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Search the School of Mathematical SciencesPeople matching "Algebraic topology: Ktheory" 
Professor Mathai Varghese Elder Professor of Mathematics, Australian Laureate Fellow, Fellow of the Australian Academy of Scie
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Courses matching "Algebraic topology: Ktheory" 
Algebraic curves The course is an introduction to algebraic geometry and complex analytic geometry with a focus on
nonsingular algebraic curves in the complex projective plane. The high point of the course is the proof
of the RiemannRoch theorem and some of its applications. The course starts with the basic theory of
algebraic sets over an arbitrary field, Hilbert's Nullstellensatz, and the Hilbert basis theorem. We then
move on to intersection theory for curves in the projective plane, the degreegenus formula, Riemann
surfaces, divisors, and holomorphic differential forms. We show that a nonsingular planar curve has a
complex structure, leading to the formulation and proof of RiemannRoch. The special case of elliptic
curves is highlighted throughout.
Assumed knowledge: Complex Analysis III, Groups and Rings III, Topology and Analysis III.
The main reference is "Complex algebraic curves" by F. Kirwan (London Mathematical Society
Student Texts, volume 23). We will cover Chapters 26. Chapter 1 is introductory; it will not be
covered in the lectures, but you are encouraged to read it. For the first part of the course, lecture
notes on algebraic sets and Hilbert's Nullstellensatz will be supplied.
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Algebraic topology The aim of Algebraic Topology is to use algebraic structures and techniques to classify topological
spaces up to homeomorphism. Algebraic objects are associated to topological spaces in such a way
that ``natural" operations on the latter correspond to ``natural" operations on the formercontinuous
maps might correspond to group homomorphisms, homeomorphisms to isomorphisms, etc. In this
way, it is often possible to distinguish between different topological spaces by demonstrating that
certain associated algebraic objects are not isomorphic. It is rarely the case that the converse can be
shown; i.e., that two topological spaces with the same associated algebraic objects are actually
homeomorphic, but when this can be done, it is often regarded as a major triumph of the theory.
Within the realms of algebraic topology, there are several basic concepts that underly the theory and
serve as the building blocks and models for subsequent generalisation, the algebraic topology of
today being a very broad and highly generalised area that has pervaded much of contemporary
mathematics. Such concepts include homotopy, homology and cohomology, and the course will be
aimed at providing students with an introduction to these key ideas.
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Number Theory III Number theory is one of the oldest branches of mathematics. It is concerned with the properties of numbers, especially the properties of the integers. Historically, it was valued as the purest form of mathematics, but in fact there are many modern applications to information technology and cryptography. Number theory is a fundamentally useful course for any mathematician, but it also attracts a general audience because of its intrinsic beauty and its emphasis on problemsolving. Topics covered are: Divisibility and primes, congruences, arithmetic functions, continued fractions and rational approximation, quadratic residues, and primitive roots. Examples of diophantine equations. Modern applications to computer science, cryptography etc. Introduction to numbertheoretic computer packages.
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Sampling Theory and Practice III Sample surveys are an important source of statistical data. A great many published statistics on demographic, economic, political and health related characteristics are based on survey data. Simple random sampling is a well known method of sampling but, for reasons of efficiency and practical constraints, methods such as stratified sampling and cluster sampling are typically used by statistical authorities such as the Australian Bureau of Statistics and by market research organisations. This course is concerned with the design of sample surveys and the statistical analysis of data collected from such surveys. Topics covered are: experiments and surveys, steps in planning a survey; randomisation approach to sampling and estimation, sampling distribution of estimator, expected values, variances, generalisation of probability sampling; prediction approach, inadequacies of approach, decomposition of population total, concomitant variables; regression through the origin, estimation by least squares, ratio estimation, variance formulae; balance and robustness; best fit sample; stratified sampling, estimation, allocation, construction of strata, stratification on size variables, poststratification; twostage sampling, estimation, allocation, cluster sampling.
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Topology and Analysis III Solving equations is a crucial aspect of working in mathematics, physics, engineering, and many other fields. These equations might be straightforward algebraic statements, or complicated systems of differential equations, but there are some fundamental questions common to all of these settings: does a solution exist? If so, is it unique? And if we know of the existence of some specific solution, how do we determine it explicitly or as accurately as possible? This course develops the foundations required to rigorously establish the existence of solutions to various equations, thereby laying the basis for the study of solutions. Through an understanding of the foundations of analysis, we obtain insight critical in numerous areas of application, such areas ranging across physics, engineering, economics and finance. Topics covered are: sets, functions, metric spaces and normed linear spaces, compactness, connectedness, and completeness. Banach fixed point theorem and applications, uniform continuity and convergence. General topological spaces, generating topologies, topological invariants, quotient spaces. Introduction to Hilbert spaces and bounded operators on Hilbert spaces.
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Events matching "Algebraic topology: Ktheory" 
Stability of timeperiodic 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
Timeperiodic 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 perturbationtype 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 socalled
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
NavierStokes 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. 

Inconsistent Mathematics 15:10 Fri 28 Apr, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Chris Mortensen
The Theory of Inconsistency arose historically from a
number of sources, such as the semantic paradoxes including The Liar
and the settheoretic paradoxes including Russell's. But these sources
are rather too closely connected with Foundationalism: the view that
mathematics has a foundation such as logic or set theory or category
theory etc. It soon became apparent that inconsistent mathematical
structures are of interest in their own right and do not depend on the
existence of foundations. This paper will survey some of the results
in inconsistent mathematics and discuss the bearing on various
philosophical positions including Platonism, Logicism, Hilbert's
Formalism, and Brouwer's Intuitionism. 

Homological algebra and applications  a historical survey 15:10 Fri 19 May, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Amnon Neeman
Homological algebra is a curious branch of
mathematics; it is a powerful tool which has been used in many diverse
places, without any clear understanding why it should be so useful.
We will give a list of applications, proceeding chronologically: first
to topology, then to complex analysis, then to algebraic geometry,
then to commutative algebra and finally (if we have time) to
noncommutative algebra. At the end of the talk I hope to be able to
say something about the part of homological algebra on which I have
worked, and its applications. That part is derived categories. 

Good and Bad Vibes 15:10 Fri 23 Feb, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Maurice Dodson
Media...Collapsing bridges and exploding rockets have been associated with vibrations in resonance with natural frequencies. As well, the stability of the solar system and the existence of solutions of SchrÃ¶dinger\'s equation and the wave equation are problematic in the presence of resonances. Such resonances can be avoided, or at least mitigated, by using ideas from Diophantine approximation, a branch of number theory. Applications of Diophantine approximation to these problems will be given and will include a connection with LISA (Laser Interferometer Space Antenna), a spacebased gravity wave detector under construction. 

Finite Geometries: Classical Problems and Recent Developments 15:10 Fri 20 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Joseph A. Thas :: Ghent University, Belgium
In recent years there has been an increasing interest in finite projective spaces, and important applications to practical topics such as coding theory, cryptography and design of experiments have made the field even more attractive. In my talk some classical problems and recent developments will be discussed. First I will mention Segre's celebrated theorem and ovals and a purely combinatorial characterization of Hermitian curves in the projective plane over a finite field here, from the beginning, the considered pointset is contained in the projective plane over a finite field. Next, a recent elegant result on semiovals in PG(2,q), due to GÃ¡cs, will be given. A second approach is where the object is described as an incidence structure satisfying certain properties; here the geometry is not a priori embedded in a projective space. This will be illustrated by a characterization of the classical inversive plane in the odd case. Another quite recent beautiful result in Galois geometry is the discovery of an infinite class of hemisystems of the Hermitian variety in PG(3,q^2), leading to new interesting classes of incidence structures, graphs and codes; before this result, just one example for GF(9), due to Segre, was known. 

Div, grad, curl, and all that 15:10 Fri 10 Aug, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Mike Eastwood :: School of Mathematical Sciences, University of Adelaide
These wellknown differential operators are, of course, important in applied mathematics. This is just the tip of an iceberg. I shall indicate some of what lies beneath the surface. There are links with topology, physics, symmetry groups, finite element schemes, and more besides. This talk will touch on these different topics by means of examples. Little prior knowledge will be assumed beyond the equality of mixed partial derivatives. 

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 industrialscale 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.


Values of transcendental entire functions at algebraic points. 15:10 Fri 28 Mar, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Eugene Poletsky :: Syracuse University, USA
Algebraic numbers are roots of polynomials with integer coefficients, so their set is countable. All other numbers are called transcendental. Although most numbers are transcendental, it was only in 1873 that Hermite proved that the base $e$ of natural logarithms is not algebraic. The proof was based on the fact that $e$ is the value at 1 of the exponential function $e^z$ which is entire and does not change under differentiation.
This achievement raised two questions: What entire functions take only transcendental values at algebraic points? Also, given an entire transcendental function $f$, describe, or at least find properties of, the set of algebraic numbers where the values of $f$ are also algebraic. The first question, developed by Siegel, Shidlovsky, and others, led to the notion of $E$functions, which have controlled derivatives. Answering the second question, Polya and Gelfond obtained restrictions for entire functions that have integer values at integer points (Polya) or Gaussian integer values at Gaussian integer points (Gelfond). For more general sets of points only counterexamples were known.
Recently D. Coman and the speaker developed new tools for the second question, which give an answer, at least partially, for general entire functions and their values at general sets of algebraic points.
In my talk we will discuss old and new results in this direction. All relevant definitions will be provided and the talk will be accessible to postgraduates and honours students. 

Adaptive Fast Convergence  Towards Optimal Reconstruction Guarantees for Phylogenetic Trees 16:00 Tue 1 Apr, 2008 :: School Board Room :: Schlomo Moran :: Computer Science Department, Technion, Haifa, Israel
One of the central challenges in phylogenetics is to be able to reliably resolve as much of the topology of the evolutionary tree from short taxonsequences. In the past decade much attention has been focused on studying fast converging reconstruction algorithms, which guarantee (w.h.p) correct reconstruction of the entire tree from sequences of nearminimal length (assuming some accepted model of sequence evolution along the tree). The major drawback of these methods is that when the sequences are too short to correctly reconstruct the tree in its entirety, they do not provide any reconstruction guarantee for sufficiently long edges. Specifically, the presence of some very short edges in the model tree may prevent these algorithms from reconstructing even edges of moderate length.
In this talk we present a stronger reconstruction guarantee called "adaptive fast convergence", which provides guarantees for the correct reconstruction of all sufficiently long edges of the original tree. We then present a general technique, which (unlike previous reconstruction techniques) employs dynamic edgecontraction during the reconstruction of the tree. We conclude by demonstrating how this technique is used to achieve adaptive fast convergence. 

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 PantheonSorbonne
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 nonstationarity 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 nonstationarity 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 nonstationary unconditional moments or nonstationary 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 nonstationarity 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 nonstationarity on the statistics computed from the global non stationary data sets?
4. How can we analyze data sets in the nonstationary global framework? Does the asymptotic theory work in nonstationary 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 Mathematics of String Theory 15:10 Fri 2 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Peter Bouwknegt :: Department of Mathematics, ANU
String Theory has had, and continues to have, a profound impact on
many areas of mathematics and vice versa. In this talk I want to
address some relatively recent developments. In particular I will
argue, following Witten and others, that Dbrane charges take values
in the Ktheory of spacetime, rather than in integral cohomology as
one might have expected. I will also explore the mathematical
consequences of a particular symmetry, called Tduality, in this context.
I will give an intuitive introduction into Dbranes and Ktheory.
No prior knowledge about either String Theory, Dbranes or Ktheory
is required. 

