  Quantising proper actions on Spin-c manifolds
                  11:00 Fri 31 Jul, 2015 :: Ingkarni Wardli Level 7 Room 7.15 :: Peter Hochs :: The University of Adelaide

                  Media...
                  For a proper action by a Lie group on a Spin-c manifold (both of which may be noncompact), we study an index of deformations of the Spin-c Dirac operator, acting on the space of spinors invariant under the group action. When applied to spinors that are square integrable transversally to orbits in a suitable sense, the kernel of this operator turns out to be finite-dimensional, under certain hypotheses of the deformation. This also allows one to show that the index has the quantisation commutes with reduction property (as proved by Meinrenken in the compact symplectic case, and by Paradan-Vergne in the compact Spin-c case), for sufficiently large powers of the determinant line bundle. Furthermore, this result extends to Spin-c Dirac operators twisted by vector bundles. A key ingredient of the arguments is the use of a family of inner products on the Lie algebra, depending on a point in the manifold. This is joint work with Mathai Varghese.
                  Science in sport: Mathematics, player tracking and machine learning
                  12:10 Mon 3 Aug, 2015 :: Benham Labs G10 :: Lachlan Bubb :: University of Adelaide

                  Media...
                  Are elite athletes really getting that much bigger and faster? Probably not. So how are we getting better at sport? Probably smart people. How? Show up and you'll probably find out.
                  Mathematical Modeling and Analysis of Active Suspensions
                  14:10 Mon 3 Aug, 2015 :: Napier 209 :: Professor Michael Shelley :: Courant Institute of Mathematical Sciences, New York University

                  Complex fluids that have a 'bio-active' microstructure, like suspensions of swimming bacteria or assemblies of immersed biopolymers and motor-proteins, are important examples of so-called active matter. These internally driven fluids can have strange mechanical properties, and show persistent activity-driven flows and self-organization. I will show how first-principles PDE models are derived through reciprocal coupling of the 'active stresses' generated by collective microscopic activity to the fluid's macroscopic flows. These PDEs have an interesting analytic structures and dynamics that agree qualitatively with experimental observations: they predict the transitions to flow instability and persistent mixing observed in bacterial suspensions, and for microtubule assemblies show the generation, propagation, and annihilation of disclination defects. I'll discuss how these models might be used to study yet more complex biophysical systems.
                  Gromov's method of convex integration and applications to minimal surfaces
                  12:10 Fri 7 Aug, 2015 :: Ingkarni Wardli B17 :: Finnur Larusson :: The University of Adelaide

                  Media...
                  We start by considering an applied problem. You are interested in buying a used car. The price is tempting, but the car has a curious defect, so it is not clear whether you can even take it for a test drive. This problem illustrates the key idea of Gromov's method of convex integration. We introduce the method and some of its many applications, including new applications in the theory of minimal surfaces, and end with a sketch of ongoing joint work with Franc Forstneric.
                  In vitro models of colorectal cancer: why and how?
                  15:10 Fri 7 Aug, 2015 :: B19 Ingkarni Wardli :: Dr Tamsin Lannagan :: Gastrointestinal Cancer Biology Group, University of Adelaide / SAHMRI

                  1 in 20 Australians will develop colorectal cancer (CRC) and it is the second most common cause of cancer death. Similar to many other cancer types, it is the metastases rather than the primary tumour that are lethal, and prognosis is defined by “how far” the tumour has spread at time of diagnosis. Modelling in vivo behavior through rapid and relatively inexpensive in vitro assays would help better target therapies as well as help develop new treatments. One such new in vitro tool is the culture of 3D organoids. Organoids are a biologically stable means of growing, storing and testing treatments against bowel cancer. To this end, we have just set up a human colorectal organoid bank across Australia. This consortium will help us to relate in vitro growth patterns to in vivo behaviour and ultimately in the selection of patients for personalized therapies. Organoid growth, however, is complex. There appears to be variable growth rates and growth patterns. Together with members of the ECMS we recently gained funding to better quantify and model spatial structures in these colorectal organoids. This partnership will aim to directly apply the expertise within the ECMS to patient care.
                  A relaxed introduction to resampling-based multiple testing
                  12:10 Mon 10 Aug, 2015 :: Benham Labs G10 :: Ngoc Vo :: University of Adelaide

                  Media...
                  P-values and false positives are two phrases that you commonly see thrown around in scientific literature. More often than not, experimenters and analysts are required to quote p-values as a measure of statistical significance — how strongly does your evidence support your hypothesis? But what happens when this "strong evidence" is just a coincidence? What happens if you have lots of theses hypotheses — up to tens of thousands — to test all at the same time and most of your significant findings end up being just "coincidences"?
                  Modelling terrorism risk - can we predict future trends?
                  12:10 Mon 10 Aug, 2015 :: Benham Labs G10 :: Stephen Crotty :: University of Adelaide

                  Media...
                  As we are all aware, the incidence of terrorism is increasing in the world today. This is confirmed when viewing terrorism events since 1970 as a time series. Can we model this increasing trend and use it to predict terrorism events in the future? Probably not, but we'll give it a go anyway.
                  Bilinear L^p estimates for quasimodes
                  12:10 Fri 14 Aug, 2015 :: Ingkarni Wardli B17 :: Melissa Tacy :: The University of Adelaide

                  Media...
                  Understanding the growth of the product of eigenfunctions $$u\cdot{}v$$ $$\Delta{}u=-\lambda^{2}u\quad{}\Delta{}v=-\mu^{2}v$$ is vital to understanding the regularity properties of non-linear PDE such as the non-linear Schr\"{o}dinger equation. In this talk I will discuss some recent results that I have obtain in collaboration with Zihua Guo and Xiaolong Han which provide a full range of estimates of the form $$||uv||_{L^{p}}\leq{}G(\lambda,\mu)||u||_{L^{2}}||v||_{L^{2}}$$ where $u$ and $v$ are approximate eigenfunctions of the Laplacian. We obtain these results by re-casting the problem to a more general related semiclassical problem.
                  Non-crossing quantiles
                  15:10 Fri 14 Aug, 2015 :: Ingkarni Wardli B21 :: Dr Yanan Fan :: UNSW

                  Media...
                  Quantile regression has received increased attention in the statistics community in recent years. However, since the quantile regression curves are estimated separately, the curves can cross, leading to invalid response distribution. Many authors have proposed remedies for this in the context of frequentist estimation. In this talk, I will explain some of the existing approaches, and then describe a new Bayesian semi-parametric approach for fitting non-crossing quantile regression models simultaneously.
                  Deformation retractions from the space of continuous maps between domains in C onto the space of holomorphic maps
                  12:10 Mon 17 Aug, 2015 :: Benham Labs G10 :: Brett Chenoweth :: University of Adelaide

                  Media...
                  Mikhail Gromov proved in 1989 that every continuous map from a Stein manifold S to an elliptic manifold X could be deformed to a holomorphic map. More generally, it is true that if X is an Oka manifold then a continuous map from a Stein source into X can always be deformed to a holomorphic map. The question is whether we can do this for all continuous maps at once, in a `nice' way that does not change a map f if f is already holomorphic. In a recent paper by Larusson, we see that ANRs play an important in producing a partial answer to this question. In this talk we will explore the question in the relatively simple situation where the source and target are domains in the complex plane.
                  Equivariant bundle gerbes
                  12:10 Fri 21 Aug, 2015 :: Ingkarni Wardli B17 :: Michael Murray :: The University of Adelaide

                  Media...
                  I will present the definitions of strong and weak group actions on a bundle gerbe and calculate the strongly equivariant class of the basic bundle gerbe on a unitary group. This is joint work with David Roberts, Danny Stevenson and Raymond Vozzo and forms part of arXiv:1506.07931.
                  Be careful not to impute something ridiculous!
                  12:20 Mon 24 Aug, 2015 :: Benham Labs G10 :: Sarah James :: University of Adelaide

                  Media...
                  When learning how to make inferences about data, we are given all of the information with no missing values. In reality data sets are often missing data, anywhere from 5% of the data to extreme cases such as 70% of the data. Instead of getting rid of the incomplete cases we can impute predictions for each missing value and make inferences on the resulting data set. But just how sensible are our predictions? In this talk, we will learn how to deal with missing data and talk about why we have to be careful with our predictions.
                  Seeing the Unseeable
                  13:10 Mon 24 Aug, 2015 :: Ingkarni Wardli 715 Conference Room :: Prof. Mike Eastwood :: School of Mathematical Sciences

                  Media...
                  How do we know what's inside the earth? How do we know what's inside sick humans? We are all familiar with sophisticated scanning devices: this talk will explain roughly how they work and something of the mathematics built into them.
                  Vanishing lattices and moduli spaces
                  12:10 Fri 28 Aug, 2015 :: Ingkarni Wardli B17 :: David Baraglia :: The University of Adelaide

                  Media...
                  Vanishing lattices are symplectic analogues of root systems. As with roots systems, they admit a classification in terms of certain Dynkin diagrams (not the usual ones from Lie theory). In this talk I will discuss this classification and if there is time I will outline my work (in progress) showing that the monodromy of the SL(n,C) Hitchin fibration is essentially a vanishing lattice.
                  Pattern Formation in Nature
                  12:10 Mon 31 Aug, 2015 :: Benham Labs G10 :: Saber Dini :: University of Adelaide

                  Media...
                  Pattern formation is a ubiquitous process in nature: embryo development, animals skin pigmentation, etc. I will talk about how Alan Turing (the British genius known for the Turing Machine) explained pattern formation by linear stability analysis of reaction-diffusion systems.
                  Integrability conditions for the Grushin operators
                  12:10 Fri 4 Sep, 2015 :: Ingkarni Wardli B17 :: Michael Eastwood :: The University of Adelaide

                  Fix a non-negative integer k and consider the vector fields in the plane X=d/dx and Y=x^kd/dy. A smooth function f(x,y) is locally constant if and only if it is annihilated by the k^th Grushin operator f\mapsto(Xf,Yf). What about the range of this operator?
                  Bezout's Theorem
                  12:10 Mon 7 Sep, 2015 :: Benham Labs G10 :: David Bowman :: University of Adelaide

                  Media...
                  Generically, a line intersects a parabola at two distinct points. Bezout’s theorem generalises this idea to the intersection of two arbitrary polynomial plane curves. We discuss exceptional cases and how they are corrected by introducing the notion of multiplicity and by extending the plane to projective space. We shall also discuss applications, time permitting.
                  T-duality and bulk-boundary correspondence
                  12:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B17 :: Guo Chuan Thiang :: The University of Adelaide

                  Media...
                  Bulk-boundary correspondences in physics can be modelled as topological boundary homomorphisms in K-theory, associated to an extension of a "bulk algebra" by a "boundary algebra". In joint work with V. Mathai, such bulk-boundary maps are shown to T-dualize into simple restriction maps in a large number of cases, generalizing what the Fourier transform does for ordinary functions. I will give examples, involving both complex and real K-theory, and explain how these results may be used to study topological phases of matter and D-brane charges in string theory.
                  Mathematics in the Moonlight
                  13:10 Mon 14 Sep, 2015 :: Ingkarni Wardli 715 Conference Room :: Dr Giang Nguyen :: School of Mathematical Sciences

                  Media...
                  While everyone remembers that Neil Amstrong was the first man to walk on the moon, not many know the name of the second astronaut to do so. Possibly even smaller is the number of people who have heard of the mathematics that guided Apollo 11 to the moon and back. In this talk, we shall explore this mathematics.
                  Base change and K-theory
                  12:10 Fri 18 Sep, 2015 :: Ingkarni Wardli B17 :: Hang Wang :: The University of Adelaide

                  Media...
                  Tempered representations of an algebraic group can be classified by K-theory of the corresponding group C^*-algebra. We use Archimedean base change between Langlands parameters of real and complex algebraic groups to compare K-theory of the corresponding C^*-algebras of groups over different number fields. This is work in progress with K.F. Chao.
                  Queues and cooperative games
                  15:00 Fri 18 Sep, 2015 :: Ingkarni Wardli B21 :: Moshe Haviv :: Department of Statistics and the Federmann Center for the Study of Rationality, The Hebrew Universit

                  Media...
                  The area of cooperative game theory deals with models in which a number of individuals, called players, can form coalitions so as to improve the utility of its members. In many cases, the formation of the grand coalition is a natural result of some negotiation or a bargaining procedure. The main question then is how the players should split the gains due to their cooperation among themselves. Various solutions have been suggested among them the Shapley value, the nucleolus and the core.

                  Servers in a queueing system can also join forces. For example, they can exchange service capacity among themselves or serve customers who originally seek service at their peers. The overall performance improves and the question is how they should split the gains, or, equivalently, how much each one of them needs to pay or be paid in order to cooperate with the others. Our major focus is in the core of the resulting cooperative game and in showing that in many queueing games the core is not empty.

                  Finally, customers who are served by the same server can also be looked at as players who form a grand coalition, now inflicting damage on each other in the form of additional waiting time. We show how cooperative game theory, specifically the Aumann-Shapley prices, leads to a way in which this damage can be attributed to individual customers or groups of customers.
                  Predicting the Winning Time of a Stage of the Tour de France
                  12:10 Mon 21 Sep, 2015 :: Benham Labs G10 :: Nic Rebuli :: University of Adelaide

                  Media...
                  Sports can be lucrative, especially popular ones. But for all of us mere mortals, the only money we will ever glean from sporting events is through gambling (responsibly). When it comes to cycling, people generally choose their favourites based on individual and team performance, throughout the world cycling calendar. But what can be said for the duration of a given stage or the winning time of the highly sort after General Classification? In this talk I discuss a basic model for predicting the winning time of the Tour de France. I then apply this model to predicting the outcome of the 2012 and 2013 Tour de France and discuss the results in context.
                  Natural Optimisation (No Artificial Colours, Flavours or Preservatives)
                  12:10 Mon 21 Sep, 2015 :: Benham Labs G10 :: James Walker :: University of Adelaide

                  Media...
                  Sometimes nature seems to have the best solutions to complicated optimisation problems. For example ant colonies have a clever way of optimising the amount of food brought to the colony using pheromones, the process of natural selection gives rise to species which are optimally suited to their environment and although this process is not technically natural, for centuries people have been using properties of crystal formation to make steel with optimal properties. In this talk I will discuss non-convex optimisation and some optimisation methods inspired by natural processes.
                  T-dual noncommutative principal torus bundles
                  12:10 Fri 25 Sep, 2015 :: Engineering Maths Building EMG07 :: Keith Hannabuss :: University of Oxford

                  Media...
                  Since the work of Mathai and Rosenberg it is known that the T-dual of a principal torus bundle can be described as a noncommutative torus bundle. This talk will look at a simple example of two T-dual bundles both of which are noncommutative. Then it will discuss a strategy for extending this to more general noncommutative bundles.
                  Can Facebook Change your Mood?
                  12:10 Mon 28 Sep, 2015 :: Benham Labs G10 :: Tessa Longstaff :: University of Adelaide

                  Media...
                  When studies are conducted on humans there are several ethical considerations that physicians must adhere to. Some people have argued that a recent study by Facebook has violated some of these ethical issues. In this talk I will introduce the ethics behind human clinical trials and then discuss a study conducted by Facebook, which considered emotional contagions on networks. The ethical considerations for this study will be explored and finally we can conclude if Facebook can change your mood.
                  Analytic complexity of bivariate holomorphic functions and cluster trees
                  12:10 Fri 2 Oct, 2015 :: Ingkarni Wardli B17 :: Timur Sadykov :: Plekhanov University, Moscow

                  The Kolmogorov-Arnold theorem yields a representation of a multivariate continuous function in terms of a composition of functions which depend on at most two variables. In the analytic case, understanding the complexity of such a representation naturally leads to the notion of the analytic complexity of (a germ of) a bivariate multi-valued analytic function. According to Beloshapka's local definition, the order of complexity of any univariate function is equal to zero while the n-th complexity class is defined recursively to consist of functions of the form a(b(x,y)+c(x,y)), where a is a univariate analytic function and b and c belong to the (n-1)-th complexity class. Such a represenation is meant to be valid for suitable germs of multi-valued holomorphic functions. A randomly chosen bivariate analytic functions will most likely have infinite analytic complexity. However, for a number of important families of special functions of mathematical physics their complexity is finite and can be computed or estimated. Using this, we introduce the notion of the analytic complexity of a binary tree, in particular, a cluster tree, and investigate its properties.
                  Real Lie Groups and Complex Flag Manifolds
                  12:10 Fri 9 Oct, 2015 :: Ingkarni Wardli B17 :: Joseph A. Wolf :: University of California, Berkeley

                  Media...
                  Let G be a complex simple direct limit group. Let G_R be a real form of G that corresponds to an hermitian symmetric space. I'll describe the corresponding bounded symmetric domain in the context of the Borel embedding, Cayley transforms, and the Bergman-Shilov boundary. Let Q be a parabolic subgroup of G. In finite dimensions this means that G/Q is a complex projective variety, or equivalently has a Kaehler metric invariant under a maximal compact subgroup of G. Then I'll show just how the bounded symmetric domains describe cycle spaces for open G_R orbits on G/Q. These cycle spaces include the complex bounded symmetric domains. In finite dimensions they are tightly related to moduli spaces for compact Kaehler manifolds and to representations of semisimple Lie groups; in infinite dimensions there are more problems than answers. Finally, time permitting, I'll indicate how some of this goes over to real and to quaternionic bounded symmetric domains.
                  Modelling Directionality in Stationary Geophysical Time Series
                  12:10 Mon 12 Oct, 2015 :: Benham Labs G10 :: Mohd Mahayaudin Mansor :: University of Adelaide

                  Media...
                  Many time series show directionality inasmuch as plots again-st time and against time-to-go are qualitatively different, and there is a range of statistical tests to quantify this effect. There are two strategies for allowing for directionality in time series models. Linear models are reversible if and only if the noise terms are Gaussian, so one strategy is to use linear models with non-Gaussian noise. The alternative is to use non-linear models. We investigate how non-Gaussian noise affects directionality in a first order autoregressive process AR(1) and compare this with a threshold autoregressive model with two thresholds. The findings are used to suggest possible improvements to an AR(9) model, identified by an AIC criterion, for the average yearly sunspot numbers from 1700 to 1900. The improvement is defined in terms of one-step-ahead forecast errors from 1901 to 2014.
                  Chern-Simons classes on loop spaces and diffeomorphism groups
                  12:10 Fri 16 Oct, 2015 :: Ingkarni Wardli B17 :: Steve Rosenberg :: Boston University

                  Media...
                  Not much is known about the topology of the diffeomorphism group Diff(M) of manifolds M of dimension four and higher. We'll show that for a class of manifolds of dimension 4k+1, Diff(M) has infinite fundamental group. This is proved by translating the problem into a question about Chern-Simons classes on the tangent bundle to the loop space LM. To build the CS classes, we use a family of metrics on LM associated to a Riemannian metric on M. The curvature of these metrics takes values in an algebra of pseudodifferential operators. The main technical step in the CS construction is to replace the ordinary matrix trace in finite dimensions with the Wodzicki residue, the unique trace on this algebra. The moral is that some techniques in finite dimensional Riemannian geometry can be extended to some examples in infinite dimensional geometry.
                  Quasi-isometry classification of certain hyperbolic Coxeter groups
                  11:00 Fri 23 Oct, 2015 :: Ingkarni Wardli Conference Room 7.15 (Level 7) :: Anne Thomas :: University of Sydney

                  Media...
                  Let Gamma be a finite simple graph with vertex set S. The associated right-angled Coxeter group W is the group with generating set S, so that s^2 = 1 for all s in S and st = ts if and only if s and t are adjacent vertices in Gamma. Moussong proved that the group W is hyperbolic in the sense of Gromov if and only if Gamma has no "empty squares". We consider the quasi-isometry classification of such Coxeter groups using the local cut point structure of their visual boundaries. In particular, we find an algorithm for computing Bowditch's JSJ tree for a class of these groups, and prove that two such groups are quasi-isometric if and only if their JSJ trees are the same. This is joint work with Pallavi Dani (Louisiana State University).
                  Typhoons and Tigers
                  12:10 Fri 23 Oct, 2015 :: Hughes Lecture Room 322 :: Assoc. Prof. Andrew Metcalfe :: School of Mathematical Sciences

                  Media...
                  The Sundarbans, situated on the north coast of India and south west Bangladesh, are one of the world's largest mangrove regions (4100 square kilometres). In India, there are over 4 million inhabitants on the deltaic islands in the region. There is a diverse flora and fauna, and it is the only remaining habitat of the Bengal tiger. The Sundarbans is an UNESCO World Heritage Site and International Biodiversity Reserve. However, the Sundarbans are prone to flooding from the cyclones that regularly develop in the Bay of Bengal. In this talk I shall describe a stochastic model for the flood risk and explain how this can be used to make decisions about flood mitigation strategies and to provide estimates of the increase in flood risk due to rising sea levels and climate change.
                  TBD
                  12:10 Mon 26 Oct, 2015 :: Benham Labs G10 :: Dwalah Alsulami :: University of Adelaide

                  Media...
                  TBD
                  TBD
                  12:10 Mon 26 Oct, 2015 :: Benham Labs G10 :: Dwalah Alsulami :: University of Adelaide

                  Media...
                  TBD
                  Covariant model structures and simplicial localization
                  12:10 Fri 30 Oct, 2015 :: Ingkarni Wardli B17 :: Danny Stevenson :: The University of Adelaide

                  Media...
                  This talk will describe some aspects of the theory of quasi-categories, in particular the notion of left fbration and the allied covariant model structure. If B is a simplicial set, then I will describe some Quillen equivalences relating the covariant model structure on simplicial sets over B to a certain localization of simplicial presheaves on the simplex category of B. I will show how this leads to a new description of Lurie's simplicial rigidification functor as a hammock localization and describe some applications to Lurie's theory of straightening and unstraightening functors.
                  Near-motion-trapping in rings of cylinders (and why this is the worst possible wave energy device)
                  15:10 Fri 30 Oct, 2015 :: Ingkarni Wardli B21 :: Dr Hugh Wolgamot :: University of Western Australia

                  Motion trapping structures can oscillate indefinitely when floating in an ideal fluid. This talk discusses a simple structure which is predicted to have very close to perfect trapping behaviour, where the structure has been investigated numerically and (for the first time) experimentally. While endless oscillations were evidently not observed experimentally, remarkable differences between 'tuned' and 'detuned' structures were still apparent, and simple theory is sufficient to explain much of the behaviour. A connection with wave energy will be briefly explored, though the link is not fruitful!
                  Ocean dynamics of Gulf St Vincent: a numerical study
                  12:10 Mon 2 Nov, 2015 :: Benham Labs G10 :: Henry Ellis :: University of Adelaide

                  Media...
                  The aim of this research is to determine the physical dynamics of ocean circulation within Gulf St. Vincent, South Australia, and the exchange of momentum, nutrients, heat, salt and other water properties between the gulf and shelf via Investigator Strait and Backstairs Passage. The project aims to achieve this through the creation of high-resolution numerical models, combined with new and historical observations from a moored instrument package, satellite data, and shipboard surveys. The quasi-realistic high-resolution models are forced using boundary conditions generated by existing larger scale ROMS models, which in turn are forced at the boundary by a global model, creating a global to regional to local model network. Climatological forcing is done using European Centres for Medium range Weather Forecasting (ECMWF) data sets and is consistent over the regional and local models. A series of conceptual models are used to investigate the relative importance of separate physical processes in addition to fully forced quasi-realistic models. An outline of the research to be undertaken is given: • Connectivity of Gulf St. Vincent with shelf waters including seasonal variation due to wind and thermoclinic patterns; • The role of winter time cooling and formation of eddies in flushing the gulf; • The formation of a temperature front within the gulf during summer time; and • The connectivity and importance of nutrient rich, cool, water upwelling from the Bonney Coast with the gulf via Backstairs Passage during summer time.
                  Locally homogeneous pp-waves
                  12:10 Fri 6 Nov, 2015 :: Ingkarni Wardli B17 :: Thomas Leistner :: The University of Adelaide

                  Media...
                  For a certain type of Lorentzian manifolds, the so-called pp-waves, we study the conditions implied on the curvature by local homogeneity of the metric. We show that under some mild genericity assumptions, these conditions are quite strong, forcing the pp-wave to be a plane wave, and yielding a classification of homogeneous pp-waves. This also leads to a generalisation of a classical result by Jordan, Ehlers and Kundt about vacuum pp-waves in dimension 4 to arbitrary dimensions. Several examples show that our genericity assumptions are essential. This is joint work with W. Globke.
                  Modelling Coverage in RNA Sequencing
                  09:00 Mon 9 Nov, 2015 :: Ingkarni Wardli 5.57 :: Arndt von Haeseler :: Max F Perutz Laboratories, University of Vienna

                  Media...
                  RNA sequencing (RNA-seq) is the method of choice for measuring the expression of RNAs in a cell population. In an RNA-seq experiment, sequencing the full length of larger RNA molecules requires fragmentation into smaller pieces to be compatible with limited read lengths of most deep-sequencing technologies. Unfortunately, the issue of non-uniform coverage across a genomic feature has been a concern in RNA-seq and is attributed to preferences for certain fragments in steps of library preparation and sequencing. However, the disparity between the observed non-uniformity of read coverage in RNA-seq data and the assumption of expected uniformity elicits a query on the read coverage profile one should expect across a transcript, if there are no biases in the sequencing protocol. We propose a simple model of unbiased fragmentation where we find that the expected coverage profile is not uniform and, in fact, depends on the ratio of fragment length to transcript length. To compare the non-uniformity proposed by our model with experimental data, we extended this simple model to incorporate empirical attributes matching that of the sequenced transcript in an RNA-seq experiment. In addition, we imposed an experimentally derived distribution on the frequency at which fragment lengths occur.

                  We used this model to compare our theoretical prediction with experimental data and with the uniform coverage model. If time permits, we will also discuss a potential application of our model.
                  Weak globularity in homotopy theory and higher category theory
                  12:10 Thu 12 Nov, 2015 :: Ingkarni Wardli B19 :: Simona Paoli :: University of Leicester

                  Media...
                  Spaces and homotopy theories are fundamental objects of study of algebraic topology. One way to study these objects is to break them into smaller components with the Postnikov decomposition. To describe such decomposition purely algebraically we need higher categorical structures. We describe one approach to modelling these structures based on a new paradigm to build weak higher categories, which is the notion of weak globularity. We describe some of their connections to both homotopy theory and higher category theory.
                  Use of epidemic models in optimal decision making
                  15:00 Thu 19 Nov, 2015 :: Ingkarni Wardli 5.57 :: Tim Kinyanjui :: School of Mathematics, The University of Manchester

                  Media...
                  Epidemic models have proved useful in a number of applications in epidemiology. In this work, I will present two areas that we have used modelling to make informed decisions. Firstly, we have used an age structured mathematical model to describe the transmission of Respiratory Syncytial Virus in a developed country setting and to explore different vaccination strategies. We found that delayed infant vaccination has significant potential in reducing the number of hospitalisations in the most vulnerable group and that most of the reduction is due to indirect protection. It also suggests that marked public health benefit could be achieved through RSV vaccine delivered to age groups not seen as most at risk of severe disease. The second application is in the optimal design of studies aimed at collection of household-stratified infection data. A design decision involves making a trade-off between the number of households to enrol and the sampling frequency. Two commonly used study designs are considered: cross-sectional and cohort. The search for an optimal design uses Bayesian methods to explore the joint parameter-design space combined with Shannon entropy of the posteriors to estimate the amount of information for each design. We found that for the cross-sectional designs, the amount of information increases with the sampling intensity while the cohort design often exhibits a trade-off between the number of households sampled and the intensity of follow-up. Our results broadly support the choices made in existing data collection studies.
                  Group meeting
                  15:10 Fri 20 Nov, 2015 :: Ingkarni Wardli B17 :: Mr Jack Keeler :: University of East Anglia / University of Adelaide

                  Title: Stability of free-surface flow over topography Abstract: The forced KdV equation is used as a model to analyse the wave behaviour on the free surface in response to prescribed topographic forcing. The research involves computing steady solutions using numeric and asymptotic techniques and then analysing the stability of these steady solutions in time-dependent calculations. Stability is analysed by computing the eigenvalue spectra of the linearised fKdV operator and by exploiting the Hamiltonian structure of the fKdV. Future work includes analysing the solution space for a corrugated topography and investigating the 3 dimensional problem using the KP equation. + Any items for group discussion
                  Group meeting
                  15:10 Fri 20 Nov, 2015 :: Ingkarni Wardli B17 :: Mr Jack Keeler :: University of East Anglia / University of Adelaide

                  Title: Stability of free-surface flow over topography Abstract: The forced KdV equation is used as a model to analyse the wave behaviour on the free surface in response to prescribed topographic forcing. The research involves computing steady solutions using numeric and asymptotic techniques and then analysing the stability of these steady solutions in time-dependent calculations. Stability is analysed by computing the eigenvalue spectra of the linearised fKdV operator and by exploiting the Hamiltonian structure of the fKdV. Future work includes analysing the solution space for a corrugated topography and investigating the 3 dimensional problem using the KP equation. + Any items for group discussion
                  A Semi-Markovian Modeling of Limit Order Markets
                  13:00 Fri 11 Dec, 2015 :: Ingkarni Wardli 5.57 :: Anatoliy Swishchuk :: University of Calgary

                  Media...
                  R. Cont and A. de Larrard (SIAM J. Financial Mathematics, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by empirical observations, we extend their framework to 1) arbitrary distributions for book events inter-arrival times (possibly non-exponential) and 2) both the nature of a new book event and its corresponding inter-arrival time depend on the nature of the previous book event. We do so by resorting to Markov renewal processes to model the dynamics of the bid and ask queues. We keep analytical tractability via explicit expressions for the Laplace transforms of various quantities of interest. Our approach is justified and illustrated by calibrating the model to the five stocks Amazon, Apple, Google, Intel and Microsoft on June 21st 2012. As in Cont and Larrard, the bid-ask spread remains constant equal to one tick, only the bid and ask queues are modelled (they are independent from each other and get reinitialized after a price change), and all orders have the same size. (This talk is based on our joint paper with Nelson Vadori (Morgan Stanley)).
                  Oka principles and the linearization problem
                  12:10 Fri 8 Jan, 2016 :: Engineering North N132 :: Gerald Schwarz :: Brandeis University