Betti's Reciprocal Theorem for Inclusion and Contact Problems 15:10 Fri 1 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University
Enrico Betti (18231892) is recognized in the mathematics community for his pioneering contributions to topology. An equally important contribution is his formulation of the reciprocity theorem applicable to elastic bodies that satisfy the classical equations of linear elasticity. Although James Clerk Maxwell (18311879) proposed a law of reciprocal displacements and rotations in 1864, the contribution of Betti is acknowledged for its underlying formal mathematical basis and generality. The purpose of this lecture is to illustrate how Betti's reciprocal theorem can be used to full advantage to develop compact analytical results for certain contact and inclusion problems in the classical theory of elasticity. Inclusion problems are encountered in number of areas in applied mechanics ranging from composite materials to geomechanics. In composite materials, the inclusion represents an inhomogeneity that is introduced to increase either the strength or the deformability characteristics of resulting material. In geomechanics, the inclusion represents a constructed material region, such as a ground anchor, that is introduced to provide load transfer from structural systems. Similarly, contact problems have applications to the modelling of the behaviour of indentors used in materials testing to the study of foundations used to distribute loads transmitted from structures. In the study of conventional problems the inclusions and the contact regions are directly loaded and this makes their analysis quite straightforward. When the interaction is induced by loads that are placed exterior to the indentor or inclusion, the direct analysis of the problem becomes inordinately complicated both in terns of formulation of the integral equations and their numerical solution. It is shown by a set of selected examples that the application of Betti's reciprocal theorem leads to the development of exact closed form solutions to what would otherwise be approximate solutions achievable only through the numerical solution of a set of coupled integral equations. 

Elliptic equation for diffusionadvection flows 15:10 Fri 15 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Pavel Bedrikovsetsky :: Australian School of Petroleum Science, University of Adelaide.
The standard diffusion equation is obtained by Einstein's method and its generalisation, FokkerPlankKolmogorovFeller theory. The time between jumps in Einstein derivation is constant.
We discuss random walks with residence time distribution, which occurs for flows of solutes and suspensions/colloids in porous media, CO2 sequestration in coal mines, several processes in chemical, petroleum and environmental engineering. The rigorous application of the Einstein's method results in new equation, containing the time and the mixed dispersion terms expressing the dispersion of the particle time steps.
Usually, adding the second time derivative results in additional initial data. For the equation derived, the condition of limited solution when time tends to infinity provides with uniqueness of the Caushy problem solution.
The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advectiondispersion) equation. This is in agreement with the experimental observations and predictions of the direct simulation.


The Role of Walls in Chaotic Mixing 15:10 Fri 22 Aug, 2008 :: G03 Napier Building University of Adelaide :: Dr JeanLuc Thiffeault :: Department of Mathematics, University of Wisconsin  Madison
I will report on experiments of chaotic mixing in closed and open
vessels, in which a highly viscous fluid is stirred by a moving
rod. In these experiments we analyze quantitatively how the
concentration field of a lowdiffusivity dye relaxes towards
homogeneity, and observe a slow algebraic decay, at odds with the
exponential decay predicted by most previous studies. Visual
observations reveal the dominant role of the vessel wall, which
strongly influences the concentration field in the entire domain and
causes the anomalous scaling. A simplified 1D model supports our
experimental results. Quantitative analysis of the concentration
pattern leads to scalings for the distributions and the variance of
the concentration field consistent with experimental and numerical
results. I also discuss possible ways of avoiding the limiting role
of walls.
This is joint work with Emmanuelle Gouillart, Olivier Dauchot, and
Stephane Roux. 

Symmetrybreaking and the Origin of Species 15:10 Fri 24 Oct, 2008 :: G03 Napier Building University of Adelaide :: Toby Elmhirst :: ARC Centre of Excellence for Coral Reef Studies, James Cook University
The theory of partial differential equations can say much about generic bifurcations from spatially homogeneous steady states, but relatively little about generic bifurcations from unimodal steady states. In many applications, spatially homogeneous steady states correspond to lowenergy physical states that are destabilized as energy is fed into the system, and in these cases standard PDE theory can yield some impressive and elegant results. However, for many macroscopic biological systems such results are less useful because lowenergy states do not hold the same priviledged position as they do in physical and chemical systems. For example, speciation  the evolutionary process by which new species are formed  can be seen as the destabilization of a unimodal density distribution over phenotype space. Given the diversity of species and environments, generic results are clearly needed, but cannot be gained from PDE theory. Indeed, such questions cannot even be adequately formulated in terms of PDEs. In this talk I will introduce 'Pod Systems' which can provide an answer to the question; 'What happens, generically, when a unimodal steady state loses stability?' In the pod system formalization, the answer involves elements of equivariant bifurcation theory and suggests that new species can arise as the result of broken symmetries. 

On the HenstockKurzweil integral (along with concerns about general math education in Europe) 15:10 Fri 13 Feb, 2009 :: Napier LG28 :: Prof JeanPierre Demailly :: University of Grenoble, France
The talk will be the occasion to take a few minutes to describe the situation of math education in France and in Europe, to motivate the interest of the lecturer in trying to bring back rigorous proofs in integration theory. The remaining 45 minutes will be devoted to explaining the basics of HenstockKurzweil integration theory, which, although not a response to education problems, is a modern and elementary approach of a very strong extension of the Riemann integral, providing easy access to several fundamental results of Lebesgue theory (monotone convergence theorem, existence of Lebesgue measure, etc.). 

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 ChernWeil 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 sidesteps 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. 

Nonlinear diffusiondriven 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 densitystratified 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 normalflux 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 `diffusivelydriven' flow in a semiinfinite domain, including in the deep ocean and with turbulent effects included. More recently, Page & Johnson (2008) described a steady linear theory for the broaderscale 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. 

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.


From linear algebra to knot theory 15:10 Fri 21 Aug, 2009 :: Badger Labs G13
Macbeth Lecture Theatre :: Prof Ross Street :: Macquarie University, Sydney
Vector spaces and linear functions form our paradigmatic monoidal category. The concepts underpinning linear algebra admit definitions, operations and constructions with analogues in many other parts of mathematics. We shall see how to generalize much of linear algebra to the context of monoidal categories. Traditional examples of such categories are obtained by replacing vector spaces by linear representations of a given compact group or by sheaves of vector spaces. More recent examples come from lowdimensional topology, in particular, from knot theory where the linear functions are replaced by braids or tangles. These geometric monoidal categories are often free in an appropriate sense, a fact that can be used to obtain algebraic invariants for manifolds. 

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, ClermontFerrand, 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 "cutoff" 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.


Curved pipe flow and its stability 15:10 Fri 11 Sep, 2009 :: Badger labs G13
Macbeth Lecture Theatre :: Dr Richard Clarke :: University of Auckland
The unsteady flow of a viscous fluid through a curved pipe is a widely occuring and well studied problem. The stability of such flows, however, has largely been overlooked; this is in marked contrast to flow through a straightpipe, examination of which forms a cornerstone of hydrodynamic stability theory. Importantly, however, flow through a curved pipe exhibits an array of flow structures that are simply not present in the zero curvature limit, and it is natural to expect these to substantially impact upon the flow's stability. By considering two very different kinds of flows through a curved pipe, we illustrate that this can indeed be the case. 

Statistical analysis for harmonized development of systemic organs in human fetuses 11:00 Thu 17 Sep, 2009 :: School Board Room :: Prof Kanta Naito :: Shimane University
The growth processes of human babies have been studied
sufficiently in scientific fields, but there have still been many issues
about the developments of human fetus which are not clarified. The aim of
this research is to investigate the developing process of systemic organs of
human fetuses based on the data set of measurements of fetus's bodies and
organs. Specifically, this talk is concerned with giving a mathematical
understanding for the harmonized developments of the organs of human
fetuses. The method to evaluate such harmonies is proposed by the use of the
maximal dilatation appeared in the theory of quasiconformal mapping. 

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 noncommutativity 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 4manifold that bounds a
given 3manifold. 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.


The proof of the Poincare conjecture 15:10 Fri 25 Sep, 2009 :: Napier 102 :: Prof Terrence Tao :: UCLA
In a series of three papers from 20022003, Grigori Perelman gave a spectacular proof of the Poincare Conjecture (every smooth compact simply connected threedimensional manifold is topologically isomorphic to a sphere), one of the most famous open problems in mathematics (and one of the seven Clay Millennium Prize Problems worth a million dollars each), by developing several new groundbreaking advances in Hamilton's theory of Ricci flow on manifolds. In this talk I describe in broad detail how the proof proceeds, and briefly discuss some of the key turning points in the argument.
About the speaker:
Terence Tao was born in Adelaide, Australia, in 1975. He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal and SASTRA Ramanujan Prize in 2006, and the MacArthur Fellowship and Ostrowski Prize in 2007. Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society and the Australian Academy of Sciences (Corresponding Member). 

A FourierMukai transform for invariant differential cohomology 13:10 Fri 9 Oct, 2009 :: School Board Room :: Mr Richard Green :: University of Adelaide
FourierMukai 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 FourierMukai transform in the context of differential
geometry, which gives an isomorphism between the invariant differential
cohomology of a real torus and its dual.


Buildings 15:10 Fri 9 Oct, 2009 :: MacBeth Lecture Theatre :: Prof Guyan Robertson :: University of Newcastle, UK
Buildings were created by J. Tits in order to give a systematic geometric interpretation of simple Lie groups (and of simple algebraic groups). Buildings have since found applications in many areas of mathematics. This talk will give an informal introduction to these beautiful objects. 

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 financethe 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. 

Finite and infinite words in number theory 15:10 Fri 12 Feb, 2010 :: Napier LG28 :: Dr Amy Glen :: Murdoch University
A 'word' is a finite or infinite sequence of symbols (called 'letters') taken from a finite nonempty set (called an 'alphabet'). In mathematics, words naturally arise when one wants to represent elements from some set (e.g., integers, real numbers, padic numbers, etc.) in a systematic way. For instance, expansions in integer bases (such as binary and decimal expansions) or continued fraction expansions allow us to associate with every real number a unique finite or infinite sequence of digits.
In this talk, I will discuss some old and new results in Combinatorics on Words and their applications to problems in Number Theory. In particular, by transforming inequalities between real numbers into (lexicographic) inequalities between infinite words representing their binary expansions, I will show how combinatorial properties of words can be used to completely describe the minimal intervals containing all fractional parts {x*2^n}, for some positive real number x, and for all nonnegative integers n. This is joint work with JeanPaul Allouche (Universite ParisSud, France). 

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 wellsuited 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. 

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. 

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 algebraicgeometric 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. 

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 Gbundle 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 pseudoisomorphisms
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 algebraicgeometric 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. 

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 todo 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". 

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 Lorenz96 system, and show that
incorporating the information on the variance on some unobservable
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
unobserved 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 EulerLagrange 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. 

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 twodimensional 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, traintracks, 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 ReshetikhinTuraev 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 (BirmanMurakamiWenzl) algebras. 

The Glass Bead Game 15:10 Fri 25 Jun, 2010 :: Napier G04 :: Prof Arun Ram :: University of Melbourne
This title is taken from the novel of Hermann Hesse. In joint work with A. Kleshchev, we were amused to discover a glass bead game for constructing representations of quiver Hecke algebras (algebras recently defined by KhovanovLauda and Rouquier whose representation theory categorifies quantum groups of KacMoody Lie algebras). In fact, the glass bead game is tantalizingly simple, and may soon be marketed in your local toy store. I will explain how this game works, and some of the fascinating numerology that appears in the scoring of the plays. 

Higher nonunital Quillen K'theory 13:10 Fri 23 Jul, 2010 :: EngineeringMaths 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. 

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. 

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. 

Index theory in Mathematics and Physics 15:10 Fri 20 Aug, 2010 :: Napier G04 :: Prof Alan Carey :: Australian National University
This lecture is a personal (and partly historical) overview in nontechnical terms of the topic described in the title, from first year linear algebra to von Neumann algebras. 

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 wellknown, some notsowellknown. We will
reexamine the proof of an old theorem of Kan in light of these
functors. We will try to keep all jargon to a minimum. 

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 kalgebras (k field) to abelian groups, called KQtheory. In this talk I will explain its relationship with
topological (homological) Tdualities and twisted Ktheory. 

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 nontriviality 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). 

Totally disconnected, locally compact groups 15:10 Fri 17 Sep, 2010 :: Napier G04 :: Prof George Willis :: University of Newcastle
Locally compact groups occur in many branches of mathematics. Their study falls into two cases: connected groups, which occur as automorphisms of smooth structures such as spheres for example; and totally disconnected groups, which occur as automorphisms of discrete structures such as trees. The talk will give an overview of the currently developing structure theory of totally disconnected locally compact groups.
Techniques for analysing totally disconnected groups will be described that correspond to the familiar Lie group methods used to treat connected groups. These techniques played an essential role in the recent solution of a problem raised by R. Zimmer and G. Margulis concerning commensurated subgroups of arithmetic groups.


Principal Component Analysis Revisited 15:10 Fri 15 Oct, 2010 :: Napier G04 :: Assoc. Prof Inge Koch :: University of Adelaide
Since the beginning of the 20th century, Principal Component Analysis (PCA) has been an important tool in the analysis of multivariate data. The principal components summarise data in fewer than the original number of variables without losing essential information, and thus allow a split of the data into signal and noise components. PCA is a linear method, based on elegant mathematical theory.
The increasing complexity of data together with the emergence of fast computers in the later parts of the 20th century has led to a renaissance of PCA. The growing numbers of variables (in particular, highdimensional low sample size problems), nonGaussian data, and functional data (where the data are curves) are posing exciting challenges to statisticians, and have resulted in new research which extends the classical theory.
I begin with the classical PCA methodology and illustrate the challenges presented by the complex data that we are now able to collect. The main part of the talk focuses on extensions of PCA: the duality of PCA and the Principal Coordinates of Multidimensional Scaling, Sparse PCA, and consistency results relating to principal components, as the dimension grows. We will also look at newer developments such as Principal Component Regression and Supervised PCA, nonlinear PCA and Functional PCA.


IGAAMSI 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 Ktheory 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/ 

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). 

Heat transfer scaling and emergence of threedimensional 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 NorthSouth Hadley circulation within the atmosphere between warmer and more temperate latitudes, as well as ocean currents driven by nonuniform 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 threedimensional flow: the effect of these transitions on the NusseltRayleigh number scaling exponents is described.


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 simplyconnected 2complex such that all 2cells are regular rightangled hyperbolic pgons, 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. 

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 Ktheory groups. This is joint work with V. Mathai. 

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 socalled CRstructure, which is the remnant of the complex structure on the ambient vector space. We impose on the CRstructure the condition of sphericity. One way to state this condition is to require a certain curvature (called the CRcurvature of the hypersurface) to vanish identically. Spherical tube hypersurfaces possess remarkable properties and are of interest from both the complexgeometric and affinegeometric 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. 

Algebraic hypersurfaces arising from Gorenstein algebras 15:10 Fri 8 Apr, 2011 :: 7.15 Ingkarni Wardli :: Associate Prof Alexander Isaev :: Australian National University
Media...To every Gorenstein algebra of finite dimension greater than 1 over a field of characteristic zero, and a projection on its maximal ideal with range equal to the annihilator of the ideal, one can associate a certain algebraic hypersurface lying in the ideal. Such hypersurfaces possess remarkable properties. They can be used, for instance, to help decide whether two given Gorenstein algebras are isomorphic, which for the case of complex numbers leads to interesting consequences in singularity theory. Also, for the case of real numbers such hypersurfaces naturally arise in CRgeometry. In my talk I will discuss these hypersurfaces and some of their applications. 

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 ValueatRisk and conditional ValueatRisk as measures. However, these measures are not time consistent and ValueatRisk 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. 

Why is a pure mathematician working in biology? 15:10 Fri 15 Apr, 2011 :: Mawson Lab G19 lecture theatre :: Associate Prof Andrew Francis :: University of Western Sydney
Media...A pure mathematician working in biology should be a contradiction in
terms. In this talk I will describe how I became interested in working in
biology, coming from an algebraic background. I will also describe some
areas of evolutionary biology that may benefit from an algebraic approach.
Finally, if time permits I will reflect on the sometimes difficult
distinction between pure and applied mathematics, and perhaps venture some
thoughts on mathematical research in general. 

The ExtendedDomainEigenfunction Method: making old mathematics work for new problems 15:10 Fri 13 May, 2011 :: 7.15 Ingkarni Wardli :: Prof Stan Miklavcic :: University of South Australia
Media...Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. Several years ago I proposed a solution technique to cope with such complicated domains. It involves the embedding of the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain is then the solution of the original boundary value problem. In this talk I will present supporting theory for this idea, some numerical results for the particular case of the Laplace equation and the Stokes flow equations in twodimensions and discuss advantages and limitations of the proposal. 

From group action to Kontsevich's SwissCheese conjecture through categorification 15:10 Fri 3 Jun, 2011 :: Mawson Lab G19 :: Dr Michael Batanin :: Macquarie University
Media...The Kontsevich SwissCheese conjecture is a deep generalization of the Deligne conjecture on Hochschild cochains which plays an important role in the deformation quantization theory.
Categorification is a method of thinking about mathematics by replacing set theoretical concepts by some higher dimensional objects. Categorification is somewhat of an art because there is no exact recipe for doing this. It is, however, a very powerful method of understanding (and producing) many deep results starting from simple facts we learned as undergraduate students.
In my talk I will explain how Kontsevich SwissCheese conjecture can be easily understood as a special case of categorification of a very familiar statement: an action of a group G (more generally, a monoid) on a set X is the same as group homomorphism from G to the group of automorphisms of X (monoid of endomorphisms of X in the case of a monoid action). 

Routing in equilibrium 15:10 Tue 21 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Timothy Griffin :: University of Cambridge
Media...Some path problems cannot be modelled
using semirings because the associated
algebraic structure is not distributive. Rather
than attempting to compute globally optimal
paths with such structures, it may be sufficient
in some cases to find locally optimal paths 
paths that represent a stable local equilibrium.
For example, this is the type of routing system that
has evolved to connect Internet Service Providers
(ISPs) where link weights implement
bilateral commercial relationships between them.
Previous work has shown that routing equilibria can
be computed for some nondistributive algebras
using algorithms in the BellmanFord family.
However, no polynomial time bound was known
for such algorithms. In this talk, we show that
routing equilibria can be computed using
Dijkstra's algorithm for one class of nondistributive
structures. This provides the first
polynomial time algorithm for computing locally
optimal solutions to path problems. 

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. 

Towards RogersRamanujan identities for the Lie algebra A_n 13:10 Fri 5 Aug, 2011 :: B.19 Ingkarni Wardli :: Prof Ole Warnaar :: University of Queensland
The RogersRamanujan identities are a pair of qseries 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 RogersRamanujan 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 RogersRamanujan 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. 

The Selberg integral 15:10 Fri 5 Aug, 2011 :: 7.15 Ingkarni Wardli :: Prof Ole Warnaar :: University of Queensland
Media...In this talk I will give a gentle introduction to the mathematics surrounding the Selberg integral. Selberg's integral, which first appeared in two rather unusual papers by Atle Selberg in the 1940s, has become famous as much for its association with (other) mathematical greats such as Enrico Bombieri and Freeman Dyson as for its importance in algebra (Coxeter groups), geometry (hyperplane arrangements) and number theory (the Riemann hypothesis). In this talk I will review the remarkable history of the Selberg integral and discuss some of its early applications. Time permitting I will end the talk by describing some of my own, ongoing work on Selberg integrals related to Lie algebras. 

AustMS/AMSI Mahler Lecture: Chaos, quantum mechanics and number theory 18:00 Tue 9 Aug, 2011 :: Napier 102 :: Prof Peter Sarnak :: Institute for Advanced Study, Princeton
Media...The correspondence principle in quantum mechanics
is concerned with the relation between a mechanical
system and its quantization.
When the mechanical system are relatively orderly ("integrable"), then this relation is well understood. However when the system is chaotic much less is understood. The key
features already appear and are well illustrated in the simplest systems which we will review. For chaotic systems defined numbertheoretically, much more is understood and the basic problems are connected with central questions in number theory.
The Mahler lectures are a biennial activity organised by the Australian Mathematical Society with the assistance of the Australian Mathematical Sciences Institute.


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 timevarying 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 nearlysteady compressible flows.


There are no magnetically charged particlelike solutions of the EinsteinYangMills 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. particlelike) solutions with nonzero total magnetic charge are not expected to exist in EinsteinYangMills 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 nonexistence results apply to the most widely studied models with Abelian residual groups. 

Comparing Einstein to Newton via the postNewtonian expansions 15:10 Fri 19 Aug, 2011 :: 7.15 Ingkarni Wardli :: Dr Todd Oliynyk :: Monash University
Media...Einstein's general relativity is presently the most accurate theory of gravity. To completely determine the gravitational field, the Einstein field equations must be solved. These equations are extremely complex and outside of a small set of idealized situations, they are impossible to solve directly. However, to make physical predictions or understand physical phenomena, it is often enough to find approximate solutions that are governed by a simpler set of equations. For example, Newtonian gravity approximates general relativity very well in regimes where the typical velocity of the gravitating matter is small compared to the speed of light. Indeed, Newtonian gravity successfully explains much of the behaviour of our solar system and is a simpler theory of gravity. However, for many situations of interest ranging from binary star systems to GPS satellites, the Newtonian approximation is not accurate enough; general relativistic effects must be included. This desire to include relativistic corrections to Newtonian gravity lead to the development of the postNewtonian expansions. 

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 nonalgebraic hypersurfaces. We provide a complete answer to this question for complements of hyperplane arrangements, and some results for graphs of meromorphic functions. 

IGAAMSI Workshop: Groupvalued moment maps with applications to mathematics and physics 10:00 Mon 5 Sep, 2011 :: 7.15 Ingkarni Wardli
Media...Lecture series by Eckhard Meinrenken, University of Toronto.
Titles of individual lectures: 1) Introduction to Gvalued moment maps. 2) Dirac geometry and Witten's volume formulas.
3) DixmierDouady theory and prequantization. 4) Quantization of groupvalued moment maps. 5) Application to Verlinde formulas. These lectures will be supplemented by additional talks by invited speakers. For more details, please see the conference webpage. 

Twisted Morava Ktheory 13:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne
Morava's extraordinary Ktheories K(n) are a family of generalized cohomology theories which behave in some ways like Ktheory (indeed, K(1) is mod 2 Ktheory). Their construction exploits Quillen's description of cobordism in terms of formal group laws and LubinTate's methods in class field theory for constructing abelian extensions of number fields. Constructed from homotopytheoretic methods, they do not admit a geometric description (like deRham cohomology, Ktheory, 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 Ktheory in this setting. Traditionally, Ktheory is twisted by a threedimensional cohomology class; in this case, K(n) admits twists by (n+2)dimensional classes. This work is joint with Hisham Sati. 

Configuration spaces in topology and geometry 15:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne
Media...Configuration spaces of points in R^n give a family of interesting geometric objects. They and their variants have numerous applications in geometry, topology, representation theory, and number theory. In this talk, we will review several of these manifestations (for instance, as moduli spaces, function spaces, and the like), and use them to address certain conjectures in number theory regarding distributions of number fields. 

Tduality via bundle gerbes I 13:10 Fri 23 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide
In physics Tduality 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 Hflux). In this talk we will use bundle gerbes to give a geometric realisation of the Hflux and explain how to construct the Tdual of a line bundle together with its Tdual bundle gerbe. 

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. 

Tduality via bundle gerbes II 13:10 Fri 21 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide
In physics Tduality 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 Hflux). In this talk we will use bundle gerbes to give a geometric realisation of the Hflux and explain how to construct the Tdual of a line bundle together with its Tdual bundle gerbe. 

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 Ktheory. Ultimately the aim is to produce a
projective family of Fredholm operators realising elements in twisted Ktheory
of a certain moduli stack. 