                  Media...
                  Let G be a reductive complex Lie group (e.g., SL(n,C)) and let X and Y be Stein manifolds (closed complex submanifolds of some C^n). Suppose that G acts freely on X and Y. Then there are quotient Stein manifolds X/G and Y/G and quotient mappings p_X:X-> X/G and p_Y: Y-> Y/G such that X and Y are principal G-bundles over X/G and Y/G. Let us suppose that Q=X/G ~= Y/G so that X and Y have the same quotient Q. A map Phi: X\to Y of principal bundles (over Q) is simply an equivariant continuous map commuting with the projections. That is, Phi(gx)=g Phi(x) for all g in G and x in X, and p_X=p_Y o Phi. The famous Oka Principle of Grauert says that any Phi as above embeds in a continuous family Phi_t: X -> Y, t in [0,1], where Phi_0=Phi, all the Phi_t satisfy the same conditions as Phi does and Phi_1 is holomorphic. This is rather amazing. We consider the case where G does not necessarily act freely on X and Y. There is still a notion of quotient and quotient mappings p_X: X-> X//G and p_Y: Y-> Y//G where X//G and Y//G are now Stein spaces and parameterize the closed G-orbits in X and Y. We assume that Q~= X//G~= Y//G and that we have a continuous equivariant Phi such that p_X=p_Y o Phi. We find conditions under which Phi embeds into a continuous family Phi_t such that Phi_1 is holomorphic. We give an application to the Linearization Problem. Let G act holomorphically on C^n. When is there a biholomorphic map Phi:C^n -> C^n such that Phi^{-1} o g o Phi in GL(n,C) for all g in G? We find a condition which is necessary and sufficient for "most" G-actions. This is joint work with F. Kutzschebauch and F. Larusson.
                  A fibered density property and the automorphism group of the spectral ball
                  12:10 Fri 15 Jan, 2016 :: Engineering North N132 :: Frank Kutzschebauch :: University of Bern

                  Media...
                  The spectral ball is defined as the set of complex n by n matrices whose eigenvalues are all less than 1 in absolute value. Its group of holomorphic automorphisms has been studied over many decades in several papers and a precise conjecture about its structure has been formulated. In dimension 2 this conjecture was recently disproved by Kosinski. We not only disprove the conjecture in all dimensions but also give the best possible description of the automorphism group. Namely we explain how the invariant theoretic quotient map divides the automorphism group of the spectral ball into a finite dimensional part of symmetries which lift from the quotient and an infinite dimensional part which leaves the fibration invariant. We prove a precise statement as to how hopelessly huge this latter part is. This is joint work with R. Andrist.
                  Quantisation of Hitchin's moduli space
                  12:10 Fri 22 Jan, 2016 :: Engineering North N132 :: Siye Wu :: National Tsing Hua Univeristy

                  In this talk, I construct prequantum line bundles on Hitchin's moduli spaces of orientable and non-orientable surfaces and study the geometric quantisation and quantisation via branes by complexification of the moduli spaces.
                  A long C^2 without holomorphic functions
                  12:10 Fri 29 Jan, 2016 :: Engineering North N132 :: Franc Forstneric :: University of Ljubljana

                  Media...
                  For every integer n>1 we construct a complex manifold of dimension n which is exhausted by an increasing sequence of biholomorphic images of C^n (i.e., a long C^n), but it does not admit any nonconstant holomorphic functions. We also introduce new biholomorphic invariants of a complex manifold, the stable core and the strongly stable core, and we prove that every compact strongly pseudoconvex and polynomially convex domain B in C^n is the strongly stable core of a long C^n; in particular, non-equivalent domains give rise to non-equivalent long C^n's. Thus, for any n>1 there exist uncountably many pairwise non-equivalent long C^n's. These results answer several long standing open questions. (Joint work with Luka Boc Thaler.)
                  A fixed point theorem on noncompact manifolds
                  12:10 Fri 12 Feb, 2016 :: Ingkarni Wardli B21 :: Peter Hochs :: University of Adelaide / Radboud University

                  Media...
                  For an elliptic operator on a compact manifold acted on by a compact Lie group, the Atiyah-Segal-Singer fixed point formula expresses its equivariant index in terms of data on fixed point sets of group elements. This can for example be used to prove Weyl’s character formula. We extend the definition of the equivariant index to noncompact manifolds, and prove a generalisation of the Atiyah-Segal-Singer formula, for group elements with compact fixed point sets. In one example, this leads to a relation with characters of discrete series representations of semisimple Lie groups. (This is joint work with Hang Wang.)
                  T-duality for elliptic curve orientifolds
                  12:10 Fri 4 Mar, 2016 :: Ingkarni Wardli B17 :: Jonathan Rosenberg :: University of Maryland

                  Media...
                  Orientifold string theories are quantum field theories based on the geometry of a space with an involution. T-dualities are certain relationships between such theories that look different on the surface but give rise to the same observable physics. In this talk I will not assume any knowledge of physics but will concentrate on the associated geometry, in the case where the underlying space is a (complex) elliptic curve and the involution is either holomorphic or anti-holomorphic. The results blend algebraic topology and algebraic geometry. This is mostly joint work with Chuck Doran and Stefan Mendez-Diez.
                  The parametric h-principle for minimal surfaces in R^n and null curves in C^n
                  12:10 Fri 11 Mar, 2016 :: Ingkarni Wardli B17 :: Finnur Larusson :: University of Adelaide

                  Media...
                  I will describe new joint work with Franc Forstneric (arXiv:1602.01529). This work brings together four diverse topics from differential geometry, holomorphic geometry, and topology; namely the theory of minimal surfaces, Oka theory, convex integration theory, and the theory of absolute neighborhood retracts. Our goal is to determine the rough shape of several infinite-dimensional spaces of maps of geometric interest. It turns out that they all have the same rough shape.
                  Group meeting
                  15:10 Fri 11 Mar, 2016 :: TBA

                  TBA + Any items for group discussion
                  Expanding maps
                  12:10 Fri 18 Mar, 2016 :: Eng & Maths EM205 :: Andy Hammerlindl :: Monash University

                  Media...
                  Consider a function from the circle to itself such that the derivative is greater than one at every point. Examples are maps of the form f(x) = mx for integers m > 1. In some sense, these are the only possible examples. This fact and the corresponding question for maps on higher dimensional manifolds was a major motivation for Gromov to develop pioneering results in the field of geometric group theory. In this talk, I'll give an overview of this and other results relating dynamical systems to the geometry of the manifolds on which they act and (time permitting) talk about my own work in the area.
                  How predictable are you? Information and happiness in social media.
                  12:10 Mon 21 Mar, 2016 :: Ingkarni Wardli Conference Room 715 :: Dr Lewis Mitchell :: School of Mathematical Sciences

                  Media...
                  The explosion of ``Big Data'' coming from online social networks and the like has opened up the new field of ``computational social science'', which applies a quantitative lens to problems traditionally in the domain of psychologists, anthropologists and social scientists. What does it mean to be influential? How do ideas propagate amongst populations? Is happiness contagious? For the first time, mathematicians, statisticians, and computer scientists can provide insight into these and other questions. Using data from social networks such as Facebook and Twitter, I will give an overview of recent research trends in computational social science, describe some of my own work using techniques like sentiment analysis and information theory in this realm, and explain how you can get involved with this highly rewarding research field as well.
                  Counting periodic points of plane Cremona maps
                  12:10 Fri 1 Apr, 2016 :: Eng & Maths EM205 :: Tuyen Truong :: University of Adelaide

                  Media...
                  In this talk, I will present recent results, join with Tien-Cuong Dinh and Viet-Anh Nguyen, on counting periodic points of plane Cremona maps (i.e. birational maps of P^2). The tools used include a Lefschetz fixed point formula of Saito, Iwasaki and Uehara for birational maps of surface whose fixed point set may contain curves; a bound on the arithmetic genus of curves of periodic points by Diller, Jackson and Sommerse; a result by Diller, Dujardin and Guedj on invariant (1,1) currents of meromorphic maps of compact Kahler surfaces; and a theory developed recently by Dinh and Sibony for non proper intersections of varieties. Among new results in the paper, we give a complete characterisation of when two positive closed (1,1) currents on a compact Kahler surface behave nicely in the view of Dinh and Sibony’s theory, even if their wedge intersection may not be well-defined with respect to the classical pluripotential theory. Time allows, I will present some generalisations to meromorphic maps (including an upper bound for the number of isolated periodic points which is sometimes overlooked in the literature) and open questions.
                  What is your favourite (4 dimensional) shape?
                  12:10 Mon 4 Apr, 2016 :: Ingkarni Wardli Conference Room 715 :: Dr Raymond Vozzo :: School of Mathematical Sciences

                  Media...
                  This is a circle, it lives in R^2: [picture of a circle]. This is a sphere, it lives in R^3: [picture of a sphere] In this talk I will (attempt to) give you a picture of what the next shape in this sequence (in R^4) looks like. I will also explain how all of this is related to a very important area of modern mathematics called topology.
                  Geometric analysis of gap-labelling
                  12:10 Fri 8 Apr, 2016 :: Eng & Maths EM205 :: Mathai Varghese :: University of Adelaide

                  Media...
                  Using an earlier result, joint with Quillen, I will formulate a gap labelling conjecture for magnetic Schrodinger operators with smooth aperiodic potentials on Euclidean space. Results in low dimensions will be given, and the formulation of the same problem for certain non-Euclidean spaces will be given if time permits. This is ongoing joint work with Moulay Benameur.
                  Hot tube tau machine
                  15:10 Fri 15 Apr, 2016 :: B17 Ingkarni Wardli :: Dr Hayden Tronnolone :: University of Adelaide

                  Abstract: Microstructured optical fibres may be fabricated by first extruding molten material from a die to produce a macroscopic version of the final design, call a preform, and then stretching this to produce a fibre. In this talk I will demonstrate how to couple an existing model of the fluid flow during the extrusion stage to a basic model of the fluid temperature and present some preliminary conclusions. This work is still in progress and is being carried out in collaboration with Yvonne Stokes, Michael Chen and Jonathan Wylie. (+ Any items for group discussion)
                  Sard Theorem for the endpoint map in sub-Riemannian manifolds
                  12:10 Fri 29 Apr, 2016 :: Eng & Maths EM205 :: Alessandro Ottazzi :: University of New South Wales

                  Media...
                  Sub-Riemannian geometries occur in several areas of pure and applied mathematics, including harmonic analysis, PDEs, control theory, metric geometry, geometric group theory, and neurobiology. We introduce sub-Riemannian manifolds and give some examples. Therefore we discuss some of the open problems, and in particular we focus on the Sard Theorem for the endpoint map, which is related to the study of length minimizers. Finally, we consider some recent results obtained in collaboration with E. Le Donne, R. Montgomery, P. Pansu and D. Vittone.
                  How to count Betti numbers
                  12:10 Fri 6 May, 2016 :: Eng & Maths EM205 :: David Baraglia :: University of Adelaide

                  Media...
                  I will begin this talk by showing how to obtain the Betti numbers of certain smooth complex projective varieties by counting points over a finite field. For singular or non-compact varieties this motivates us to consider the "virtual Hodge numbers" encoded by the "Hodge-Deligne polynomial", a refinement of the topological Euler characteristic. I will then discuss the computation of Hodge-Deligne polynomials for certain singular character varieties (i.e. moduli spaces of flat connections).
                  Mathematical modelling of the immune response to influenza
                  15:00 Thu 12 May, 2016 :: Ingkarni Wardli B20 :: Ada Yan :: University of Melbourne

                  Media...
                  The immune response plays an important role in the resolution of primary influenza infection and prevention of subsequent infection in an individual. However, the relative roles of each component of the immune response in clearing infection, and the effects of interaction between components, are not well quantified.

                  We have constructed a model of the immune response to influenza based on data from viral interference experiments, where ferrets were exposed to two influenza strains within a short time period. The changes in viral kinetics of the second virus due to the first virus depend on the strains used as well as the interval between exposures, enabling inference of the timing of innate and adaptive immune response components and the role of cross-reactivity in resolving infection. Our model provides a mechanistic explanation for the observed variation in viruses' abilities to protect against subsequent infection at short inter-exposure intervals, either by delaying the second infection or inducing stochastic extinction of the second virus. It also explains the decrease in recovery time for the second infection when the two strains elicit cross-reactive cellular adaptive immune responses. To account for inter-subject as well as inter-virus variation, the model is formulated using a hierarchical framework. We will fit the model to experimental data using Markov Chain Monte Carlo methods; quantification of the model will enable a deeper understanding of the effects of potential new treatments.
                  Harmonic analysis of Hodge-Dirac operators
                  12:10 Fri 13 May, 2016 :: Eng & Maths EM205 :: Pierre Portal :: Australian National University

                  Media...
                  When the metric on a Riemannian manifold is perturbed in a rough (merely bounded and measurable) manner, do basic estimates involving the Hodge Dirac operator $D = d+d^*$ remain valid? Even in the model case of a perturbation of the euclidean metric on $\mathbb{R}^n$, this is a difficult question. For instance, the fact that the $L^2$ estimate $\|Du\|_2 \sim \|\sqrt{D^{2}}u\|_2$ remains valid for perturbed versions of $D$ was a famous conjecture made by Kato in 1961 and solved, positively, in a ground breaking paper of Auscher, Hofmann, Lacey, McIntosh and Tchamitchian in 2002. In the past fifteen years, a theory has emerged from the solution of this conjecture, making rough perturbation problems much more tractable. In this talk, I will give a general introduction to this theory, and present one of its latest results: a flexible approach to $L^p$ estimates for the holomorphic functional calculus of $D$. This is joint work with D. Frey (Delft) and A. McIntosh (ANU).
                  Smooth mapping orbifolds
                  12:10 Fri 20 May, 2016 :: Eng & Maths EM205 :: David Roberts :: University of Adelaide

                  It is well-known that orbifolds can be represented by a special kind of Lie groupoid, namely those that are étale and proper. Lie groupoids themselves are one way of presenting certain nice differentiable stacks. In joint work with Ray Vozzo we have constructed a presentation of the mapping stack Hom(disc(M),X), for M a compact manifold and X a differentiable stack, by a Fréchet-Lie groupoid. This uses an apparently new result in global analysis about the map C^\infty(K_1,Y) \to C^\infty(K_2,Y) induced by restriction along the inclusion K_2 \to K_1, for certain compact K_1,K_2. We apply this to the case of X being an orbifold to show that the mapping stack is an infinite-dimensional orbifold groupoid. We also present results about mapping groupoids for bundle gerbes.
                  Behavioural Microsimulation Approach to Social Policy and Behavioural Economics
                  15:10 Fri 20 May, 2016 :: S112 Engineering South :: Dr Drew Mellor :: Ernst & Young

                  SIMULAIT is a general purpose, behavioural micro-simulation system designed to predict behavioural trends in human populations. This type of predictive capability grew out of original research initially conducted in conjunction with the Defence Science and Technology Group (DSTO) in South Australia, and has been fully commercialised and is in current use by a global customer base. To our customers, the principal value of the system lies in its ability to predict likely outcomes to scenarios that challenge conventional approaches based on extrapolation or generalisation. These types of scenarios include: the impact of disruptive technologies, such as the impact of wide-spread adoption of autonomous vehicles for transportation or batteries for household energy storage; and the impact of effecting policy elements or interventions, such as the impact of imposing water usage restrictions. SIMULAIT employs a multi-disciplinary methodology, drawing from agent-based modelling, behavioural science and psychology, microeconomics, artificial intelligence, simulation, game theory, engineering, mathematics and statistics. In this seminar, we start with a high-level view of the system followed by a look under the hood to see how the various elements come together to answer questions about behavioural trends. The talk will conclude with a case study of a recent application of SIMULAIT to a significant policy problem - how to address the deficiency of STEM skilled teachers in the Victorian teaching workforce.
                  Some free boundary value problems in mean curvature flow and fully nonlinear curvature flows
                  12:10 Fri 27 May, 2016 :: Eng & Maths EM205 :: Valentina Wheeler :: University of Wollongong