Oka theory of blowups 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 recentlyobtained 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 :: BenGurion 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 threedimensional flows (exact
solutions of the NavierStokes equations)
is studied via separation of variables using a semianalytical, seminumerical 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 stagnationtype 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 lowdimensional topology. 

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=Xp
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.) 

String Theory and the Quest for Quantum Spacetime 15:10 Fri 9 Mar, 2012 :: Ligertwood 333 Law Lecture Theatre 2 :: Prof Rajesh Gopakumar :: HarishChandra Research Institute
Media...Space and time together constitute one of the most basic
elements of physical reality. Since Einstein spacetime has become an
active participant in the dynamics of the gravitational force.
However, our notion of a quantum spacetime is still rudimentary.
String theory, building upon hints provided from the physics of black
holes, seems to be suggesting a very novel, "holographic" picture of
what quantum spacetime might be. This relies on some very surprising
connections of gravity with quantum field theories (which provide the
framework for the description of the other fundamental interactions of
nature). In this talk, I will try and convey some of the flavour of
these connections as well as its significance. 

The Lorentzian conformal analogue of CalabiYau manifolds 13:10 Fri 16 Mar, 2012 :: B.20 Ingkarni Wardli :: Prof Helga Baum :: Humboldt University
CalabiYau manifolds are Riemannian manifolds with holonomy group SU(m). They are Ricciflat and Kahler and admit a 2parameter 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 CalabiYau manifolds. Such Lorentzian
metrics g, known as Fefferman metrics, appear on S^1bundles over strictly pseudoconvex CR spin manifolds and admit a 2parameter family of conformal Killing spinors.


IGA Workshop: Dualities in field theories and the role of Ktheory 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. 

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. 

Bundle gerbes and the FaddeevMickelssonShatashvili anomaly 13:10 Fri 30 Mar, 2012 :: B.20 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide
The FaddeevMickelssonShatashvili 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 noncentral. 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 (noncentral) lifting problem directly. This is joint work with Pedram Hekmati, Michael Murray and Danny Stevenson. 

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 BaumslagSolitar
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. 

What is a selfsimilar group? 15:10 Fri 20 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Murray Elder :: University of Newcastle
Media...I will give a brief introduction to the theory of
selfsimilar groups, focusing on a couple of pertinent examples:
Grigorchuk's group of intermediate growth, and the basilica group.


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.


Index type invariants for twisted signature complexes 13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide
AtiyahPatodiSinger proved an index theorem for nonlocal 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. 

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
lowdimensional topology. Here we study the problem of finding a taut
structure on a 3manifold 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 NPcomplete.
We also prove that detecting taut structures is "not too hard", by showing
it to be fixedparameter tractable. This is joint work with Jonathan Spreer.


Unknot recognition and the elusive polynomial time algorithm 15:10 Fri 18 May, 2012 :: B.21 Ingkarni Wardli :: Dr Benjamin Burton :: The University of Queensland
Media...What do practical topics such as linear programming and greedy
heuristics have to do with theoretical problems such as unknot
recognition and the Poincare conjecture? In this talk we explore new
approaches to old and difficult computational problems from geometry and
topology: how to tell whether a loop of string is knotted, or whether a
3dimensional space has no interesting topological features. Although
the best known algorithms for these problems run in exponential time,
there is increasing evidence that a polynomial time solution might be
possible. We outline several promising approaches in which
computational geometry, linear programming and greedy algorithms all
play starring roles. 

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 RiskNeutral 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 reformulate 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. 

Adventures with group theory: counting and constructing polynomial invariants for applications in quantum entanglement and molecular phylogenetics 15:10 Fri 8 Jun, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Jarvis :: The University of Tasmania
Media...In many modelling problems in mathematics and physics, a standard
challenge is dealing with several repeated instances of a system under
study. If linear transformations are involved, then the machinery of
tensor products steps in, and it is the job of group theory to control how
the relevant symmetries lift from a single system, to having many copies.
At the level of group characters, the construction which does this is
called PLETHYSM.
In this talk all this will be contextualised via two case studies:
entanglement invariants for multipartite quantum systems, and Markov
invariants for tree reconstruction in molecular phylogenetics. By the end
of the talk, listeners will have understood why Alice, Bob and Charlie
love Cayley's hyperdeterminant, and they will know why the three squangles
 polynomial beasts of degree 5 in 256 variables, with a modest 50,000
terms or so  can tell us a lot about quartet trees! 

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 2hour 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 nontrivial results were established. For instance, it was established that dendroidal sets provide models for homotopy operads in a way that extends the JoyalLurie approach to homotopy categories. It can be shown that dendroidal sets provide new models in the study of nfold 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 noncommutative topology with the aim of providing a concrete noncommutative 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. 

Ktheory 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 selfadjoint 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 lowdimensional 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 antiholomorphic 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.


The BanachTarski Paradox 11:10 Mon 30 Jul, 2012 :: G.07 Engineering Mathematics :: Mr William Crawford :: University of Adelaide
Media...The BanachTarski 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 nonmeasurable, 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 nonempty 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 propertieswith 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 nonexplicit. 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 padic 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 nontopological cohomology theories. 

Geometry  algebraic to arithmetic to absolute 15:10 Fri 3 Aug, 2012 :: B.21 Ingkarni Wardli :: Dr James Borger :: Australian National University
Media...Classical algebraic geometry is about studying solutions to systems of polynomial equations with complex coefficients. In arithmetic algebraic geometry, one digs deeper and studies the arithmetic properties of the solutions when the coefficients are rational, or even integral. From the usual point of view, it's impossible to go deeper than this for the simple reason that no smaller rings are available  the integers have no proper subrings. In this talk, I will explain how an emerging subject, lambdaalgebraic geometry, allows one to do just this and why one might care. 

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 Temperaturedependent 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 NavierStokes
equation we provide a theory that describes the nature of this instability
and explains the seemingly counterintuitive behavior.


The fundamental theorems of invariant theory, classical and quantum 15:10 Fri 10 Aug, 2012 :: B.21 Ingkarni Wardli :: Prof Gus Lehrer :: The University of Sydney
Media... Let V = C^n, and let (,) be a nondegenerate bilinear form
on V , which is either symmetric or antisymmetric. Write G for the isometry
group of (V , (,)); thus G = O_n (C) or Sp_n (C). The first fundamental
theorem (FFT) provides a set of generators for End_G(V^{\otimes r} ) (r = 1, 2, . . . ),
while the second fundamental theorem (SFT) gives all relations among the
generators. In 1937, Brauer formulated the FFT in terms of his celebrated
'Brauer algebra' B_r (\pm n), but there has hitherto been no similar version of
the SFT. One problem has been the generic nonsemisimplicity of B_r (\pm n),
which caused H Weyl to call it, in his work on invariants 'that enigmatic
algebra'. I shall present a solution to this problem, which shows that there is
a single idempotent in B_r (\pm n), which describes all the relations. The proof
is through a new 'Brauer category', in which the fundamental theorems are
easily formulated, and where a calculus of tangles may be used to prove these
results. There are quantum analogues of the fundamental theorems which I
shall also discuss. There are numerous applications in representation theory,
geometry and topology. This is joint work with Ruibin Zhang. 

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 surfacestrying to fill in a gap
in the EnriquesKodaira classification.
Attempting to classify some collection of mathematical
objects is a very common activity for pure mathematicians,
and there are many wellknown examples of successful
classification schemes; for example, the classification of
finite simple groups, and the classification of simply
connected topological 4manifolds.
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. 

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. 

Two classes of network structures that enable efficient information transmission 15:10 Fri 7 Sep, 2012 :: B.20 Ingkarni Wardli :: A/Prof Sanming Zhou :: The University of Melbourne
Media...What network topologies should we use in order to achieve efficient information transmission? Of course answer to this question depends on how we measure efficiency of information dissemination. If we measure it by the minimum gossiping time under the storeandforward, allport and fullduplex model, we show that certain Cayley graphs associated with Frobenius groups are `perfect' in a sense. (A Frobenius group is a permutation group which is transitive but not regular such that only the identity element can fix two points.) Such graphs are also optimal for alltoall routing in the sense that the maximum load on edges achieves the minimum. In this talk we will discuss this theory of optimal network design. 

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! 

Quantisation commutes with reduction 15:10 Fri 14 Sep, 2012 :: B.20 Ingkarni Wardli :: Dr Peter Hochs :: Leibniz University Hannover
Media...The "Quantisation commutes with reduction" principle is an idea from physics, which has powerful applications in mathematics. It basically states that the ways in which symmetry can be used to simplify a physical system in classical and quantum mechanics, are compatible. This provides a strong link between the areas in mathematics used to describe symmetry in classical and quantum mechanics: symplectic geometry and representation theory, respectively. It has been proved in the 1990s that quantisation indeed commutes with reduction, under the important assumption that all spaces and symmetry groups involved are compact. This talk is an introduction to this principle and, if time permits, its mathematical relevance. 

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 nonstationary iterative methods which are currently the methodsofchoice 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. 

Electrokinetics of concentrated suspensions of spherical particles 15:10 Fri 28 Sep, 2012 :: B.21 Ingkarni Wardli :: Dr Bronwyn BradshawHajek :: 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 selfconsistent cellmodel 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 cellmodel leads to some interesting conclusions. 

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 4fold and use it to give a description of the BRST transformations, to compute the "supermeasure" of the moduli space, and the Nekrasov partition function. 

Moduli spaces of instantons in algebraic geometry and physics 15:10 Fri 19 Oct, 2012 :: B.20 Ingkarni Wardli :: Prof Ugo Bruzzo :: International School for Advanced Studies Trieste
Media...I will give a quick introduction to the notion of instanton, stressing its role in physics and in mathematics.
I will also show how algebraic geometry provides powerful tools to study the geometry of the moduli spaces of instantons. 

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 Cconnectedness. 

Numerical Free Probability: Computing Eigenvalue Distributions of Algebraic Manipulations of Random Matrices 15:10 Fri 2 Nov, 2012 :: B.20 Ingkarni Wardli :: Dr Sheehan Olver :: The University of Sydney
Media...Suppose that the global eigenvalue distributions
of two large random matrices A and B are known. It is a
remarkable fact that, generically, the eigenvalue distribution
of A + B and (if A and B are positive definite) A*B are
uniquely determined from only the eigenvalue distributions
of A and B; i.e., no information about eigenvectors are
required. These operations on eigenvalue distributions
are described by free probability theory. We construct a
numerical toolbox that can efficiently and reliably
calculate these operations with spectral accuracy, by
exploiting the complex analytical framework that underlies
free probability theory.


Modern trends in dynamo theory 15:10 Fri 16 Nov, 2012 :: B.20 Ingkarni Wardli :: Prof Michael Proctor :: University of Cambridge
Media...Dynamo action is the process by which magnetic fields in astrophysical bodies (and recently, laboratory fluids) are maintained against resistive losses by Faraday induction. For many years a favoured model of this process, known as meanfield electrodynamics, has been widely used to produce tractable models. I shall present a critique of this theory and contrast it it with another dynamo process (small scale dynamo action) that does not, unlike meanfield electrodynamics, rely on broken reflection symmetry or scale separation. Finally, I shall talk about very recent rigorous results concerning the Archontis dynamo, in which the magnetic and velocity fields are closely aligned.


Twisted analytic torsion and adiabatic limits 13:10 Wed 5 Dec, 2012 :: Ingkarni Wardli B17 :: Mr Ryan Mickler :: University of Adelaide
We review MathaiWu's recent extension of RaySinger 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 MathaiWu's paper.


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 FeichtnerSturmfels, FeichtnerYuzvinsky, ArdilaKlivans, and others). Recently, these ideas have played a role in Huh and Katz's proof of a longstanding 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. 

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 theory and the harmonic hull 15:10 Fri 8 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Michael Eastwood :: Australian National University
Media...Harmonic functions are realanalytic and so automatically extend as functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated conformal geometry. Nothing will be supposed about such matters: I shall base the constructions on an elementary yet mysterious formula of Bateman from 1904. This is joint work with Feng Xu. 