                  Media...
                  In this talk we present an overview of the current research in mean curvature flow and fully nonlinear curvature flows with free boundaries, with particular focus on our own results. Firstly we consider the scenario of a mean curvature flow solution with a ninety-degree angle condition on a fixed hypersurface in Euclidean space, that we call the contact hypersurface. We prove that under restrictions on either the initial hypersurface (such as rotational symmetry) or restrictions on the contact hypersurface the flow exists for all times and converges to a self-similar solution. We also discuss the possibility of a curvature singularity appearing on the free boundary contained in the contact hypersurface. We extend some of these results to the setting of a hypersurface evolving in its normal direction with speed given by a fully nonlinear functional of the principal curvatures.
                  On the Strong Novikov Conjecture for Locally Compact Groups in Low Degree Cohomology Classes
                  12:10 Fri 3 Jun, 2016 :: Eng & Maths EM205 :: Yoshiyasu Fukumoto :: Kyoto University

                  Media...
                  The main result I will discuss is non-vanishing of the image of the index map from the G-equivariant K-homology of a G-manifold X to the K-theory of the C*-algebra of the group G. The action of G on X is assumed to be proper and cocompact. Under the assumption that the Kronecker pairing of a K-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero. Neither discreteness of the locally compact group G nor freeness of the action of G on X are required. The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.
                  Student Performance Issues in First Year University Calculus
                  15:10 Fri 10 Jun, 2016 :: Engineering South S112 :: Dr Christine Mangelsdorf :: University of Melbourne

                  Media...
                  MAST10006 Calculus 2 is the largest subject in the School of Mathematics and Statistics at the University of Melbourne, accounting for about 2200 out of 7400 first year enrolments. Despite excellent and consistent feedback from students on lectures, tutorials and teaching materials, scaled failure rates in Calculus 2 averaged an unacceptably high 29.4% (with raw failure rates reaching 40%) by the end of 2014. To understand the issues behind the poor student performance, we studied the exam papers of students with grades of 40-49% over a three-year period. In this presentation, I will present data on areas of poor performance in the final exam, show samples of student work, and identify possible causes for their errors. Many of the performance issues are found to relate to basic weaknesses in the students’ secondary school mathematical skills that inhibit their ability to successfully complete Calculus 2. Since 2015, we have employed a number of approaches to support students’ learning that significantly improved student performance in assessment. I will discuss the changes made to assessment practices and extra support materials provided online and in person, that are driving the improvement.
                  Algebraic structures associated to Brownian motion on Lie groups
                  13:10 Thu 16 Jun, 2016 :: Ingkarni Wardli B17 :: Steve Rosenberg :: University of Adelaide / Boston University

                  Media...
                  In (1+1)-d TQFT, products and coproducts are associated to pairs of pants decompositions of Riemann surfaces. We consider a toy model in dimension (0+1) consisting of specific broken paths in a Lie group. The products and coproducts are constructed by a Brownian motion average of holonomy along these paths with respect to a connection on an auxiliary bundle. In the trivial case over the torus, we (seem to) recover the Hopf algebra structure on the symmetric algebra. In the general case, we (seem to) get deformations of this Hopf algebra. This is a preliminary report on joint work with Michael Murray and Raymond Vozzo.
                  Multi-scale modeling in biofluids and particle aggregation
                  15:10 Fri 17 Jun, 2016 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide

                  In today's seminar I will give 2 examples in mathematical biology which describes the multi-scale organization at 2 levels: the meso/micro level and the continuum/macro level. I will then detail suitable tools in statistical mechanics to link these different scales. The first problem arises in mathematical physiology: swelling-de-swelling mechanism of mucus, an ionic gel. Mucus is packaged inside cells at high concentration (volume fraction) and when released into the extracellular environment, it expands in volume by two orders of magnitude in a matter of seconds. This rapid expansion is due to the rapid exchange of calcium and sodium that changes the cross-linked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a two-phase, polymer/solvent mixture theory (in the continuum level description), together with the chemistry of the polymer, its nearest neighbor interaction and its binding with the dissolved ionic species (in the micro-scale description). The problem is posed as a free-boundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibrium-states of the ionic gels are analyzed. In the second example, we numerically study the adhesion fragmentation dynamics of rigid, round particles clusters subject to a homogeneous shear flow. In the macro level we describe the dynamics of the number density of these cluster. The description in the micro-scale includes (a) binding/unbinding of the bonds attached on the particle surface, (b) bond torsion, (c) surface potential due to ionic medium, and (d) flow hydrodynamics due to shear flow.
                  Chern-Simons invariants of Seifert manifolds via Loop spaces
                  14:10 Tue 28 Jun, 2016 :: Ingkarni Wardli B17 :: Ryan Mickler :: Northeastern University

                  Over the past 30 years the Chern-Simons functional for connections on G-bundles over three-manfolds has lead to a deep understanding of the geometry of three-manfiolds, as well as knot invariants such as the Jones polynomial. Here we study this functional for three-manfolds that are topologically given as the total space of a principal circle bundle over a compact Riemann surface base, which are known as Seifert manifolds. We show that on such manifolds the Chern-Simons functional reduces to a particular gauge-theoretic functional on the 2d base, that describes a gauge theory of connections on an infinite dimensional bundle over this base with structure group given by the level-k affine central extension of the loop group LG. We show that this formulation gives a new understanding of results of Beasley-Witten on the computability of quantum Chern-Simons invariants of these manifolds as well as knot invariants for knots that wrap a single fiber of the circle bundle. A central tool in our analysis is the Caloron correspondence of Murray-Stevenson-Vozzo.
                  Twists over etale groupoids and twisted vector bundles
                  12:10 Fri 22 Jul, 2016 :: Ingkarni Wardli B18 :: Elizabeth Gillaspy :: University of Colorado, Boulder

                  Media...
                  Given a twist over an etale groupoid, one can construct an associated C*-algebra which carries a good deal of geometric and physical meaning; for example, the K-theory group of this C*-algebra classifies D-brane charges in string theory. Twisted vector bundles, when they exist, give rise to particularly important elements in this K-theory group. In this talk, we will explain how to use the classifying space of the etale groupoid to construct twisted vector bundles, under some mild hypotheses on the twist and the classifying space. My hope is that this talk will be accessible to a broad audience; in particular, no prior familiarity with groupoids, their twists, or the associated C*-algebras will be assumed. This is joint work with Carla Farsi.
                  Holomorphic Flexibility Properties of Spaces of Elliptic Functions
                  12:10 Fri 29 Jul, 2016 :: Ingkarni Wardli B18 :: David Bowman :: University of Adelaide

                  The set of meromorphic functions on an elliptic curve naturally possesses the structure of a complex manifold. The component of degree 3 functions is 6-dimensional and enjoys several interesting complex-analytic properties that make it, loosely speaking, the opposite of a hyperbolic manifold. Our main result is that this component has a 54-sheeted branched covering space that is an Oka manifold.
                  Etale ideas in topological and algebraic dynamical systems
                  12:10 Fri 5 Aug, 2016 :: Ingkarni Wardli B18 :: Tuyen Truong :: University of Adelaide

                  Media...
                  In etale topology, instead of considering open subsets of a space, we consider etale neighbourhoods lying over these open subsets. In this talk, I define an etale analog of dynamical systems: to understand a dynamical system f:(X,\Omega )->(X,\Omega ), we consider other dynamical systems lying over it. I then propose to use this to resolve the following two questions: Question 1: What should be the topological entropy of a dynamical system (f,X,\Omega ) when (X,\Omega ) is not a compact space? Question 2: What is the relation between topological entropy of a rational map or correspondence (over a field of arbitrary characteristic) to the pullback on cohomology groups and algebraic cycles?
                  Approaches to modelling cells and remodelling biological tissues
                  14:10 Wed 10 Aug, 2016 :: Ingkarni Wardli 5.57 :: Professor Helen Byrne :: University of Oxford

                  Biological tissues are complex structures, whose evolution is characterised by multiple biophysical processes that act across diverse space and time scales. For example, during normal wound healing, fibroblast cells located around the wound margin exert contractile forces to close the wound while those located in the surrounding tissue synthesise new tissue in response to local growth factors and mechanical stress created by wound contraction. In this talk I will illustrate how mathematical modelling can provide insight into such complex processes, taking my inspiration from recent studies of cell migration, vasculogenesis and wound healing.
                  Calculus on symplectic manifolds
                  12:10 Fri 12 Aug, 2016 :: Ingkarni Wardli B18 :: Mike Eastwood :: University of Adelaide

                  Media...
                  One can use the symplectic form to construct an elliptic complex replacing the de Rham complex. Then, under suitable curvature conditions, one can form coupled versions of this complex. Finally, on complex projective space, these constructions give rise to a series of elliptic complexes with geometric consequences for the Fubini-Study metric and its X-ray transform. This talk, which will start from scratch, is based on the work of many authors but, especially, current joint work with Jan Slovak.
                  Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type
                  12:10 Fri 19 Aug, 2016 :: Ingkarni Wardli B18 :: Lesley Ward :: University of South Australia

                  Media...
                  Much effort has been devoted to generalizing the Calder'on-Zygmund theory in harmonic analysis from Euclidean spaces to metric measure spaces, or spaces of homogeneous type. Here the underlying space R^n with Euclidean metric and Lebesgue measure is replaced by a set X with general metric or quasi-metric and a doubling measure. Further, one can replace the Laplacian operator that underpins the Calderon-Zygmund theory by more general operators L satisfying heat kernel estimates. I will present recent joint work with P. Chen, X.T. Duong, J. Li and L.X. Yan along these lines. We develop the theory of product Hardy spaces H^p_{L_1,L_2}(X_1 x X_2), for 1
                  Predicting turbulence
                  14:10 Tue 30 Aug, 2016 :: Napier 209 :: Dr Trent Mattner :: School of Mathematical Sciences

                  Media...
                  Turbulence is characterised by three-dimensional unsteady fluid motion over a wide range of spatial and temporal scales. It is important in many problems of technological and scientific interest, such as drag reduction, energy production and climate prediction. Turbulent flows are governed by the Navier--Stokes equations, which are a nonlinear system of partial differential equations. Typically, numerical methods are needed to find solutions to these equations. In turbulent flows, however, the resulting computational problem is usually intractable. Filtering or averaging the Navier--Stokes equations mitigates the computational problem, but introduces new quantities into the equations. Mathematical models of turbulence are needed to estimate these quantities. One promising turbulence model consists of a random collection of fluid vortices, which are themselves approximate solutions of the Navier--Stokes equations.
                  Singular vector bundles and topological semi-metals
                  12:10 Fri 2 Sep, 2016 :: Ingkarni Wardli B18 :: Guo Chuan Thiang :: University of Adelaide

                  Media...
                  The elusive Weyl fermion was recently realised as quasiparticle excitations of a topological semimetal. I will explain what a semi-metal is, and the precise mathematical sense in which they can be "topological", in the sense of the general theory of topological insulators. This involves understanding vector bundles with singularities, with the aid of Mayer-Vietoris principles, gerbes, and generalised degree theory.
                  What is the best way to count votes?
                  13:10 Mon 12 Sep, 2016 :: Hughes 322 :: Dr Stuart Johnson :: School of Mathematical Sciences

                  Media...
                  Around the world there are many different ways of counting votes in elections, and even within Australia there are different methods in use in various states. Which is the best method? Even for the simplest case of electing one person in a single electorate there is no easy answer to this, in fact there is a famous result - Arrow's Theorem - which tells us that there is no perfect way of counting votes. I will describe a number of different methods along with their problems before giving a more precise statement of the theorem and outlining a proof
                  Geometry of pseudodifferential algebra bundles
                  12:10 Fri 16 Sep, 2016 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide

                  Media...
                  I will motivate the construction of pseudodifferential algebra bundles arising in index theory, and also outline the construction of general pseudodifferential algebra bundles (and the associated sphere bundles), showing that there are many that are purely infinite dimensional that do not come from usual constructions in index theory. I will also discuss characteristic classes of such bundles. This is joint work with Richard Melrose.
                  Hilbert schemes of points of some surfaces and quiver representations
                  12:10 Fri 23 Sep, 2016 :: Ingkarni Wardli B17 :: Ugo Bruzzo :: International School for Advanced Studies, Trieste

                  Media...
                  Hilbert schemes of points on the total spaces of the line bundles O(-n) on P1 (desingularizations of toric singularities of type (1/n)(1,1)) can be given an ADHM description, and as a result, they can be realized as varieties of quiver representations.
                  SIR epidemics with stages of infection
                  12:10 Wed 28 Sep, 2016 :: EM218 :: Matthieu Simon :: Universite Libre de Bruxelles

                  Media...
                  This talk is concerned with a stochastic model for the spread of an epidemic in a closed homogeneously mixing population. The population is subdivided into three classes of individuals: the susceptibles, the infectives and the removed cases. In short, an infective remains infectious during a random period of time. While infected, it can contact all the susceptibles present, independently of the other infectives. At the end of the infectious period, it becomes a removed case and has no further part in the infection process.

                  We represent an infectious period as a set of different stages that an infective can go through before being removed. The transitions between stages are ruled by either a Markov process or a semi-Markov process. In each stage, an infective makes contaminations at the epochs of a Poisson process with a specific rate.

                  Our purpose is to derive closed expressions for a transform of different statistics related to the end of the epidemic, such as the final number of susceptibles and the area under the trajectories of all the infectives. The analysis is performed by using simple matrix analytic methods and martingale arguments. Numerical illustrations will be provided at the end of the talk.
                  Transmission Dynamics of Visceral Leishmaniasis: designing a test and treat control strategy
                  12:10 Thu 29 Sep, 2016 :: EM218 :: Graham Medley :: London School of Hygiene & Tropical Medicine

                  Media...
                  Visceral Leishmaniasis (VL) is targeted for elimination from the Indian Sub-Continent. Progress has been much better in some areas than others. Current control is based on earlier diagnosis and treatment and on insecticide spraying to reduce the density of the vector. There is a surprising dearth of specific information on the epidemiology of VL, which makes modelling more difficult. In this seminar, I describe a simple framework that gives some insight into the transmission dynamics. We conclude that the majority of infection comes from cases prior to diagnosis. If this is the case then, early diagnosis will be advantageous, but will require a test with high specificity. This is a paradox for many clinicians and public health workers, who tend to prioritise high sensitivity.

                  Medley, G.F., Hollingsworth, T.D., Olliaro, P.L. & Adams, E.R. (2015) Health-seeking, diagnostics and transmission in the control of visceral leishmaniasis. Nature 528, S102-S108 (3 December 2015), DOI: 10.1038/nature16042
                  Energy quantisation for the Willmore functional
                  11:10 Fri 7 Oct, 2016 :: Ligertwood 314 Flinders Room :: Yann Bernard :: Monash University

                  Media...
                  We prove a bubble-neck decomposition and an energy quantisation result for sequences of Willmore surfaces immersed into R^(m>=3) with uniformly bounded energy and non-degenerating conformal structure. We deduce the strong compactness (modulo the action of the Moebius group) of closed Willmore surfaces of a given genus below some energy threshold. This is joint-work with Tristan Riviere (ETH Zuerich).
                  Character Formula for Discrete Series
                  12:10 Fri 14 Oct, 2016 :: Ingkarni Wardli B18 :: Hang Wang :: University of Adelaide

                  Media...
                  Weyl character formula describes characters of irreducible representations of compact Lie groups. This formula can be obtained using geometric method, for example, from the Atiyah-Bott fixed point theorem or the Atiyah-Segal-Singer index theorem. Harish-Chandra character formula, the noncompact analogue of the Weyl character formula, can also be studied from the point of view of index theory. We apply orbital integrals on K-theory of Harish-Chandra Schwartz algebra of a semisimple Lie group G, and then use geometric method to deduce Harish-Chandra character formulas for discrete series representations of G. This is work in progress with Peter Hochs.
                  Some results on the stability of flat Stokes layers
                  15:10 Fri 14 Oct, 2016 :: Ingkarni Wardli 5.57 :: Professor Andrew Bassom :: University of Tasmania

                  The flat Stokes layer is one of the relatively few exact solutions of the incompressible Navier-Stokes equations. For that reason the temporal stability of the layer has attracted considerable interest over the years. Fortunately, not only is the issue one solely of academic curiosity, but some kind of Stokes layer is likely to be set up at the boundaries of any physical time-periodic flow making its stability of practical interest as well. In this talk I shall review progress made in the understanding of the linear stability properties of the flow. In particular I will discuss the fact that theoretical predictions of critical conditions are wildly different from those observed in the laboratory.
                  Parahoric bundles, invariant theory and the Kazhdan-Lusztig map
                  12:10 Fri 21 Oct, 2016 :: Ingkarni Wardli B18 :: David Baraglia :: University of Adelaide

                  Media...
                  In this talk I will introduce the notion of parahoric groups, a loop group analogue of parabolic subgroups. I will also discuss a global version of this, namely parahoric bundles on a complex curve. This leads us to a problem concerning the behaviour of invariant polynomials on the dual of the Lie algebra, a kind of "parahoric invariant theory". The key to solving this problem turns out to be the Kazhdan-Lusztig map, which assigns to each nilpotent orbit in a semisimple Lie algebra a conjugacy class in the Weyl group. Based on joint work with Masoud Kamgarpour and Rohith Varma.
                  Measuring and mapping carbon dioxide from remote sensing satellite data
                  15:10 Fri 21 Oct, 2016 :: Napier G03 :: Prof Noel Cressie :: University of Wollongong

                  Media...
                  This talk is about environmental statistics for global remote sensing of atmospheric carbon dioxide, a leading greenhouse gas. An important compartment of the carbon cycle is atmospheric carbon dioxide (CO2), where it (and other gases) contribute to climate change through a greenhouse effect. There are a number of CO2 observational programs where measurements are made around the globe at a small number of ground-based locations at somewhat regular time intervals. In contrast, satellite-based programs are spatially global but give up some of the temporal richness. The most recent satellite launched to measure CO2 was NASA's Orbiting Carbon Observatory-2 (OCO-2), whose principal objective is to retrieve a geographical distribution of CO2 sources and sinks. OCO-2's measurement of column-averaged mole fraction, XCO2, is designed to achieve this, through a data-assimilation procedure that is statistical at its basis. Consequently, uncertainty quantification is key, starting with the spectral radiances from an individual sounding to borrowing of strength through spatial-statistical modelling.
                  Toroidal Soap Bubbles: Constant Mean Curvature Tori in S ^ 3 and R ^3
                  12:10 Fri 28 Oct, 2016 :: Ingkarni Wardli B18 :: Emma Carberry :: University of Sydney

                  Media...
                  Constant mean curvature (CMC) tori in S ^ 3, R ^ 3 or H ^ 3 are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes and whether tori can be deformed. I will address these questions for the spherical and Euclidean cases, using Whitham deformations.
                  Fault tolerant computation of hyperbolic PDEs with the sparse grid combination technique
                  15:10 Fri 28 Oct, 2016 :: Ingkarni Wardli 5.57 :: Dr Brendan Harding :: University of Adelaide

                  Computing solutions to high dimensional problems is challenging because of the curse of dimensionality. The sparse grid combination technique allows one to significantly reduce the cost of computing solutions such that they become manageable on current supercomputers. However, as these supercomputers increase in size the rate of failure also increases. This poses a challenge for our computations. In this talk we look at the problem of computing solutions to hyperbolic partial differential equations with the combination technique in an environment where faults occur. A fault tolerant generalisation of the combination technique will be presented along with results that demonstrate its effectiveness.
                  Introduction to Lorentz Geometry: Riemann vs Lorentz
                  12:10 Fri 18 Nov, 2016 :: Engineering North N132 :: Abdelghani Zeghib :: Ecole Normale Superieure de Lyon

                  Media...
                  The goal is to compare Riemannian and Lorentzian geometries and see what one loses and wins when going from the Riemann to Lorentz. Essentially, one loses compactness and ellipticity, but wins causality structure and mathematical and physical situations when natural Lorentzian metrics emerge.
                  Leavitt path algebras
                  12:10 Fri 2 Dec, 2016 :: Engineering & Math EM213 :: Roozbeh Hazrat :: Western Sydney University

                  Media...
                  From a directed graph one can generate an algebra which captures the movements along the graph. One such algebras are Leavitt path algebras. Despite being introduced only 10 years ago, Leavitt path algebras have arisen in a variety of different contexts as diverse as analysis, symbolic dynamics, noncommutative geometry and representation theory. In fact, Leavitt path algebras are algebraic counterpart to graph C*-algebras, a theory which has become an area of intensive research globally. There are strikingly parallel similarities between these two theories. Even more surprisingly, one cannot (yet) obtain the results in one theory as a consequence of the other; the statements look the same, however the techniques to prove them are quite different (as the names suggest, one uses Algebra and other Analysis). These all suggest that there might be a bridge between Algebra and Analysis yet to be uncovered. In this talk, we introduce Leavitt path algebras and try to classify them by means of (graded) Grothendieck groups. We will ask nice questions!
                  Segregation of particles in incompressible flows due to streamline topology and particle-boundary interaction
                  15:10 Fri 2 Dec, 2016 :: Ingkarni Wardli 5.57 :: Professor Hendrik C. Kuhlmann :: Institute of Fluid Mechanics and Heat Transfer, TU Wien, Vienna, Austria

                  Media...
                  The incompressible flow in a number of classical benchmark problems (e.g. lid-driven cavity, liquid bridge) undergoes an instability from a two-dimensional steady to a periodic three-dimensional flow, which is steady or in form of a traveling wave, if the Reynolds number is increased. In the supercritical regime chaotic as well as regular (quasi-periodic) streamlines can coexist for a range of Reynolds numbers. The spatial structures of the regular regions in three-dimensional Navier-Stokes flows has received relatively little attention, partly because of the high numerical effort required for resolving these structures. Particles whose density does not differ much from that of the liquid approximately follow the chaotic or regular streamlines in the bulk. Near the boundaries, however, their trajectories strongly deviate from the streamlines, in particular if the boundary (wall or free surface) is moving tangentially. As a result of this particle-boundary interaction particles can rapidly segregate and be attracted to periodic or quasi-periodic orbits, yielding particle accumulation structures (PAS). The mechanism of PAS will be explained and results from experiments and numerical modelling will be presented to demonstrate the generic character of the phenomenon.
                  An equivariant parametric Oka principle for bundles of homogeneous spaces
                  12:10 Fri 3 Mar, 2017 :: Napier 209 :: Finnur Larusson :: University of Adelaide

                  I will report on new joint work with Frank Kutzschebauch and Gerald Schwarz (arXiv:1612.07372). Under certain conditions, every continuous section of a holomorphic fibre bundle can be deformed to a holomorphic section. In fact, the inclusion of the space of holomorphic sections into the space of continuous sections is a weak homotopy equivalence. What if a complex Lie group acts on the bundle and its sections? We have proved an analogous result for equivariant sections. The result has a wide scope. If time permits, I will describe some interesting special cases and mention two applications.
                  Diffeomorphisms of discs, harmonic spinors and positive scalar curvature
                  11:10 Fri 17 Mar, 2017 :: Engineering Nth N218 :: Diarmuid Crowley :: University of Melbourne

                  Media...
                  Let Diff(D^k) be the space of diffeomorphisms of the k-disc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have non-zero 8-periodic 2-torsion detected in real K-theory. I will then discuss applications for spin manifolds M of dimension 6 or greater: 1) Our results input to arguments of Hitchin which now show that M admits a metric with a harmonic spinor. 2) If non-empty, space of positive scalar curvature metrics on M has non-zero 8-periodic 2-torsion in its homotopy groups which is detected in real K-theory. This is part of joint work with Thomas Schick and Wolfgang Steimle.
                  What is index theory?
                  12:10 Tue 21 Mar, 2017 :: Inkgarni Wardli 5.57 :: Dr Peter Hochs :: School of Mathematical Sciences

                  Media...
                  Index theory is a link between topology, geometry and analysis. A typical theorem in index theory says that two numbers are equal: an analytic index and a topological index. The first theorem of this kind was the index theorem of Atiyah and Singer, which they proved in 1963. Index theorems have many applications in maths and physics. For example, they can be used to prove that a differential equation must have a solution. Also, they imply that the topology of a space like a sphere or a torus determines in what ways it can be curved. Topology is the study of geometric properties that do not change if we stretch or compress a shape without cutting or glueing. Curvature does change when we stretch something out, so it is surprising that topology can say anything about curvature. Index theory has many surprising consequences like this.
                  Minimal surfaces and complex analysis
                  12:10 Fri 24 Mar, 2017 :: Napier 209 :: Antonio Alarcon :: University of Granada

                  Media...
                  A surface in the Euclidean space R^3 is said to be minimal if it is locally area-minimizing, meaning that every point in the surface admits a compact neighborhood with the least area among all the surfaces with the same boundary. Although the origin of minimal surfaces is in physics, since they can be realized locally as soap films, this family of surfaces lies in the intersection of many fields of mathematics. In particular, complex analysis in one and several variables plays a fundamental role in the theory. In this lecture we will discuss the influence of complex analysis in the study of minimal surfaces.
                  Geometric structures on moduli spaces
                  12:10 Fri 31 Mar, 2017 :: Napier 209 :: Nicholas Buchdahl :: University of Adelaide

                  Media...
                  Moduli spaces are used to classify various kinds of objects, often arising from solutions of certain differential equations on manifolds; for example, the complex structures on a compact surface or the anti-self-dual Yang-Mills equations on an oriented smooth 4-manifold. Sometimes these moduli spaces carry important information about the underlying manifold, manifested most clearly in the results of Donaldson and others on the topology of smooth 4-manifolds. It is also the case that these moduli spaces themselves carry interesting geometric structures; for example, the Weil-Petersson metric on moduli spaces of compact Riemann surfaces, exploited to great effect by Maryam Mirzakhani. In this talk, I shall elaborate on the theme of geometric structures on moduli spaces, with particular focus on some recent-ish work done in conjunction with Georg Schumacher.
                  K-types of tempered representations
                  12:10 Fri 7 Apr, 2017 :: Napier 209 :: Peter Hochs :: University of Adelaide

                  Media...
                  Tempered representations of a reductive Lie group G are the irreducible unitary representations one needs in the Plancherel decomposition of L^2(G). They are relevant to harmonic analysis because of this, and also occur in the Langlands classification of the larger class of admissible representations. If K in G is a maximal compact subgroup, then there is a considerable amount of information in the restriction of a tempered representation to K. In joint work with Yanli Song and Shilin Yu, we give a geometric expression for the decomposition of such a restriction into irreducibles. The multiplicities of these irreducibles are expressed as indices of Dirac operators on reduced spaces of a coadjoint orbit of G corresponding to the representation. These reduced spaces are Spin-c analogues of reduced spaces in symplectic geometry, defined in terms of moment maps that represent conserved quantities. This result involves a Spin-c version of the quantisation commutes with reduction principle for noncompact manifolds. For discrete series representations, this was done by Paradan in 2003.
                  Poisson-Lie T-duality and integrability
                  11:10 Thu 13 Apr, 2017 :: Engineering & Math EM213 :: Ctirad Klimcik :: Aix-Marseille University, Marseille

                  Media...
                  The Poisson-Lie T-duality relates sigma-models with target spaces symmetric with respect to mutually dual Poisson-Lie groups. In the special case if the Poisson-Lie symmetry reduces to the standard non-Abelian symmetry one of the corresponding mutually dual sigma-models is the standard principal chiral model which is known to enjoy the property of integrability. A natural question whether this non-Abelian integrability can be lifted to integrability of sigma model dualizable with respect to the general Poisson-Lie symmetry has been answered in the affirmative by myself in 2008. The corresponding Poisson-Lie symmetric and integrable model is a one-parameter deformation of the principal chiral model and features a remarkable explicit appearance of the standard Yang-Baxter operator in the target space geometry. Several distinct integrable deformations of the Yang-Baxter sigma model have been then subsequently uncovered which turn out to be related by the Poisson-Lie T-duality to the so called lambda-deformed sigma models. My talk gives a review of these developments some of which found applications in string theory in the framework of the AdS/CFT correspondence.
                  Geometric limits of knot complements
                  12:10 Fri 28 Apr, 2017 :: Napier 209 :: Jessica Purcell :: Monash University

                  Media...
                  The complement of a knot often admits a hyperbolic metric: a metric with constant curvature -1. In this talk, we will investigate sequences of hyperbolic knots, and the possible spaces they converge to as a geometric limit. In particular, we show that there exist hyperbolic knots in the 3-sphere such that the set of points of large injectivity radius in the complement take up the bulk of the volume. This is joint work with Autumn Kent.
                  Algae meet the mathematics of multiplicative multifractals
                  12:10 Tue 2 May, 2017 :: Inkgarni Wardli Conference Room 715 :: Professor Tony Roberts :: School of Mathematical Sciences

                  Media...
                  There is much that is fragmented and rough in the world around us: clouds and landscapes are examples, as is algae. We need fractal geometry to encompass these. In practice we need multifractals: a composite of interwoven sets, each with their own fractal structure. Multiplicative multifractals have known properties. Optimising a fit between them and the data then empowers us to quantify subtle details of fractal geometry in applications, such as in algae distribution.
                  Hodge theory on the moduli space of Riemann surfaces
                  12:10 Fri 5 May, 2017 :: Napier 209 :: Jesse Gell-Redman :: University of Melbourne

                  Media...
                  The Hodge theorem on a closed Riemannian manifold identifies the deRham cohomology with the space of harmonic differential forms. Although there are various extensions of the Hodge theorem to singular or complete but non-compact spaces, when there is an identification of L^2 Harmonic forms with a topological feature of the underlying space, it is highly dependent on the nature of infinity (in the non-compact case) or the locus of incompleteness; no unifying theorem treats all cases. We will discuss work toward extending the Hodge theorem to singular Riemannian manifolds where the singular locus is an incomplete cusp edge. These can be pictured locally as a bundle of horns, and they provide a model for the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Joint with J. Swoboda and R. Melrose.
                  Graded K-theory and C*-algebras
                  11:10 Fri 12 May, 2017 :: Engineering North 218 :: Aidan Sims :: University of Wollongong