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 welldefined expressions. 

How fast? Bounding the mixing time of combinatorial Markov chains 15:10 Fri 22 Mar, 2013 :: B.18 Ingkarni Wardli :: Dr Catherine Greenhill :: University of New South Wales
Media...A Markov chain is a stochastic process which is "memoryless",
in that the next state of the chain depends only on the current state,
and not on how it got there. It is a classical result that an ergodic
Markov chain has a unique stationary distribution.
However, classical theory does not provide any information on the rate of
convergence to stationarity. Around 30 years ago, the mixing time of
a Markov chain was introduced to measure the number of steps required
before the distribution of the chain is within some small distance of
the stationary distribution. One reason why this is important is that
researchers in areas such as physics and biology use Markov chains to
sample from large sets of interest. Rigorous bounds on the mixing time
of their chain allows these researchers to have confidence in their results.
Bounding the mixing time of combinatorial Markov chains can be a challenge, and there are only a few approaches available. I will discuss the main methods and give examples for each (with pretty pictures). 

Gauge groupoid cocycles and CheegerSimons 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 2cocycle 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 CheegerSimons differential characters. 

A stability theorem for elliptic Harnack inequalities 15:10 Fri 5 Apr, 2013 :: B.18 Ingkarni Wardli :: Prof Richard Bass :: University of Connecticut
Media...Harnack inequalities are an important tool in probability theory,
analysis, and partial differential equations. The classical Harnack
inequality is just the one you learned in your graduate complex analysis
class, but there have been many extensions, to different spaces, such as
manifolds, fractals, infinite graphs, and to various sorts of elliptic operators.
A landmark result was that of Moser in 1961, where he proved the Harnack
inequality for solutions to a class of partial differential equations.
I will talk about the stability of Harnack inequalities. The main result
says that if the Harnack inequality holds for an operator on a space,
then the Harnack inequality will also hold for a large class of other operators
on that same space. This provides a generalization of the result of Moser. 

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. 

Mtheory and higher gauge theory 13:10 Fri 12 Apr, 2013 :: Ingkarni Wardli B20 :: Dr Christian Saemann :: HeriotWatt University
I will review my recent work on integrability of Mbrane configurations and
the description of Mbrane models in higher gauge theory. In particular, I
will discuss categorified analogues of instantons and present superconformal equations of motion for the nonabelian tensor multiplet in six dimensions. The latter are derived from considering nonabelian gerbes on certain twistor spaces. 

A glimpse at the Langlands program 15:10 Fri 12 Apr, 2013 :: B.18 Ingkarni Wardli :: Dr Masoud Kamgarpour :: University of Queensland
Media...Abstract: In the late 1960s, Robert Langlands made a series of surprising conjectures relating fundamental concepts from number theory, representation theory, and algebraic geometry. Langlands' conjectures soon developed into a highprofile international research program known as the Langlands program. Many fundamental problems, including the ShimuraTaniyamaWeil conjecture (partially settled by Andrew Wiles in his proof of the Fermat's Last Theorem), are particular cases of the Langlands program. In this talk, I will discuss some of the motivation and results in this program. 

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 wellapproximated 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". 

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. 

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 nonobservable Markov process. So in order to prices some financial product, we have to use some of the filtering theory to deal with the nonobservable process, these techniques are gaining very much of interest from practitioners and researchers in the field of financial mathematics. 

Neuronal excitability and canards 15:10 Fri 10 May, 2013 :: B.18 Ingkarni Wardli :: A/Prof Martin Wechselberger :: University of Sydney
Media...The notion of excitability was first introduced in an attempt to understand firing properties of neurons. It was Alan Hodgkin who identified three basic types (classes) of excitable axons (integrator, resonator and differentiator) distinguished by their different responses to injected steps of currents of various amplitudes.
Pioneered by Rinzel and Ermentrout, bifurcation theory explains repetitive (tonic) firing patterns for adequate steady inputs in integrator (type I) and resonator (type II) neuronal models. In contrast, the dynamic behavior of differentiator (type III) neurons cannot be explained by standard dynamical systems theory. This third type of excitable neuron encodes a dynamic change in the input and leads naturally to a transient response of the neuron.
In this talk, I will show that "canards"  peculiar mathematical creatures  are well suited to explain the nature of transient responses of neurons due to dynamic (smooth) inputs. I will apply this geometric theory to a simple driven FitzHughNagumo/MorrisLecar type neural model and to a more complicated neural model that describes paradoxical excitation due to propofol anesthesia. 

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 ndimensional
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 spacefilling crystal pattern.
For higher dimensions, Hilbert posed his famous 18th problem:
"Is there in ndimensional 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 torsionfree,
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.


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 pseudoRiemannian manifolds.
Still more generally, one might study group of affine transformation on nspace
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 pseudoRiemannian
spaces. 

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. 

Invariant Theory: The 19th Century and Beyond 15:10 Fri 21 Jun, 2013 :: B.18 Ingkarni Wardli :: Dr Jarod Alper :: Australian National University
Media...A central theme in 19th century mathematics was invariant theory, which was viewed as a bridge between geometry and algebra. David Hilbert revolutionized the field with two seminal papers in 1890 and 1893 with techniques such as Hilbert's basis theorem, Hilbert's Nullstellensatz and Hilbert's syzygy theorem that spawned the modern field of commutative algebra. After Hilbert's groundbreaking work, the field of invariant theory remained largely inactive until the 1960's when David Mumford revitalized the field by reinterpreting Hilbert's ideas in the context of algebraic geometry which ultimately led to the influential construction of the moduli space of smooth curves. Today invariant theory remains a vital research area with connections to various mathematical disciplines: representation theory, algebraic geometry, commutative algebra, combinatorics and nonlinear differential operators.
The goal of this talk is to provide an introduction to invariant theory with an emphasis on Hilbert's and Mumford's contributions. Time permitting, I will explain recent research with Maksym Fedorchuk and David Smyth which exploits the ideas of Hilbert, Mumford as well as Kempf to answer a classical question concerning the stability of algebraic 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 HarishChandra), aspects of noncommutative geometry (in the sense of Alain Connes) and aspects of operator Ktheory (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. 

Khomology 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 mid1990s 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 Khomology theory that are studied in noncommutative geometry. I shall try to make the case for Khomology as a useful conceptual framework for the solutions and (at least some of) their various generalizations. 

Quantization, Representations and the Orbit Philosophy 15:10 Fri 5 Jul, 2013 :: B.18 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University
Media...This talk will be about the mathematics of quantization and about representation theory, where the concept of quantization seems to be especially relevant. It was discovered by Kirillov in the 1960's that the representation theory of nilpotent Lie groups (such as the group that encodes Heisenberg's commutation relations) can be beautifully and efficiently described using a vocabulary drawn from geometry and quantum mechanics. The description was soon adapted to other classes of Lie groups, and the expectation that it ought to apply almost universally has come to be called the "orbit philosophy." But despite early successes, the orbit philosophy is in a decidedly unfinished state. I'll try to explain some of the issues and some possible new directions. 

The search for the exotic  subfactors and conformal field theory 13:10 Fri 26 Jul, 2013 :: EngineeringMaths 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, WessZuminoWitten models and finite groups. 

Subfactors and twisted equivariant Ktheory 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. FreedHopkinsTeleman have expressed the Verlinde ring for the CFTs associated to loop groups as twisted equivariant Ktheory. In joint work with Terry Gannon, we build on their work to express Ktheoretically 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), alphainduction etc. 

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. 

A survey of nonabelian 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 Gbundles 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. 

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 Gbundles, 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  Tduality. This is joint work with Pedram Hekmati. 

The LowenheimSkolem 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 LowenheimSkolem 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. 

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 (WeilPetersson 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 WeilPetersson metric, hyperbolicity of moduli spaces, and construction of positive/ample line bundles on compactified moduli spaces can be answered. 

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. 

Knots and Quantum Computation 15:10 Fri 6 Sep, 2013 :: B.18 Ingkarni Wardli :: Dr Scott Morrison :: Australian National University
Media...I'll begin with the Jones polynomial, a knot invariant discovered 30 years ago that radically changed our view of topology. From there, we'll visit the complexity of evaluating the Jones polynomial, the topological field theories related to the Jones polynomial, and how all these ideas come together to offer an unorthodox model for quantum computation. 

Ktheory 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 ninefold 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 Ktheory. In this talk I shall give a survey of the ideas, and a brief outline of work with Guo Chuan Thiang. 

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 PoincareEinstein metrics. The results are formulated in terms of Weyl conformal invariants defined via the ambient metric of FeffermanGraham. 

Symmetry gaps for geometric structures 15:10 Fri 20 Sep, 2013 :: B.18 Ingkarni Wardli :: Dr Dennis The :: Australian National University
Media...Klein's Erlangen program classified geometries based on their (transitive) groups of symmetries, e.g. Euclidean geometry is the quotient of the rigid motion group by the subgroup of rotations. While this perspective is homogeneous, Riemann's generalization of Euclidean geometry is in general very "lumpy"  i.e. there exist Riemannian manifolds that have no symmetries at all. A common generalization where a group still plays a dominant role is Cartan geometry, which first arose in Cartan's solution to the equivalence problem for geometric structures, and which articulates what a "curved version" of a flat (homogeneous) model means. Parabolic geometries are Cartan geometries modelled on (generalized) flag varieties (e.g. projective space, isotropic Grassmannians) which are wellknown objects from the representation theory of semisimple Lie groups. These curved versions encompass a zoo of interesting geometries, including conformal, projective, CR, systems of 2nd order ODE, etc. This interaction between differential geometry and representation theory has proved extremely fruitful in recent years. My talk will be an examplebased tour of various types of parabolic geometries, which I'll use to outline some of the main aspects of the theory (suppressing technical details). The main thread throughout the talk will be the symmetry gap problem: For a given type of Cartan geometry, the maximal symmetry dimension is realized by the flat model, but what is the next possible ("submaximal") symmetry dimension? I'll sketch a recent solution (in joint work with Boris Kruglikov) for a wide class of parabolic geometries which gives a combinatorial recipe for reading the submaximal symmetry dimension from a Dynkin diagram. 

The irrational line on the torus 12:35 Mon 23 Sep, 2013 :: B.19 Ingkarni Wardli :: Kelli FrancisStaite :: 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 counterexamples. 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? 

Dynamics and the geometry of numbers 14:10 Fri 27 Sep, 2013 :: Horace Lamb Lecture Theatre :: Prof Akshay Venkatesh :: Stanford University
Media...It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in R^n. (A lattice is simply a grid of points.) This technique is called the "geometry of numbers." We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects. 

Modelling and optimisation of group doseresponse 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 doseresponse challenge experiments for the bacteria Campylobacter jejuni in chickens. 

The geometry of rolling surfaces and nonholonomic mechanics 15:10 Fri 1 Nov, 2013 :: B.18 Ingkarni Wardli :: Prof Robert Bryant :: Duke University
Media...In mechanics, the system of a sphere rolling over a plane without slipping or twisting is a fundamental example of what is called a nonholonomic mechanical system, the study of which belongs to the subject of control theory. The more general case of one surface rolling over another without slipping or twisting is, similarly, of great interest for both practical and theoretical reasons. In this talk, which is intended for a general mathematical audience (i.e., no familiarity with control theory or differential geometry will be assumed), I will describe some of the basic features of this problem, a bit of its history, and some of the surprising developments that its study reveals, such as the unexpected appearance of the exceptional group G_2. 

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.


A few flavours of optimal control of Markov chains 11:00 Thu 12 Dec, 2013 :: B18 :: Dr Sam Cohen :: Oxford University
Media...In this talk we will outline a general view of optimal control of a continuoustime Markov chain, and how this naturally leads to the theory of Backward Stochastic Differential Equations. We will see how this class of equations gives a natural setting to study these problems, and how we can calculate numerical solutions in many settings. These will include problems with payoffs with memory, with random terminal times, with ergodic and infinitehorizon value functions, and with finite and infinitely many states. Examples will be drawn from finance, networks and electronic engineering. 

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. 

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. 

Scattering theory and noncommutative geometry 01:10 Mon 31 Mar, 2014 :: Ingkarni Wardli B20 :: Alan Carey :: Australian National University


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. 

TDuality 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 3cocycle H, Tduality yields another manifold with a torus action and integral 3cocyle. It induces a number of surprising automorphisms between structures on these manifolds. In this talk I will review Tduality and describe some work on two generalizations which are realized in string theory: NS5branes and heterotic strings. These respectively correspond to nonclosed 3classes H and to principal bundles fibered over M. 

A generalised KacPeterson cocycle 11:10 Thu 17 Apr, 2014 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide
The KacPeterson 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 Ktheory. This is joint work with Jouko Mickelsson. 

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 Diracdual Dirac method to derive the Lefschetz number on Ktheory 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. 

A geometric model for odd differential Ktheory 12:10 Fri 9 May, 2014 :: Ingkarni Wardli B20 :: Raymond Vozzo :: University of Adelaide
Odd Ktheory has the interesting property thatunlike even Ktheoryit admits an infinite number of inequivalent differential refinements. In this talk I will give a description of odd differential Ktheory 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. 

Computing with groups 15:10 Fri 30 May, 2014 :: B.21 Ingkarni Wardli :: Dr Heiko Dietrich :: Monash University
Media...Groups are algebraic structures which show up in many branches of
mathematics and other areas of science; Computational Group Theory is
on the cutting edge of pure research in group theory and its interplay
with computational methods.
In this talk, we consider a practical aspect
of Computational Group Theory: how to represent a group in a computer,
and how to work with such a description efficiently. We will first
recall some wellestablished methods for permutation group; we will
then discuss some recent progress for matrix groups. 

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 infinitedimensional manifold in any recognised sense. Still, our work shows that in some ways it behaves like a finitedimensional Oka manifold. 

Not nots, knots. 12:10 Mon 16 Jun, 2014 :: B.19 Ingkarni Wardli :: Luke KeatingHughes :: 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. 

Fast computation of eigenvalues and eigenfunctions on bounded plane domains 15:10 Fri 1 Aug, 2014 :: B.18 Ingkarni Wardli :: Professor Andrew Hassell :: Australian National University
Media...I will describe a new method for numerically computing eigenfunctions and eigenvalues on certain plane domains, derived from the socalled "scaling method" of Vergini and Saraceno. It is based on properties of the DirichlettoNeumann map on the domain, which relates a function f on the boundary of the domain to the normal derivative (at the boundary) of the eigenfunction with boundary data f. This is a topic of independent interest in pure mathematics. In my talk I will try to emphasize the inteplay between theory and applications, which is very rich in this situation. This is joint work with numerical analyst Alex Barnett (Dartmouth). 

Hydrodynamics and rheology of selfpropelled colloids 15:10 Fri 8 Aug, 2014 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide
The subcellular 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 nonequilibrium 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 selfpropelled particles of an arbitrary shape from first principles, in a sufficiently dilute suspension limit, moving in a 3dimensional space inside a viscous solvent. The model is then restricted to particles with ellipsoidal geometry to quantify the interplay of the longrange excluded volume and the shortrange selfpropulsion 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 timestepping to determine the dynamical phases/structures as well as phasetransitions 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.


Boundaryvalue problems for the Ricci flow 15:10 Fri 15 Aug, 2014 :: B.18 Ingkarni Wardli :: Dr Artem Pulemotov :: The University of Queensland
Media...The Ricci flow is a differential equation describing the evolution of a Riemannian manifold (i.e., a "curved" geometric object) into an Einstein manifold (i.e., an object with a "constant" curvature). This equation is particularly famous for its key role in the proof of the Poincare Conjecture. Understanding the Ricci flow on manifolds with boundary is a difficult problem with applications to a variety of fields, such as topology and mathematical physics. The talk will survey the current progress towards the resolution of this problem. In particular, we will discuss new results concerning spaces with symmetries. 

Quasimodes that do not Equidistribute 13:10 Tue 19 Aug, 2014 :: Ingkarni Wardli B17 :: Shimon Brooks :: BarIlan University
The QUE Conjecture of RudnickSarnak 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 highlydegenerate 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. 

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 logicbased 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. 

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. 

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 continuoustime Markov chain (CTMC), how to adapt a Markov chain to include nonmemoryless distributions, how to simulate CTMC's and some key results. 

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 noncompact Riemann surfaces are Stein; which loosely speaking means that their function theory is similar to that of C. 

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. 

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 shocklike travelling wave solutions for two advectionreactiondiffusion 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 shockfronted 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 SerreGrothendieck theorem by geometric means 12:10 Fri 24 Oct, 2014 :: Ingkarni Wardli B20 :: David Roberts :: University of Adelaide
The SerreGrothendieck theorem implies that every torsion
integral 3rd cohomology class on a finite CWcomplex 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 Ktheory. 

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 highprofile 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 remotesensing of populationlevel 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 largescale 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 highprofile 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 remotesensing of populationlevel 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 largescale 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. 

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. 

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. 

Symmetric groups via categorical representation theory 15:10 Fri 20 Mar, 2015 :: Engineering North N132 :: Dr Oded Yacobi :: University of Sydney
The symmetric groups play a fundamental role in representation theory and, while their characteristic zero representations are well understood, over fields of positive characteristic most foundational questions are still unanswered. In the 1990's Kleshchev made a spectacular breakthrough, and computed certain modular restriction multiplicities. It was observed by Lascoux, Leclerc, and Thibon that Kleshchev's numerology encodes a seemingly unrelated object: the crystal graph associated to an affine Lie algebra! We will explain how this mysterious connection opens the door to categorical representation theory, and, moreover, how the categorical perspective allows one to prove new theorems about representations of symmetric groups. We will also discuss other problems/applications in the landscape of categorical representation theory. 

Topological matter and its Ktheory 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 Ktheory provides a powerful language for describing quantum mechanical symmetries, homotopies of their realisations, and topological insulators. Real Ktheory 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 Ktheory to the ADHM construction of instantons/holomorphic bundles to extend the BraamAustin 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. 

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. FigueroaO'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 worldleading scientists from both, geometry and mathematical physics, as well as young researchers and students, to meet and learn about each others work. 

Spherical Tduality: the nonprincipal case 12:10 Fri 1 May, 2015 :: Napier 144 :: Mathai Varghese :: University of Adelaide
Spherical Tduality is related to Mtheory 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 nonprincipal case for most of the talk, ending with the relation to SUGRA/Mtheory. 

Big things are weird 12:10 Mon 25 May, 2015 :: Napier LG29 :: Luke KeatingHughes :: 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) noncontractible 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. 

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 nonabelian 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. 

Instantons and Geometric Representation Theory 12:10 Thu 23 Jul, 2015 :: Engineering and Maths EM212 :: Professor Richard Szabo :: HeriotWatt University
We give an overview of the various approaches to studying
supersymmetric quiver gauge theories on ALE spaces, and their conjectural
connections to twodimensional conformal field theory via AGTtype
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 infinitedimensional
Lie algebras. We introduce an orbifold compactification of the minimal
resolution of the Atype 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 Gspaces is given by Bott, defined as the index of the SpincDirac operator on the manifold. In this talk, I will explain how to generalize this idea to the Hamiltonian LGspaces. Instead of quantizing infinitedimensional manifolds directly, we use its equivalent finitedimensional model, the quasiHamiltonian Gspaces. By constructing twisted spinor bundle and twisted prequantum bundle on the quasiHamiltonian Gspace, 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 LGspaces 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 farreaching and powerful results. This workshop features a large number of international speakers, who are all wellknown 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. 

Dynamics on Networks: The role of local dynamics and global networks on hypersynchronous neural activity 15:10 Fri 31 Jul, 2015 :: Ingkarni Wardli B21 :: Prof John Terry :: University of Exeter, UK
Media...Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of mathematical modelling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit.
In the talk we introduce some of these concepts with application to epilepsy, introducing a dynamic network approach to study resting state EEG recordings from a cohort of 35 people with epilepsy and 40 adult controls. Using this framework we demonstrate a strongly significant difference between networks inferred from the background activity of people with epilepsy in comparison to normal controls. Our findings demonstrate that a mathematical model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which may ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics. 

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. 

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. 

Tduality and bulkboundary correspondence 12:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B17 :: Guo Chuan Thiang :: The University of Adelaide
Media...Bulkboundary correspondences in physics can be modelled as topological boundary homomorphisms in Ktheory, associated to an extension of a "bulk algebra" by a "boundary algebra". In joint work with V. Mathai, such bulkboundary maps are shown to Tdualize 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 Ktheory, and explain how these results may be used to study topological phases of matter and Dbrane charges in string theory. 

Base change and Ktheory 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 Ktheory of the corresponding group C^*algebra. We use Archimedean base change between Langlands parameters of real and complex algebraic groups to compare Ktheory 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 AumannShapley prices, leads to a way in which this damage can be attributed to individual customers or groups of customers. 

ChernSimons 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 ChernSimons 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.


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 quasicategories, 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. 

Nearmotiontrapping 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! 

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. 

Tduality 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. Tdualities 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
antiholomorphic. The results blend algebraic topology
and algebraic geometry. This is mostly joint work with
Chuck Doran and Stefan MendezDiez. 

The parametric hprinciple 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 infinitedimensional spaces of maps of geometric interest. It turns out that they all have the same rough shape. 

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 TienCuong Dinh and VietAnh 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 SibonyÃÂ¢ÃÂÃÂs theory, even if their wedge intersection may not be welldefined 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.


Sard Theorem for the endpoint map in subRiemannian manifolds 12:10 Fri 29 Apr, 2016 :: Eng & Maths EM205 :: Alessandro Ottazzi :: University of New South Wales
Media...SubRiemannian 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 subRiemannian 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. 

Harmonic analysis of HodgeDirac 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).


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 microsimulation 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 widespread 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 multidisciplinary methodology, drawing from agentbased modelling, behavioural science and psychology, microeconomics, artificial intelligence, simulation, game theory, engineering, mathematics and statistics. In this seminar, we start with a highlevel 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. 

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 nonvanishing of the image of the index map from the Gequivariant Khomology of a Gmanifold X to the Ktheory 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 Khomology class with a lowdimensional cohomology class is nonzero, we prove that the image of this class under the index map is nonzero. 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.


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. 

Multiscale 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 multiscale 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: swellingdeswelling 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 crosslinked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a twophase, 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 microscale description). The problem is posed as a freeboundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibriumstates 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 microscale 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. 

ChernSimons 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 ChernSimons functional for connections on Gbundles over threemanfolds has lead to a deep understanding of the geometry of threemanfiolds, as well as knot invariants such as the Jones polynomial. Here we study this functional for threemanfolds 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 ChernSimons functional reduces to a particular gaugetheoretic 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 levelk affine central extension of the loop group LG. We show that this formulation gives a new understanding of results of BeasleyWitten on the computability of quantum ChernSimons 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 MurrayStevensonVozzo.


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 Ktheory group of this C*algebra classifies Dbrane charges in string theory. Twisted vector bundles, when they exist, give rise to particularly important elements in this Ktheory 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.


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?


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'onZygmund 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 quasimetric and a doubling measure. Further, one can
replace the Laplacian operator that underpins the
CalderonZygmund 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 

Singular vector bundles and topological semimetals 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 semimetal 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 MayerVietoris principles, gerbes, and generalised degree theory. 

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. 