                  Media...
                  C*-algebras can be regarded, in a very natural way, as noncommutative algebras of continuous functions on topological spaces. The analogy is strong enough that topological K-theory in terms of formal differences of vector bundles has a direct analogue for C*-algebras. There is by now a substantial array of tools out there for computing C*-algebraic K-theory. However, when we want to model physical phenomena, like topological phases of matter, we need to take into account various physical symmetries, some of which are encoded by gradings of C*-algebras by the two-element group. Even the definition of graded C*-algebraic K-theory is not entirely settled, and there are relatively few computational tools out there. I will try to outline what a C*-algebra (and a graded C*-algebra is), indicate what graded K-theory ought to look like, and discuss recent work with Alex Kumjian and David Pask linking this with the deep and powerful work of Kasparov, and using this to develop computational tools.
                  Lagrangian transport in deterministic flows: from theory to experiment
                  16:10 Tue 16 May, 2017 :: Engineering North N132 :: Dr Michel Speetjens :: Eindhoven University of Technology

                  Transport of scalar quantities (e.g. chemical species, nutrients, heat) in deterministic flows is key to a wide range of phenomena and processes in industry and Nature. This encompasses length scales ranging from microns to hundreds of kilometres, and includes systems as diverse as viscous flows in the processing industry, micro-fluidic flows in labs-on-a-chip and porous media, large-scale geophysical and environmental flows, physiological and biological flows and even continuum descriptions of granular flows. Essential to the net transport of a scalar quantity is its advection by the fluid motion. The Lagrangian perspective (arguably) is the most natural way to investigate advection and leans on the fact that fluid trajectories are organized into coherent structures that geometrically determine the advective transport properties. Lagrangian transport is typically investigated via theoretical and computational studies and often concerns idealized flow situations that are difficult (or even impossible) to create in laboratory experiments. However, bridging the gap from theoretical and computational results to realistic flows is essential for their physical meaningfulness and practical relevance. This presentation highlights a number of fundamental Lagrangian transport phenomena and properties in both two-dimensional and three-dimensional flows and demonstrates their physical validity by way of representative and experimentally realizable flows.
                  Real bundle gerbes
                  12:10 Fri 19 May, 2017 :: Napier 209 :: Michael Murray :: University of Adelaide

                  Media...
                  Bundle gerbe modules, via the notion of bundle gerbe K-theory provide a realisation of twisted K-theory. I will discuss the existence or Real bundle gerbes which are the corresponding objects required to construct Real twisted K-theory in the sense of Atiyah. This is joint work with Richard Szabo (Heriot-Watt), Pedram Hekmati (Auckland) and Raymond Vozzo which appeared in arXiv:1608.06466.
                  Serotonin Movement Through the Human Colonic Mucosa
                  15:10 Fri 19 May, 2017 :: Ingkarni Wardli 5.57 :: Helen Dockrell :: Flinders University / Flinders Medical Centre

                  The control of gut motility remains poorly defined and this makes it difficult to treat disorders associated with dysmotility in patient populations. Intestinal serotonin can elicit and modulate colonic motor patterns and is released in response to a variety of stimuli including nutrient ingestion and pressure change. I will describe a computational model of intestinal tissue and the predicted movement of serotonin through this tissue by advection and diffusion following pressure-dependent release. I have developed this model as a PhD candidate under the supervision of Associate Professor Phil Dinning, Professor Damien Keating and Dr Lukasz Wilendt.
                  Plumbing regular closed polygonal curves
                  12:10 Mon 22 May, 2017 :: Inkgarni Wardli Conference Room 715 :: Dr Barry Cox :: School of Mathematical Sciences

                  Media...
                  In 1980 the following puzzle appeared in Mathematics Magazine: A certain mathematician, in order to make ends meet, moonlights as an apprentice plumber. One night, as the mathematician contemplated a pile of straight pipes of equal lengths and right-angled elbows, the following question occurred to this mathematician: ``For which positive integers n could I form a closed polygonal curve using n such straight pipes and n elbows?'' It turns out that it is possible for any even number n greater than or equal to 4 and any odd number n greater than or equal to 7. However the case n=7 is particularly interesting because it can be done one of two ways and the problem is related to that of determining all the possible conformations of the molecule cyclo-heptane, although the angles in cyclo-heptane are not right angles. This raises the questions: ``Do the two solutions to the maths puzzle with right-angles correspond to the two principal conformations of cyclo-heptane?'', and ``How many solutions/conformations exist for other elbow angles?'' These and other issues will be discussed.
                  Schubert Calculus on Lagrangian Grassmannians
                  12:10 Tue 23 May, 2017 :: EM 213 :: Hiep Tuan Dang :: National centre for theoretical sciences, Taiwan

                  Media...
                  The Lagrangian Grassmannian $LG = LG(n,2n)$ is the projective complex manifold which parametrizes Lagrangian (i.e. maximal isotropic) subspaces in a symplective vector space of dimension $2n$. This talk is mainly devoted to Schubert calculus on $LG$. We first recall the definition of Schubert classes in this context. Then we present basic results which are similar to the classical formulas due to Pieri and Giambelli. These lead to a presentation of the cohomology ring of $LG$. Finally, we will discuss recent results related to the Schubert structure constants and Gromov-Witten invariants of $LG$.
                  Holomorphic Legendrian curves
                  12:10 Fri 26 May, 2017 :: Napier 209 :: Franc Forstneric :: University of Ljubljana, Slovenia

                  Media...
                  I will present recent results on the existence and behaviour of noncompact holomorphic Legendrian curves in complex contact manifolds. We show that these curves are ubiquitous in \C^{2n+1} with the standard holomorphic contact form \alpha=dz+\sum_{j=1}^n x_jdy_j; in particular, every open Riemann surface embeds into \C^3 as a proper holomorphic Legendrian curves. On the other hand, for any integer n>= 1 there exist Kobayashi hyperbolic complex contact structures on \C^{2n+1} which do not admit any nonconstant Legendrian complex lines. Furthermore, we construct a holomorphic Darboux chart around any noncompact holomorphic Legendrian curve in an arbitrary complex contact manifold. As an application, we show that every bordered holomorphic Legendrian curve can be uniformly approximated by complete bounded Legendrian curves.
                  Stokes' Phenomenon in Translating Bubbles
                  15:10 Fri 2 Jun, 2017 :: Ingkarni Wardli 5.57 :: Dr Chris Lustri :: Macquarie University

                  This study of translating air bubbles in a Hele-Shaw cell containing viscous fluid reveals the critical role played by surface tension in these systems. The standard zero-surface-tension model of Hele-Shaw flow predicts that a continuum of bubble solutions exists for arbitrary flow translation velocity. The inclusion of small surface tension, however, eliminates this continuum of solutions, instead producing a discrete, countably infinite family of solutions, each with distinct translation speeds. We are interested in determining this discrete family of solutions, and understanding why only these solutions are permitted. Studying this problem in the asymptotic limit of small surface tension does not seem to give any particular reason why only these solutions should be selected. It is only by using exponential asymptotic methods to study the Stokes’ structure hidden in the problem that we are able to obtain a complete picture of the bubble behaviour, and hence understand the selection mechanism that only permits certain solutions to exist. In the first half of my talk, I will explain the powerful ideas that underpin exponential asymptotic techniques, such as analytic continuation and optimal truncation. I will show how they are able to capture behaviour known as Stokes' Phenomenon, which is typically invisible to classical asymptotic series methods. In the second half of the talk, I will introduce the problem of a translating air bubble in a Hele-Shaw cell, and show that the behaviour can be fully understood by examining the Stokes' structure concealed within the problem. Finally, I will briefly showcase other important physical applications of exponential asymptotic methods, including submarine waves and particle chains.
                  Constructing differential string structures
                  14:10 Wed 7 Jun, 2017 :: EM213 :: David Roberts :: University of Adelaide

                  Media...
                  String structures on a manifold are analogous to spin structures, except instead of lifting the structure group through the extension Spin(n)\to SO(n) of Lie groups, we need to lift through the extension String(n)\to Spin(n) of Lie *2-groups*. Such a thing exists if the first fractional Pontryagin class (1/2)p_1 vanishes in cohomology. A differential string structure also lifts connection data, but this is rather complicated, involving a number of locally defined differential forms satisfying cocycle-like conditions. This is an expansion of the geometric string structures of Stolz and Redden, which is, for a given connection A, merely a 3-form R on the frame bundle such that dR = tr(F^2) for F the curvature of A; in other words a trivialisation of the de Rham class of (1/2)p_1. I will present work in progress on a framework (and specific results) that allows explicit calculation of the differential string structure for a large class of homogeneous spaces, which also yields formulas for the Stolz-Redden form. I will comment on the application to verifying the refined Stolz conjecture for our particular class of homogeneous spaces. Joint work with Ray Vozzo.
                  Quaternionic Kaehler manifolds of co-homogeneity one
                  12:10 Fri 16 Jun, 2017 :: Ligertwood 231 :: Vicente Cortes :: Universitat Hamburg

                  Media...
                  Quaternionic Kaehler manifolds form an important class of Riemannian manifolds of special holonomy. They provide examples of Einstein manifolds of non-zero scalar curvature. I will show how to construct explicit examples of complete quaternionic Kaehler manifolds of negative scalar curvature beyond homogeneous spaces. In particular, I will present a series of examples of co-homogeneity one, based on arXiv:1701.07882.
                  Aggregation patterns from local and non-local interactions
                  15:10 Fri 30 Jun, 2017 :: Ingkarni Wardli 5.57 :: Dr Emily Hackett-Jones :: Centre for Cancer Biology, University of South Australia

                  Biological aggregations are ubiquitous in nature and may arise from a number of different mechanisms - both local and non-local. I will discuss two such mechanisms with particular application to the enteric nervous system; the nervous system in the gut responsible for peristalsis. Aggregates of neurons with a particular form are necessary for normal gut development. Our work suggests possible explanations for observations in normal and abnormal gut development.
                  Complex methods in real integral geometry
                  12:10 Fri 28 Jul, 2017 :: Engineering Sth S111 :: Mike Eastwood :: University of Adelaide

                  There are well-known analogies between holomorphic integral transforms such as the Penrose transform and real integral transforms such as the Radon, Funk, and John transforms. In fact, one can make a precise connection between them and hence use complex methods to establish results in the real setting. This talk will introduce some simple integral transforms and indicate how complex analysis may be applied.
                  Curvature contraction of axially symmetric hypersurfaces in the sphere
                  12:10 Fri 4 Aug, 2017 :: Engineering Sth S111 :: James McCoy :: University of Wollongong

                  Media...
                  We show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of S^{n+1}. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.
                  Weil's Riemann hypothesis (RH) and dynamical systems
                  12:10 Fri 11 Aug, 2017 :: Engineering Sth S111 :: Tuyen Truong :: University of Adelaide

                  Media...
                  Weil proposed an analogue of the RH in finite fields, aiming at counting asymptotically the number of solutions to a given system of polynomial equations (with coefficients in a finite field) in finite field extensions of the base field. This conjecture influenced the development of Algebraic Geometry since the 1950’s, most important achievements include: Grothendieck et al.’s etale cohomology, and Bombieri and Grothendieck’s standard conjectures on algebraic cycles (inspired by a Kahlerian analogue of a generalisation of Weil’s RH by Serre). Weil’s RH was solved by Deligne in the 70’s, but the finite field analogue of Serre’s result is still open (even in dimension 2). This talk presents my recent work proposing a generalisation of Weil’s RH by relating it to standard conjectures and a relatively new notion in complex dynamical systems called dynamical degrees. In the course of the talk, I will present the proof of a question proposed by Esnault and Srinivas (which is related to a result by Gromov and Yomdin on entropy of complex dynamical systems), which gives support to the finite field analogue of Serre’s result.
                  Conway's Rational Tangle
                  12:10 Tue 15 Aug, 2017 :: Inkgarni Wardli 5.57 :: Dr Hang Wang :: School of Mathematical Sciences

                  Media...
                  Many researches in mathematics essentially feature some classification problems. In this context, invariants are created in order to associate algebraic quantities, such as numbers and groups, to elements of interested classes of geometric objects, such as surfaces. A key property of an invariant is that it does not change under ``allowable moves'' which can be specified in various geometric contexts. We demonstrate these lines of ideas by rational tangles, a notion in knot theory. A tangle is analogous to a link except that it has free ends. Conway's rational tangles are the simplest tangles that can be ``unwound'' under a finite sequence of two simple moves, and they arise as building blocks for knots. A numerical invariant will be introduced for Conway's rational tangles and it provides the only known example of a complete invariant in knot theory.
                  Compact pseudo-Riemannian homogeneous spaces
                  12:10 Fri 18 Aug, 2017 :: Engineering Sth S111 :: Wolfgang Globke :: University of Adelaide

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                  A pseudo-Riemannian homogeneous space $M$ of finite volume can be presented as $M=G/H$, where $G$ is a Lie group acting transitively and isometrically on $M$, and $H$ is a closed subgroup of $G$. The condition that $G$ acts isometrically and thus preserves a finite measure on $M$ leads to strong algebraic restrictions on $G$. In the special case where $G$ has no compact semisimple normal subgroups, it turns out that the isotropy subgroup $H$ is a lattice, and that the metric on $M$ comes from a bi-invariant metric on $G$. This result allows us to recover Zeghib’s classification of Lorentzian compact homogeneous spaces, and to move towards a classification for metric index 2. As an application we can investigate which pseudo-Riemannian homogeneous spaces of finite volume are Einstein spaces. Through the existence questions for lattice subgroups, this leads to an interesting connection with the theory of transcendental numbers, which allows us to characterize the Einstein cases in low dimensions. This talk is based on joint works with Oliver Baues, Yuri Nikolayevsky and Abdelghani Zeghib.
                  Time-reversal symmetric topology from physics
                  12:10 Fri 25 Aug, 2017 :: Engineering Sth S111 :: Guo Chuan Thiang :: University of Adelaide

                  Media...
                  Time-reversal plays a crucial role in experimentally discovered topological insulators (2008) and semimetals (2015). This is mathematically interesting because one is forced to use "Quaternionic" characteristic classes and differential topology --- a previously ill-motivated generalisation. Guided by physical intuition, an equivariant Poincare-Lefschetz duality, Euler structures, and a new type of monopole with torsion charge, will be introduced.
                  In space there is no-one to hear you scream
                  12:10 Tue 12 Sep, 2017 :: Inkgarni Wardli 5.57 :: A/Prof Gary Glonek :: School of Mathematical Sciences

                  Media...
                  Modern data problems often involve data in very high dimensions. For example, gene expression profiles, used to develop cancer screening models, typically have at least 30,000 dimensions. When dealing with such data, it is natural to apply intuition from low dimensional cases. For example, in a sample of normal observations, a typical data point will be near the centre of the distribution with only a small number of points at the edges. In this talk, simple probability theory will be used to show that the geometry of data in high dimensional space is very different from what we can see in one and two-dimensional examples. We will show that the typical data point is at the edge of the distribution, a long way from its centre and even further from any other points.
                  Measuring the World's Biggest Bubble
                  13:10 Tue 19 Sep, 2017 :: Napier LG23 :: Prof Matt Roughan :: School of Mathematical Sciences

                  Media...
                  Recently I had a bit of fun helping Graeme Denton measure his Guinness World Record (GWR) Largest (Indoor) Soap Bubble. It was a lot harder than I initially thought it would be. Soap films are interesting mathematically -- in principle they form minimal surfaces, and have constant curvature. So it should have been fairly easy. But really big bubbles aren't ideal, so measuring the GWR bubble required a mix of maths and pragmatism. It's a good example of mathematical modeling in general, so I thought it was worth a few words. I'll tell you what we did, and how we estimated how big the bubble actually was. Some links: http://www.9news.com.au/good-news/2017/08/02/13/44/adelaide-man-wins-world-record-for-largest-bubble http://www.abc.net.au/news/2017-08-03/science-performer-creates-worlds-largest-indoor-soap-bubble/8770260
                  Dynamics of transcendental Hanon maps
                  11:10 Wed 20 Sep, 2017 :: Engineering & Math EM212 :: Leandro Arosio :: University of Rome