On the Willmore energy 15:10 Fri 7 Oct, 2016 :: Napier G03 :: Dr Yann Bernard :: Monash University
Media...The Willmore energy of a surface captures its bending. Originally discovered 200 years ago by Sophie Germain in the context of elasticity theory, it has since then been rediscovered numerous times in several areas of science: general relativity, optics, string theory, conformal geometry, and cell biology. For example, our red blood cells assume a peculiar shape that minimises the Willmore energy.
In this talk, I will present the thrilling history of the Willmore energy, its applications, and its main properties. The presentation will be accessible to all mathematicians as well as to advanced undergraduate students. 

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 AtiyahBott fixed point theorem or the AtiyahSegalSinger index theorem. HarishChandra 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 Ktheory of HarishChandra Schwartz algebra of a semisimple Lie group G, and then use geometric method to deduce HarishChandra character formulas for discrete series representations of G. This is work in progress with Peter Hochs.


Parahoric bundles, invariant theory and the KazhdanLusztig 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 KazhdanLusztig 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. 

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 particleboundary 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. liddriven cavity, liquid bridge) undergoes an instability from a twodimensional steady to a periodic threedimensional 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 (quasiperiodic) streamlines can coexist for a range of Reynolds numbers. The spatial structures of the regular regions in threedimensional NavierStokes 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 particleboundary interaction particles can rapidly segregate and be attracted to periodic or quasiperiodic 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. 

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 kdisc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have nonzero 8periodic 2torsion detected in real Ktheory. 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 nonempty, space of positive scalar curvature metrics on M has nonzero 8periodic 2torsion in its homotopy groups which is detected in real Ktheory. 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 areaminimizing, 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 antiselfdual YangMills equations on an oriented
smooth 4manifold. 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 4manifolds. It is also the case that these moduli spaces
themselves carry interesting geometric structures; for example,
the WeilPetersson 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 recentish work done
in conjunction with Georg Schumacher. 

PoissonLie Tduality and integrability 11:10 Thu 13 Apr, 2017 :: Engineering & Math EM213 :: Ctirad Klimcik :: AixMarseille University, Marseille
Media...The PoissonLie Tduality relates sigmamodels with target spaces symmetric with respect to mutually dual PoissonLie groups. In the special case if the PoissonLie symmetry reduces to the standard nonAbelian symmetry one of the corresponding mutually dual sigmamodels is the standard principal chiral model which is known to enjoy the property of integrability. A natural question whether this nonAbelian integrability can be lifted to integrability of sigma model dualizable with respect to the general PoissonLie symmetry has been answered in the affirmative by myself in 2008. The corresponding PoissonLie symmetric and integrable model is a oneparameter deformation of the principal chiral model and features a remarkable explicit appearance of the standard YangBaxter operator in the target space geometry. Several distinct integrable deformations of the YangBaxter sigma model have been then subsequently uncovered which turn out to be related by the PoissonLie Tduality to the so called lambdadeformed 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. 

Hyperbolic geometry and knots 15:10 Fri 28 Apr, 2017 :: Engineering South S111 :: A/Prof Jessica Purcell :: Monash University
It has been known since the early 1980s that the complement of a knot or link decomposes into geometric pieces, and the most common geometry is hyperbolic. However, the connections between hyperbolic geometry and other knot and link invariants are not wellunderstood. Conjectured connections have applications to quantum topology and physics, 3manifold geometry and topology, and knot theory. In this talk, we will describe several results relating the hyperbolic geometry of a knot or link to other invariants, and their implications. 

Hodge theory on the moduli space of Riemann surfaces 12:10 Fri 5 May, 2017 :: Napier 209 :: Jesse GellRedman :: 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 noncompact 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 noncompact 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 WeilPetersson metric on the compactified Riemann moduli space near the interior of a divisor. Joint with J. Swoboda and R. Melrose. 

Graded Ktheory 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 Ktheory 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 Ktheory. 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 twoelement group. Even the definition of graded C*algebraic Ktheory 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 Ktheory 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, microfluidic flows in labsonachip and porous media, largescale 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 twodimensional and threedimensional 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 Ktheory provide a realisation of twisted Ktheory. I will discuss the existence or Real bundle gerbes which are the corresponding objects required to construct Real twisted Ktheory in the sense of Atiyah. This is joint work with Richard Szabo (HeriotWatt), Pedram Hekmati (Auckland) and Raymond Vozzo which appeared in arXiv:1608.06466. 

Probabilistic approaches to human cognition: What can the math tell us? 15:10 Fri 26 May, 2017 :: Engineering South S111 :: Dr Amy Perfors :: School of Psychology, University of Adelaide
Why do people avoid vaccinating their children? Why, in groups, does it seem like the most extreme positions are weighted more highly? On the surface, both of these examples look like instances of nonoptimal or irrational human behaviour. This talk presents preliminary evidence suggesting, however, that in both cases this pattern of behaviour is sensible given certain assumptions about the structure of the world and the nature of beliefs. In the case of vaccination, we model people's choices using expected utility theory. This reveals that their ignorance about the nature of diseases like whooping cough makes them underweight the negative utility attached to contracting such a disease. When that ignorance is addressed, their values and utilities shift. In the case of extreme positions, we use simulations of chains of Bayesian learners to demonstrate that whenever information is propagated in groups, the views of the most extreme learners naturally gain more traction. This effect emerges as the result of basic mathematical assumptions rather than human irrationality. 

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 1950Ã¢ÂÂs, most important achievements include: Grothendieck et al.Ã¢ÂÂs etale cohomology, and Bombieri and GrothendieckÃ¢ÂÂs standard conjectures on algebraic cycles (inspired by a Kahlerian analogue of a generalisation of WeilÃ¢ÂÂs RH by Serre). WeilÃ¢ÂÂs RH was solved by Deligne in the 70Ã¢ÂÂs, but the finite field analogue of SerreÃ¢ÂÂs result is still open (even in dimension 2). This talk presents my recent work proposing a generalisation of WeilÃ¢ÂÂs 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 SerreÃ¢ÂÂs result. 

Mathematics is Biology's Next Microscope (Only Better!) 15:10 Fri 11 Aug, 2017 :: Ingkarni Wardli B17 :: Dr Robyn Araujo :: Queensland University of Technology
While mathematics has long been considered "an essential tool for physics", the foundations of biology and the life sciences have received significantly less influence from mathematical ideas and theory. In this talk, I will give a brief discussion of my recent research on robustness in molecular signalling networks, as an example of a complex biological question that calls for a mathematical answer. In particular, it has been a longstanding mystery how the extraordinarily complex communication networks inside living cells, comprising thousands of different interacting molecules, are able to function robustly since complexity is generally associated with fragility. Mathematics has now suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from a just small number of welldefined universal modules (or "motifs"), connected together. The existence of these newlydiscovered modules has important implications for evolutionary biology, embryology and development, cancer research, and drug development. 

Mathematics is Biology'ÂÂs Next Microscope (Only Better!) 15:10 Fri 11 Aug, 2017 :: Ingkarni Wardli B17 :: Dr Robyn Araujo :: Queensland University of Technology
While mathematics has long been considered Ã¢ÂÂan essential tool for physics", the foundations of biology and the life sciences have received significantly less influence from mathematical ideas and theory. In this talk, I will give a brief discussion of my recent research on robustness in molecular signalling networks, as an example of a complex biological question that calls for a mathematical answer. In particular, it has been a longstanding mystery how the extraordinarily complex communication networks inside living cells, comprising thousands of different interacting molecules, are able to function robustly since complexity is generally associated with fragility. Mathematics has now suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from a just small number of welldefined universal modules (or Ã¢ÂÂmotifsÃ¢ÂÂ), connected together. The existence of these newlydiscovered modules has important implications for evolutionary biology, embryology and development, cancer research, and drug development. 

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 pseudoRiemannian homogeneous spaces 12:10 Fri 18 Aug, 2017 :: Engineering Sth S111 :: Wolfgang Globke :: University of Adelaide
Media...A pseudoRiemannian 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 biinvariant metric on $G$.
This result allows us to recover Zeghibâs classification of Lorentzian compact homogeneous spaces, and to move towards a classification for metric index 2.
As an application we can investigate which pseudoRiemannian 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. 

Timereversal symmetric topology from physics 12:10 Fri 25 Aug, 2017 :: Engineering Sth S111 :: Guo Chuan Thiang :: University of Adelaide
Media...Timereversal 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 illmotivated generalisation. Guided by physical intuition, an equivariant PoincareLefschetz duality, Euler structures, and a new type of monopole with torsion charge, will be introduced. 

Topology as a tool in algebra 15:10 Fri 8 Sep, 2017 :: Ingkarni Wardli B17 :: Dr Zsuzsanna Dancso :: University of Sydney
Topologists often use algebra in order to understand the shape of a space: invariants such as homology and cohomology are basic, and very successful, examples of this principle. Although topology is used as a tool in algebra less often, I will describe a recurring pattern on the border of knot theory and quantum algebra where this is possible. We will explore how the tangled topology of "flying circles in R^3" is deeply related to a famous problem in Lie theory: the KashiwaraVergne (KV) problem (first solved in 2006 by AlekseevMeinrenken). I will explain how this relationship illuminates the intricate algebra of the KV problem. 

In space there is noone 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 twodimensional 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. 

On the fundamental of RayleighTaylor instability and interfacial mixing 15:10 Fri 15 Sep, 2017 :: Ingkarni Wardli B17 :: Prof Snezhana Abarzhi :: University of Western Australia
RayleighTaylor instability (RTI) develops when fluids of different densities are accelerated against their density gradient. Extensive interfacial mixing of the fluids ensues with time. RayleighTaylor (RT) mixing controls a broad variety of processes in fluids, plasmas and materials, in high and low energy density regimes, at astrophysical and atomistic scales. Examples include formation of hot spot in inertial confinement, supernova explosion, stellar and planetary convection, flows in atmosphere and ocean, reactive and supercritical fluids, material transformation under impact and lightmaterial interaction. In some of these cases (e.g. inertial confinement fusion) RT mixing should be tightly mitigated; in some others (e.g. turbulent combustion) it should be strongly enhanced. Understanding the fundamentals of RTI is crucial for achieving a better control of nonequilibrium processes in nature and technology.
Traditionally, it was presumed that RTI leads to uncontrolled growth of smallscale imperfections, singlescale nonlinear dynamics, and extensive mixing that is similar to canonical turbulence. The recent success of the theory and experiments in fluids and plasmas suggests an alternative scenario of RTI evolution. It finds that the interface is necessary for RT mixing to accelerate, the acceleration effects are strong enough to suppress the development of turbulence, and the RT dynamics is multiscale and has significant degree of order.
This talk presents a physicsbased consideration of fundamentals of RTI and RT mixing, and summarizes what is certain and what is not so certain in our knowledge of RTI. The focus question  How to influence the regularization process in RT mixing? We also discuss new opportunities for improvements of predictive modeling capabilities, physical description, and control of RT mixing in fluids, plasmas and materials. 

Equivariant formality of homogeneous spaces 12:10 Fri 29 Sep, 2017 :: Engineering Sth S111 :: Alex ChiKwong Fok :: University of Adelaide
Equivariant formality, a notion in equivariant topology introduced by GoreskyKottwitzMacpherson, 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 wellknown 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 Ktheory. 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. 

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. 

A Hecke module structure on the KKtheory 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 BorelSerre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the BruhatTits 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 QuirogaBarranco :: CIMAT, Guanajuato, Mexico
Media...The Bergman spaces on a complex domain are defined as the space of holomorphic squareintegrable 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. 

Family gauge theory and characteristic classes of bundles of 4manifolds 13:10 Fri 16 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Hokuto Konno :: University of Tokyo
Media...I will define a nontrivial characteristic class of bundles of
4manifolds using families of SeibergWitten 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 nontriviality of this
characteristic class. If time permits, I will mention a relation between
our characteristic class and positive scalar curvature metrics. 