                  The dynamics of a polynomial in the complex plane is a classical topic studied already at the beginning of the 20th century by Fatou and Julia. The complex plane is partitioned in two natural invariant sets: a compact set called the Julia set, with (usually) fractal structure and chaotic behaviour, and the Fatou set, where dynamics has no sensitive dependence on initial conditions. The dynamics of a transcendental map was first studied by Baker fifty years ago, and shows striking differences with the polynomial case: for example, there are wandering Fatou components. Moving to C^2, an analogue of polynomial dynamics is given by Hanon maps, polynomial automorphisms with interesting dynamics. In this talk I will introduce a natural generalisation of transcendental dynamics to C^2, and show how to construct wandering domains for such maps.
                  An action of the Grothendieck-Teichmuller group on stable curves of genus zero
                  11:10 Fri 22 Sep, 2017 :: Engineering South S111 :: Marcy Robertson :: University of Melbourne

                  Media...
                  In this talk, we show that the group of homotopy automorphisms of the profinite completion of the framed little 2-discs operad is isomorphic to the (profinite) Grothendieck-Teichmuller group. We deduce that the Grothendieck-Teichmuller group acts nontrivially on an operadic model of the genus zero Teichmuller tower. This talk will be aimed at a general audience and will not assume previous knowledge of the Grothendieck-Teichmuller group or operads. This is joint work with Pedro Boavida and Geoffroy Horel.
                  On directions and operators
                  11:10 Wed 27 Sep, 2017 :: Engineering & Math EM213 :: Malabika Pramanik :: University of British Columbia

                  Media...
                  Many fundamental operators arising in harmonic analysis are governed by sets of directions that they are naturally associated with. This talk will survey a few representative results in this area, and report on some new developments.
                  Equivariant formality of homogeneous spaces
                  12:10 Fri 29 Sep, 2017 :: Engineering Sth S111 :: Alex Chi-Kwong Fok :: University of Adelaide

                  Equivariant formality, a notion in equivariant topology introduced by Goresky-Kottwitz-Macpherson, is a desirable property of spaces with group actions, which allows the application of localisation formula to evaluate integrals of any top closed forms and enables one to compute easily the equivariant cohomology. Broad classes of spaces of especial interest are well-known to be equivariantly formal, e.g., compact symplectic manifolds equipped with Hamiltonian compact Lie group actions and projective varieties equipped with linear algebraic torus actions, of which flag varieties are examples. Less is known about compact homogeneous spaces G/K equipped with the isotropy action of K, which is not necessarily of maximal rank. In this talk we will review previous attempts of characterizing equivariant formality of G/K, and present our recent results on this problem using an analogue of equivariant formality in K-theory. Part of the work presented in this talk is joint with Jeffrey Carlson.
                  Operator algebras in rigid C*-tensor categories
                  12:10 Fri 6 Oct, 2017 :: Engineering Sth S111 :: Corey Jones :: Australian National University

                  Media...
                  In noncommutative geometry, operator algebras are often regarded as the algebras of functions on noncommutative spaces. Rigid C*-tensor categories are algebraic structures that appear in the study of quantum field theories, subfactors, and compact quantum groups. We will explain how they can be thought of as ``noncommutative'' versions of the tensor category of Hilbert spaces. Combining these two viewpoints, we describe a notion of operator algebras internal to a rigid C*-tensor category, and discuss applications to the theory of subfactors.
                  End-periodic K-homology and spin bordism
                  12:10 Fri 20 Oct, 2017 :: Engineering Sth S111 :: Michael Hallam :: University of Adelaide

                  This talk introduces new "end-periodic" variants of geometric K-homology and spin bordism theories that are tailored to a recent index theorem for even-dimensional manifolds with periodic ends. This index theorem, due to Mrowka, Ruberman and Saveliev, is a generalisation of the Atiyah-Patodi-Singer index theorem for manifolds with odd-dimensional boundary. As in the APS index theorem, there is an (end-periodic) eta invariant that appears as a correction term for the periodic end. Invariance properties of the standard relative eta invariants are elegantly expressed using K-homology and spin bordism, and this continues to hold in the end-periodic case. In fact, there are natural isomorphisms between the standard K-homology/bordism theories and their end-periodic versions, and moreover these isomorphisms preserve relative eta invariants. The study is motivated by results on positive scalar curvature, namely obstructions and distinct path components of the moduli space of PSC metrics. Our isomorphisms provide a systematic method for transferring certain results on PSC from the odd-dimensional case to the even-dimensional case. This work is joint with Mathai Varghese.
                  How oligomerisation impacts steady state gradient in a morphogen-receptor system
                  15:10 Fri 20 Oct, 2017 :: Ingkarni Wardli 5.57 :: Mr Phillip Brown :: University of Adelaide

                  In developmental biology an important process is cell fate determination, where cells start to differentiate their form and function. This is an element of the broader concept of morphogenesis. It has long been held that cell differentiation can occur by a chemical signal providing positional information to 'undecided' cells. This chemical produces a gradient of concentration that indicates to a cell what path it should develop along. More recently it has been shown that in a particular system of this type, the chemical (protein) does not exist purely as individual molecules, but can exist in multi-protein complexes known as oligomers. Mathematical modelling has been performed on systems of oligomers to determine if this concept can produce useful gradients of concentration. However, there are wide range of possibilities when it comes to how oligomer systems can be modelled and most of them have not been explored. In this talk I will introduce a new monomer system and analyse it, before extending this model to include oligomers. A number of oligomer models are proposed based on the assumption that proteins are only produced in their oligomer form and can only break apart once they have left the producing cell. It will be shown that when oligomers are present under these conditions, but only monomers are permitted to bind with receptors, then the system can produce robust, biologically useful gradients for a significantly larger range of model parameters (for instance, degradation, production and binding rates) compared to the monomer system. We will also show that when oligomers are permitted to bind with receptors there is negligible difference compared to the monomer system.
                  Springer correspondence for symmetric spaces
                  12:10 Fri 17 Nov, 2017 :: Engineering Sth S111 :: Ting Xue :: University of Melbourne

                  Media...
                  The Springer theory for reductive algebraic groups plays an important role in representation theory. It relates nilpotent orbits in the Lie algebra to irreducible representations of the Weyl group. We develop a Springer theory in the case of symmetric spaces using Fourier transform, which relates nilpotent orbits in this setting to irreducible representations of Hecke algebras of various Coxeter groups with specified parameters. This in turn gives rise to character sheaves on symmetric spaces, which we describe explicitly in the case of classical symmetric spaces. A key ingredient in the construction is the nearby cycle sheaves associated to the adjoint quotient map. The talk is based on joint work with Kari Vilonen and partly based on joint work with Misha Grinberg and Kari Vilonen.
                  Stochastic Modelling of Urban Structure
                  11:10 Mon 20 Nov, 2017 :: Engineering Nth N132 :: Mark Girolami :: Imperial College London, and The Alan Turing Institute

                  Media...
                  Urban systems are complex in nature and comprise of a large number of individuals that act according to utility, a measure of net benefit pertaining to preferences. The actions of individuals give rise to an emergent behaviour, creating the so-called urban structure that we observe. In this talk, I develop a stochastic model of urban structure to formally account for uncertainty arising from the complex behaviour. We further use this stochastic model to infer the components of a utility function from observed urban structure. This is a more powerful modelling framework in comparison to the ubiquitous discrete choice models that are of limited use for complex systems, in which the overall preferences of individuals are difficult to ascertain. We model urban structure as a realization of a Boltzmann distribution that is the invariant distribution of a related stochastic differential equation (SDE) that describes the dynamics of the urban system. Our specification of Boltzmann distribution assigns higher probability to stable configurations, in the sense that consumer surplus (demand) is balanced with running costs (supply), as characterized by a potential function. We specify a Bayesian hierarchical model to infer the components of a utility function from observed structure. Our model is doubly-intractable and poses significant computational challenges that we overcome using recent advances in Markov chain Monte Carlo (MCMC) methods. We demonstrate our methodology with case studies on the London retail system and airports in England.
                  TBA
                  15:10 Fri 16 Feb, 2018 :: Ingkarni Wardli 5.57 :: Dr Guillermo Gomez :: Centre for Cancer Research, University of South Australia

                  A multiscale approximation of a Cahn-Larche system with phase separation on the microscale
                  15:10 Thu 22 Feb, 2018 :: Ingkarni Wardli 5.57 :: Ms Lisa Reischmann :: University of Augsberg

                  We consider the process of phase separation of a binary system under the influence of mechanical deformation and we derive a mathematical multiscale model, which describes the evolving microstructure taking into account the elastic properties of the involved materials. Motivated by phase-separation processes observed in lipid monolayers in film-balance experiments, the starting point of the model is the Cahn-Hilliard equation coupled with the equations of linear elasticity, the so-called Cahn-Larche system. Owing to the fact that the mechanical deformation takes place on a macrosopic scale whereas the phase separation happens on a microscopic level, a multiscale approach is imperative. We assume the pattern of the evolving microstructure to have an intrinsic length scale associated with it, which, after nondimensionalisation, leads to a scaled model involving a small parameter epsilon>0, which is suitable for periodic-homogenisation techniques. For the full nonlinear problem the so-called homogenised problem is then obtained by letting epsilon tend to zero using the method of asymptotic expansion. Furthermore, we present a linearised Cahn-Larche system and use the method of two-scale convergence to obtain the associated limit problem, which turns out to have the same structure as in the nonlinear case, in a mathematically rigorous way. Properties of the limit model will be discussed.
                  A Hecke module structure on the KK-theory of arithmetic groups
                  13:10 Fri 2 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Bram Mesland :: University of Bonn

                  Media...
                  Let $G$ be a locally compact group, $\Gamma$ a discrete subgroup and $C_{G}(\Gamma)$ the commensurator of $\Gamma$ in $G$. The cohomology of $\Gamma$ is a module over the Shimura Hecke ring of the pair $(\Gamma,C_G(\Gamma))$. This construction recovers the action of the Hecke operators on modular forms for $SL(2,\mathbb{Z})$ as a particular case. In this talk I will discuss how the Shimura Hecke ring of a pair $(\Gamma, C_{G}(\Gamma))$ maps into the $KK$-ring associated to an arbitrary $\Gamma$-C*-algebra. From this we obtain a variety of $K$-theoretic Hecke modules. In the case of manifolds the Chern character provides a Hecke equivariant transformation into cohomology, which is an isomorphism in low dimensions. We discuss Hecke equivariant exact sequences arising from possibly noncommutative compactifications of $\Gamma$-spaces. Examples include the Borel-Serre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the Bruhat-Tits tree of $SL(2,\mathbb{Z})$. This is joint work with M.H. Sengun (Sheffield).
                  Radial Toeplitz operators on bounded symmetric domains
                  11:10 Fri 9 Mar, 2018 :: Lower Napier LG11 :: Raul Quiroga-Barranco :: CIMAT, Guanajuato, Mexico

                  Media...
                  The Bergman spaces on a complex domain are defined as the space of holomorphic square-integrable functions on the domain. These carry interesting structures both for analysis and representation theory in the case of bounded symmetric domains. On the other hand, these spaces have some bounded operators obtained as the composition of a multiplier operator and a projection. These operators are highly noncommuting between each other. However, there exist large commutative C*-algebras generated by some of these Toeplitz operators very much related to Lie groups. I will construct an example of such C*-algebras and provide a fairly explicit simultaneous diagonalization of the generating Toeplitz operators.
                  Quantum Airy structures and topological recursion
                  13:10 Wed 14 Mar, 2018 :: Ingkarni Wardli B17 :: Gaetan Borot :: MPI Bonn

                  Media...
                  Quantum Airy structures are Lie algebras of quadratic differential operators -- their classical limit describes Lagrangian subvarieties in symplectic vector spaces which are tangent to the zero section and cut out by quadratic equations. Their partition function -- which is the function annihilated by the collection of differential operators -- can be computed by the topological recursion. I will explain how to obtain quantum Airy structures from spectral curves, and explain how we can retrieve from them correlation functions of semi-simple cohomological field theories, by exploiting the symmetries. This is based on joint work with Andersen, Chekhov and Orantin.
                  Family gauge theory and characteristic classes of bundles of 4-manifolds
                  13:10 Fri 16 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Hokuto Konno :: University of Tokyo

                  Media...
                  I will define a non-trivial characteristic class of bundles of 4-manifolds using families of Seiberg-Witten equations. The basic idea of the construction is to consider an infinite dimensional analogue of the Euler class used in the usual theory of characteristic classes. I will also explain how to prove the non-triviality of this characteristic class. If time permits, I will mention a relation between our characteristic class and positive scalar curvature metrics.
                  Computing trisections of 4-manifolds
                  13:10 Fri 23 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Stephen Tillmann :: University of Sydney

                  Media...
                  Gay and Kirby recently generalised Heegaard splittings of 3-manifolds to trisections of 4-manifolds. A trisection describes a 4–dimensional manifold as a union of three 4–dimensional handlebodies. The complexity of the 4–manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies. The minimal genus of such a surface is the trisection genus of the 4-manifold. After defining trisections and giving key examples and applications, I will describe an algorithm to compute trisections of 4–manifolds using arbitrary triangulations as input. This results in the first explicit complexity bounds for the trisection genus of a 4–manifold in terms of the number of pentachora (4–simplices) in a triangulation. This is joint work with Mark Bell, Joel Hass and Hyam Rubinstein. I will also describe joint work with Jonathan Spreer that determines the trisection genus for each of the standard simply connected PL 4-manifolds.
                  Chaos in higher-dimensional complex dynamics
                  13:10 Fri 20 Apr, 2018 :: Barr Smith South Polygon Lecture theatre :: Finnur Larusson :: University of Adelaide

                  Media...
                  I will report on new joint work with Leandro Arosio (University of Rome, Tor Vergata). Complex manifolds can be thought of as laid out across a spectrum characterised by rigidity at one end and flexibility at the other. On the rigid side, Kobayashi-hyperbolic manifolds have at most a finite-dimensional group of symmetries. On the flexible side, there are manifolds with an extremely large group of holomorphic automorphisms, the prototypes being the affine spaces $\mathbb C^n$ for $n \geq 2$. From a dynamical point of view, hyperbolicity does not permit chaos. An endomorphism of a Kobayashi-hyperbolic manifold is non-expansive with respect to the Kobayashi distance, so every family of endomorphisms is equicontinuous. We show that not only does flexibility allow chaos: under a strong anti-hyperbolicity assumption, chaotic automorphisms are generic. A special case of our main result is that if $G$ is a connected complex linear algebraic group of dimension at least 2, not semisimple, then chaotic automorphisms are generic among all holomorphic automorphisms of $G$ that preserve a left- or right-invariant Haar form. For $G=\mathbb C^n$, this result was proved (although not explicitly stated) some 20 years ago by Fornaess and Sibony. Our generalisation follows their approach. I will give plenty of context and background, as well as some details of the proof of the main result.
                  Index of Equivariant Callias-Type Operators
                  13:10 Fri 27 Apr, 2018 :: Barr Smith South Polygon Lecture theatre :: Hao Guo :: University of Adelaide

                  Media...
                  Suppose M is a smooth Riemannian manifold on which a Lie group G acts properly and isometrically. In this talk I will explore properties of a particular class of G-invariant operators on M, called G-Callias-type operators. These are Dirac operators that have been given an additional Z_2-grading and a perturbation so as to be "invertible outside of a cocompact set in M". It turns out that G-Callias-type operators are equivariantly Fredholm and so have an index in the K-theory of the maximal group C*-algebra of G. This index can be expressed as a KK-product of a class in K-homology and a class in the K-theory of the Higson G-corona. In fact, one can show that the K-theory of the Higson G-corona is highly non-trivial, and thus the index theory of G-Callias-type operators is not obviously trivial. As an application of the index theory of G-Callias-type operators, I will mention an obstruction to the existence of G-invariant metrics of positive scalar curvature on M.
                  Braid groups and higher representation theory
                  13:10 Fri 4 May, 2018 :: Barr Smith South Polygon Lecture theatre :: Tony Licata :: Australian National University

                  Media...
                  The Artin braid group arise in a number of different parts of mathematics. The goal of this talk will be to explain how basic group-theoretic questions about the Artin braid group can be answered using some modern tools of linear and homological algebra, with an eye toward proving some open conjectures about other groups.
                  Cobordism maps on PFH induced by Lefschetz fibration over higher genus base
                  13:10 Fri 11 May, 2018 :: Barr Smith South Polygon Lecture theatre :: Guan Heng Chen :: University of Adelaide

                  In this talk, we will discuss the cobordism maps on periodic Floer homology(PFH) induced by Lefschetz fibration. Periodic Floer homology is a Gromov types invariant for three dimensional mapping torus and it is isomorphic to a version of Seiberg Witten Floer cohomology(SWF). Our result is to define the cobordism maps on PFH induced by certain types of Lefschetz fibration via using holomorphic curves method. Also, we show that the cobordism maps is equivalent to the cobordism maps on Seiberg Witten cohomology under the isomorphism PFH=SWF.
                  Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory
                  13:10 Fri 25 May, 2018 :: Barr Smith South Polygon Lecture theatre :: David Baraglia :: University of Adelaide

                  Media...
                  Let X be a smooth, compact, oriented 4-manifold and consider the following problem. Let G be a group which acts on the second cohomology of X preserving the intersection form. Can this action of G on H^2(X) be lifted to an action of G on X by diffeomorphisms? We study a parametrised version of Seiberg-Witten theory for smooth families of 4-manifolds and obtain obstructions to the existence of such lifts. For example, we construct compact simply-connected 4-manifolds X and involutions on H^2(X) that can be realised by a continuous involution on X, or by a diffeomorphism, but not by an involutive diffeomorphism for any smooth structure on X.
                  The mass of Riemannian manifolds
                  13:10 Fri 1 Jun, 2018 :: Barr Smith South Polygon Lecture theatre :: Matthias Ludewig :: MPIM Bonn

                  We will define the mass of differential operators L on compact Riemannian manifolds. In odd dimensions, if L is a conformally covariant differential operator, then its mass is also conformally covariant, while in even dimensions, one has a more complicated transformation rule. In the special case that L is the Yamabe operator, its mass is related to the ADM mass of an associated asymptotically flat spacetime. In particular, one expects positive mass theorems in various settings. Here we highlight some recent results.
                  Hitchin's Projectively Flat Connection for the Moduli Space of Higgs Bundles
                  13:10 Fri 15 Jun, 2018 :: Barr Smith South Polygon Lecture theatre :: John McCarthy :: University of Adelaide

                  In this talk I will discuss the problem of geometrically quantizing the moduli space of Higgs bundles on a compact Riemann surface using Kahler polarisations. I will begin by introducing geometric quantization via Kahler polarisations for compact manifolds, leading up to the definition of a Hitchin connection as stated by Andersen. I will then describe the moduli spaces of stable bundles and Higgs bundles over a compact Riemann surface, and discuss their properties. The problem of geometrically quantizing the moduli space of stables bundles, a compact space, was solved independently by Hitchin and Axelrod, Del PIetra, and Witten. The Higgs moduli space is non-compact and therefore the techniques used do not apply, but carries an action of C*. I will finish the talk by discussing the problem of finding a Hitchin connection that preserves this C* action. Such a connection exists in the case of Higgs line bundles, and I will comment on the difficulties in higher rank.
                  Comparison Theorems under Weak Assumptions
                  11:10 Fri 29 Jun, 2018 :: EMG06 :: Kwok Kun Kwong :: National Cheng Kung University

                  TBA
                  The topology and geometry of spaces of Yang-Mills-Higgs flow lines
                  11:10 Fri 27 Jul, 2018 :: Barr Smith South Polygon Lecture theatre :: Graeme Wilkin :: National University of Singapore

                  Given a smooth complex vector bundle over a compact Riemann surface, one can define the space of Higgs bundles and an energy functional on this space: the Yang-Mills-Higgs functional. The gradient flow of this functional resembles a nonlinear heat equation, and the limit of the flow detects information about the algebraic structure of the initial Higgs bundle (e.g. whether or not it is semistable). In this talk I will explain my work to classify ancient solutions of the Yang-Mills-Higgs flow in terms of their algebraic structure, which leads to an algebro-geometric classification of Yang-Mills-Higgs flow lines. Critical points connected by flow lines can then be interpreted in terms of the Hecke correspondence, which appears in Witten’s recent work on Geometric Langlands. This classification also gives a geometric description of spaces of unbroken flow lines in terms of secant varieties of the underlying Riemann surface, and in the remaining time I will describe work in progress to relate the (analytic) Morse compactification of these spaces by broken flow lines to an algebro-geometric compactification by iterated blowups of secant varieties.
                  Carleman approximation of maps into Oka manifolds.
                  11:10 Fri 3 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Brett Chenoweth :: University of Ljubljana

                  In 1927 Torsten Carleman proved a remarkable extension of the Stone-Weierstrass theorem. Carleman’s theorem is ostensibly the first result concerning the approximation of functions on unbounded closed subsets of C by entire functions. In this talk we introduce Carleman’s theorem and several of its recent generalisations including the titled generalisation which was proved by the speaker in arXiv:1804.10680.
                  Equivariant Index, Traces and Representation Theory
                  11:10 Fri 10 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Hang Wang :: University of Adelaide

                  K-theory of C*-algebras associated to a semisimple Lie group can be understood both from the geometric point of view via Baum-Connes assembly map and from the representation theoretic point of view via harmonic analysis of Lie groups. A K-theory generator can be viewed as the equivariant index of some Dirac operator, but also interpreted as a (family of) representation(s) parametrised by the noncompact abelian part in the Levi component of a cuspidal parabolic subgroup. Applying orbital traces to the K-theory group, we obtain the equivariant index as a fixed point formula which, for each K-theory generators for (limit of) discrete series, recovers Harish-Chandra’s character formula on the representation theory side. This is a noncompact analogue of Atiyah-Segal-Singer fixed point theorem in relation to the Weyl character formula. This is joint work with Peter Hochs.
                  Min-max theory for hypersurfaces of prescribed mean curvature
                  11:10 Fri 17 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Jonathan Zhu :: Harvard University

                  We describe the construction of closed prescribed mean curvature (PMC) hypersurfaces using min-max methods. Our theory allows us to show the existence of closed PMC hypersurfaces in a given closed Riemannian manifold for a generic set of ambient prescription functions. This set includes, in particular, all constant functions as well as analytic functions if the manifold is real analytic. The described work is joint with Xin Zhou.
                  Discrete fluxes and duality in gauge theory
                  11:10 Fri 24 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Siye Wu :: National Tsinghua University

                  We explore the notions of discrete electric and magnetic fluxes introduced by 't Hooft in the late 1970s. After explaining their physics origin, we consider the description in mathematical terminology. We finally study their role in duality.
                  Projected Particle Filters
                  15:10 Fri 24 Aug, 2018 :: Lower Napier LG15 :: Dr John Maclean :: University of Adelaide

                  cientific advances owe equally to models and data, and both will remain relevant and key to further understanding. Observations drive model development, and model development often drives data acquisition. It therefore is particularly prudent to have these two sides of the scientific coin work in concert. This is a mathematical and statistical question: how to combine the output of model investigations and observational data. The area that is dedicated to studying and developing the best approaches to this issue is called Data Assimilation (DA). Perhaps the most crucial modern-day application of DA is numerical weather prediction, but it is also used in GPS systems and studies of atmospheric conditions on other planets. I will take the probabilistic or Bayesian approach to DA. At a particular time at which data are available, the question of data assimilation is how to approximate the posterior or analysis distribution, that is found by conditioning the "forecast distribution" on the data. A key method under this umbrella is the particle filter, that approximates the forecast and posterior distributions with an ensemble of weighted particles. The talk will focus on a contribution to particle filtering made from a dynamical systems point of view. I will introduce a framework for Particle Filtering, PF-AUS, in which only the components of data corresponding to the unstable and neutral modes of the forecast model are assimilated. The particle filter is well suited to nonlinear forecast models, and non-Gaussian forecast distributions, but would normally require exponentially more computational effort as the dimension of the DA problem increases. The PF-AUS implementation is shown to correspond to assimilating observations of a lower dimension, equal to the number of Lyapunov exponents. The dimension of the observations is crucial in the computational cost of the particle filter and this approach is a framework to drastically lower that cost while preserving as much relevant information as possible, in that the unstable and neutral modes correspond to the most uncertain model predictions. Particle filters are an active area of research in both the DA and the statistical communities, and there are many competing algorithms. One nice feature of PF-AUS is that it is not exactly an algorithm but rather a framework for filtering: any particle filter can be applied in the PF-AUS framework.
                  Geometry and Topology of Crystals
                  11:10 Fri 31 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Vanessa Robins :: Australian National University

                  This talk will cover some highlights of the mathematical description of crystal structure from the platonic polyhedra of ancient Greece to the current picture of crystallographic groups as orbifolds. Modern materials synthesis raises fascinating questions about the enumeration and classification of periodic interwoven or entangled frameworks, that might be addressed by techniques from 3-manifold topology and knot theory.
                  Noncommutative principal G-bundles
                  11:10 Fri 14 Sep, 2018 :: Barr Smith South Polygon Lecture theatre :: Keith Hannabuss :: University of Oxford

                  Noncommutative geometry provides greater flexibility for studying some problems. This seminar will survey some work on noncommutative principal G-bundles. These were classified for abelian groups some years ago, but nonabelian groups require a different approach, using tools developed for a totally different reason in the 1980s. This uncovers links with ergodic theory, quantum groups and the Yang-Baxter equation.
                  TBA
                  11:10 Fri 5 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Scott Morrison :: Australian National University

                  TBA
                  11:10 Fri 26 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg

                  News matching "Statistics Seminar"

                  The Armitage Lecture
                  Associate Professor Patty Solomon (Statistics) has been invited to present the prestigious Armitage Lecture for 2007 in Cambridge. Posted Thu 18 Jan 07.
                  Positions available in the School (5)
                  The School is currently seeking a Professor of Statistics, an Associate Professor of Statistics, a Lecturer/Senior Lecturer in Applied Mathematics, a Lecturer in Applied Mathematics and a Lecturer in Pure Mathematics. See the University's jobs website for full details, including the selection criteria. Posted Fri 23 May 08.
                  Teaching Fellow Position

                  Visiting Teaching Fellow School of Mathematical Sciences (Ref: 3808)

                  We are seeking a Visiting Teaching Fellow (Associate Lecturer) who will be responsible for developing better links between the University of Adelaide and secondary schools and developing new approaches for first-year undergraduate teaching. You will be required to conduct tutorials in first year mathematics and statistics subjects for up to 16 hours per week, and assist in subject assessment and curriculum development.

                  This position would suit an experienced mathematics teacher with strong mathematical training and an interest and recent involvement in teaching advanced mathematics units in years 11 and 12. Fixed-term position available from 19 January 2009 to 31 December 2009. Salary: (Level A) $49,053 - $66,567 per annum.Plus an employer superannuation contribution of 17% applies. (Closing date 14/11/08.)

                  Please see the University web site for further details.

                  Posted Wed 17 Sep 08.
                  ARC Future Fellowship success
                  Associate Professor Zudi Lu has been awarded an ARC Future Fellowship. Associate Professor Lu, and Associate Professor in Statistics, will use the support provided by his Future Fellowship to further improve the theory and practice of econometric modelling of nonlinear spatial time series. Congratulations Zudi. Posted Thu 12 May 11.
                  Two contract positions are available
                  As a result of the School's success in securing two prestigious Australian Research Council Future Fellowships, we now have two limited term positions available, one in Pure Mathematics and one in Statistics. Posted Wed 14 Dec 11.
                  A/Prof Joshua Ross, 2017 Moran Medal recipient
                  Congratulations to Associate Professor Joshua Ross who has won the 2017 Moran Medal, awarded by the Australian Academy of Science. The Moran Medal recognises outstanding research by scientists up to 10 years post-PhD in applied probability, biometrics, mathematical genetics, psychometrics and statistics. Associate Professor Ross has made influential contributions to public health and conservation biology using mathematical modelling and statistics to help in decision making. Posted Fri 23 Dec 16.

                  More information...

                  Publications matching "Statistics Seminar"

                  Publications
                  Conditional expectation formulae for copulas
                  Crane, Glenis Jayne; Van Der Hoek, John, Australian & New Zealand Journal of Statistics 50 (53–67) 2008
                  Some U-Statistics in goodness-of-fit tests derived from characterizations via record values
                  Morris, Kerwin; Szynal, D, International Journal of Pure and Applied Mathematics 46 (507–582) 2008
                  Goodness-of-fit tests based on characterizations involving moments of order statistics
                  Morris, Kerwin; Szynal, D, International Journal of Pure and Applied Mathematics 38 (83–121) 2007
                  Optimal multilinear estimation of a random vector under constraints of casualty and limited memory
                  Howlett, P; Torokhti, Anatoli; Pearce, Charles, Computational Statistics & Data Analysis 52 (869–878) 2007
                  Statistics in review; Part 1: graphics, data summary and linear models
                  Moran, John; Solomon, Patricia, Critical care and Resuscitation 9 (81–90) 2007
                  Statistics in review; Part 2: Generalised linear models, time-to-event and time-series analysis, evidence synthesis and clinical trials
                  Moran, John; Solomon, Patricia, Critical care and Resuscitation 9 (187–197) 2007
                  The effect on survival of early detection of breast cancer in South Australia
                  Tallis, George; Leppard, Phillip; O'Neill, Terence, Model Assisted Statistics and Applications 1 (115–123) 2006
                  A note on some mahonian statistics
                  Clarke, Robert, Seminaire Lotharingien de Combinatoire 53 (1–5) 2005
                  Designing follow-up intervals
                  Raab, G; Davies, J; Salter, Amy, Statistics in Medicine 23 (3125–3137) 2004
                  Goodness-of-fit tests using dual versions of characterizations via moments of order statistics
                  Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 122 (3365–3383) 2004
                  On dual characterizations of continuous distributions in terms of expected values of two functions of order statistics and record values
                  Alinowska, I; Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 121 (2664–2673) 2004
                  A note on the sensitivities of self-reporting and screen detection of primary breast tumours
                  Tallis, George; Leppard, Phillip; O'Neill, Terence, Australian & New Zealand Journal of Statistics 45 (7–18) 2003
                  Goodness-of-fit tests based on characterizations in terms of moments of order statistics
                  Morris, Kerwin; Szynal, D, Applicationes Mathematicae 29 (251–283) 2002

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