Complexity of 3Manifolds 15:10 Fri 23 Mar, 2018 :: Horace Lamb 1022 :: A/Prof Stephan Tillmann :: University of Sydney
In this talk, I will give a general introduction to complexity of
3manifolds and explain the connections between combinatorics, algebra,
geometry, and topology that arise in its study.
The complexity of a 3manifold is the minimum number of tetrahedra in a
triangulation of the manifold. It was defined and first studied by Matveev
in 1990. The complexity is generally difficult to compute, and various
upper and lower bounds have been derived during the last decades using
fundamental group, homology or hyperbolic volume.
Effective bounds have only been found in joint work with Jaco, Rubinstein
and, more recently, Spreer. Our bounds not only allowed us to determine the
first infinite classes of minimal triangulations of closed 3manifolds, but
they also lead to a structure theory of minimal triangulations of
3manifolds. 

Chaos in higherdimensional 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, Kobayashihyperbolic manifolds have at most a finitedimensional 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 Kobayashihyperbolic manifold is nonexpansive 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 antihyperbolicity 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 rightinvariant 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 CalliasType 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 Ginvariant operators on M, called GCalliastype operators. These are Dirac operators that have been given an additional Z_2grading and a perturbation so as to be "invertible outside of a cocompact set in M". It turns out that GCalliastype operators are equivariantly Fredholm and so have an index in the Ktheory of the maximal group C*algebra of G. This index can be expressed as a KKproduct of a class in Khomology and a class in the Ktheory of the Higson Gcorona. In fact, one can show that the Ktheory of the Higson Gcorona is highly nontrivial, and thus the index theory of GCalliastype operators is not obviously trivial. As an application of the index theory of GCalliastype operators, I will mention an obstruction to the existence of Ginvariant 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 grouptheoretic 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. 

Knot homologies 15:10 Fri 4 May, 2018 :: Horace Lamb 1022 :: Dr Anthony Licata :: Australian National University
The last twenty years have seen a lot of interaction between lowdimensional topology and representation theory. One facet of this interaction concerns "knot homologies," which are homological invariants of knots; the most famous of these, Khovanov homology, comes from the higher representation theory of sl_2. The goal of this talk will be to give a gentle introduction to this subject to nonexperts by telling you a bit about Khovanov homology. 

Obstructions to smooth group actions on 4manifolds from families SeibergWitten 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 4manifold 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 SeibergWitten theory for smooth families of 4manifolds and obtain obstructions to the existence of such lifts. For example, we construct compact simplyconnected 4manifolds 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 topology and geometry of spaces of YangMillsHiggs 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 YangMillsHiggs 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 YangMillsHiggs flow in terms of their algebraic structure, which leads to an algebrogeometric classification of YangMillsHiggs flow lines. Critical points connected by flow lines can then be interpreted in terms of the Hecke correspondence, which appears in Wittenâs 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 algebrogeometric compactification by iterated blowups of secant varieties. 
News matching "Algebraic topology: Ktheory" 
ARC success The School of Mathematical Sciences was again very successful in attracting Australian Research Council funding for 2008. Recipients of ARC Discovery Projects are (with staff from the School highlighted):
Prof NG Bean; Prof PG Howlett; Prof CE Pearce; Prof SC Beecham; Dr AV Metcalfe; Dr JW Boland:
WaterLog  A mathematical model to implement recommendations of The Wentworth Group.
20082010: $645,000
Prof RJ Elliott:
Dynamic risk measures.
(Australian Professorial Fellowship)
20082012: $897,000
Dr MD Finn:
Topological Optimisation of Fluid Mixing.
20082010: $249,000
Prof PG Bouwknegt; Prof M Varghese; A/Prof S Wu:
Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program.
20082010: $240,000
The latter grant is held through the ANU Posted Wed 26 Sep 07. 

Stoneham Prize The inaugural Stoneham Prize, awarded for the best poster by a graduate student in the first two years of their candidature, was awarded on the 4th of April. The winner was Ric Green, for his poster "What is Geometry?". Two Viewers' Choice prizes were also awarded to Ray Vozzo for his poster "The 7 Bridges of Koenigsberg  The 1st Theorem in Topology" and David Butler for his poster "The Queen of Hearts Plays Noughts and Crosses". Posted Sun 13 Apr 08. 

Sam Cohen wins prize for best student talk at ANZIAM 2009 Congratulations to Mr Sam Cohen, a PhD student within the School, who was awarded the T. M. Cherry Prize for the best student paper at the 2009 meeting of ANZIAM for his talk on
A general theory of backward stochastic difference equations. Posted Fri 6 Feb 09. 

ARC Grant successes Congratulations to Tony Roberts, Charles Pearce, Robert Elliot, Andrew Metcalfe and all their collaborators on their success in the current round of ARC grants. The projects are "Development of innovative technologies for oil production based on the advanced theory of suspension flows in porous media" (Tony Roberts et al.), "Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems" (Charles Pearce et al.),
"Risk Measures and Management in Finance and Actuarial Science Under RegimeSwitching Models" (Robert Elliott et al.) and "A new flood design methodology for a variable and changing climate" (Andrew Metcalfe et al.) Posted Mon 26 Oct 09. 

ARC Grant successes The School of Mathematical Sciences has again had outstanding success in the ARC Discovery and Linkage Projects schemes.
Congratulations to the following staff for their success in the Discovery Project scheme:
Prof Nigel Bean, Dr Josh Ross, Prof Phil Pollett, Prof Peter Taylor, New methods for improving active adaptive management in biological systems, $255,000 over 3 years;
Dr Josh Ross, New methods for integrating population structure and stochasticity into models of disease dynamics, $248,000 over three years;
A/Prof Matt Roughan, Dr Walter Willinger, Internet trafficmatrix synthesis, $290,000 over three years;
Prof Patricia Solomon, A/Prof John Moran, Statistical methods for the analysis of critical care data, with application to the Australian and New Zealand Intensive Care Database, $310,000 over 3 years;
Prof Mathai Varghese, Prof Peter Bouwknegt, Supersymmetric quantum field theory, topology and duality, $375,000 over 3 years;
Prof Peter Taylor, Prof Nigel Bean, Dr Sophie Hautphenne, Dr Mark Fackrell, Dr Malgorzata O'Reilly, Prof Guy Latouche, Advanced matrixanalytic methods with applications, $600,000 over 3 years.
Congratulations to the following staff for their success in the Linkage Project scheme:
Prof Simon Beecham, Prof Lee White, A/Prof John Boland, Prof Phil Howlett, Dr Yvonne Stokes, Mr John Wells, Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements, $370,000 over 3 years;
Dr Amie Albrecht, Prof Phil Howlett, Dr Andrew Metcalfe, Dr Peter Pudney, Prof Roderick Smith, Saving energy on trains  demonstration, evaluation, integration, $540,000 over 3 years
Posted Fri 29 Oct 10. 

New Fellow of the Australian Academy of Science Professor Mathai Varghese, Professor of Pure Mathematics and ARC Professorial Fellow within the School of Mathematical Sciences, was elected to the Australian Academy of Science. Professor Varghese's citation read "for his distinguished for his work in geometric analysis involving the topology of manifolds, including the MathaiQuillen formalism in topological field theory.". Posted Tue 30 Nov 10. 

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. 

IGAAMSI Workshop: Groupvalued moment maps with applications to mathematics and physics (5–9 September 2011) Lecture series by Eckhard Meinrenken, University of Toronto. Titles of
individual lectures: 1) Introduction to Gvalued moment maps. 2) Dirac
geometry and Witten's volume formulas. 3) DixmierDouady theory and
prequantization. 4) Quantization of groupvalued moment maps. 5)
Application to Verlinde formulas. These lectures will be supplemented by
additional talks by invited speakers. For more details, please see the
conference webpage
Posted Wed 27 Jul 11.More information... 

ARC Grant Success Congratulations to the following staff who were successful in securing funding from the Australian Research Council Discovery Projects Scheme. Associate Professor Finnur Larusson awarded $270,000 for his project Flexibility and symmetry in complex geometry; Dr Thomas Leistner, awarded $303,464 for his project Holonomy groups in Lorentzian geometry, Professor Michael Murray Murray and Dr Daniel Stevenson (Glasgow), awarded $270,000 for their project Bundle gerbes: generalisations and applications; Professor Mathai Varghese, awarded $105,000 for his project Advances in index theory and Prof Anthony Roberts and Professor Ioannis Kevrekidis (Princeton) awarded $330,000 for their project Accurate modelling of large multiscale dynamical systems for engineering and scientific
simulation and analysis Posted Tue 8 Nov 11. 

Dualities in field theories and the role of Ktheory Between Monday 19 and Friday 23 March 2012, the Institute for Geometry and its Applications will host a lecture series by Professor Jonathan Rosenberg from the University of Maryland. There
will be additional talks by other invited speakers. Posted Tue 6 Dec 11.More information... 

Elder Professor Mathai Varghese Awarded Australian Laureate Fellowship Professor Mathai Varghese, Elder Professor of Mathematics in the School of Mathematical Sciences, has been awarded an Australian Laureate Fellowship worth $1.64 million to advance Index Theory and its applications. The project is expected to enhance Australiaâs position at the forefront of international research in geometric analysis. Posted Thu 15 Jun 17.More information... 

Elder Professor Mathai Varghese Awarded Australian Laureate Fellowship Professor Mathai Varghese, Elder Professor of Mathematics in the School of Mathematical Sciences, has been awarded an Australian Laureate Fellowship worth $1.64 million to advance Index Theory and its applications. The project will enhance Australia's position at the forefront of international research in geometric analysis. Posted Thu 15 Jun 17.More information... 
Publications matching "Algebraic topology: Ktheory"Publications 

Noncommutative correspondences, duality and Dbranes in bivariant Ktheory Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009  Portfolio risk minimization and differential games Elliott, Robert; Siu, T, Nonlinear AnalysisTheory Methods & Applications In Press (–) 2009  The maximum size of the intersection of two ovoids Butler, David, Journal of Combinatorial Theory Series A 116 (242–245) 2009  Algebraic deformations of compact kahler surfaces II Buchdahl, Nicholas, Mathematische Zeitschrift 258 (493–498) 2008  Dbranes, KKtheory and duality on noncommutative spaces Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Journal of Physics: Conference Series (Print Edition) 103 (1–13) 2008  Topology of chaotic mixing patterns Thiffeault, J; Finn, Matthew; Gouillart, E; Hall, T, Chaos 18 (0331231–03312316) 2008  Multicast Topology Inference and Its Applications Tian, Hui; Shen, Hong, chapter in Handbook of Approximation Alggorithms and Metaheuristics (Taylor & Francis) 691–6914, 2007  Topology reconstruction and characterisation of wireless ad hoc networks Arnold, Jonathan; Bean, Nigel; Kraetzl, Miro; Roughan, Matthew; Sorell, Matthew, 2007 IEEE International Conference on Communications, Glasgow, Scotland 24/06/07  Nonclassical symmetry solutions for reactiondiffusion equations with explicity spatial dependence Hajek, Bronwyn; Edwards, M; Broadbridge, P; Williams, G, Nonlinear AnalysisTheory Methods & Applications 67 (2541–2552) 2007  Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras Eastwood, Michael; Somberg, P; Soucek, V, Journal of Geometry and Physics 57 (2539–2546) 2007  TDuality in type II string theory via noncommutative geometry and beyond Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007  Building an AStopology model that captures route diversity Muhlbauer, W; Feldmann, A; Maennel, Olaf; Roughan, Matthew; Uhlig, S, sigcomm 2006, Pisa, Italy 11/09/06  Algebraic deformations of compact Khler surfaces Buchdahl, Nicholas, Mathematische Zeitschrift 253 (453–459) 2006  Duality symmetry and the form fields of Mtheory Sati, Hicham, The Journal of High Energy Physics (Print Edition) 6 (0–10) 2006  Dynamic portfolio allocation, the dual theory of choice and probability distortion functions Hamada, M; Sherris, M; Van Der Hoek, John, Astin Bulletin 31 (187–217) 2006  Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q) Barwick, Susan; Brown, Matthew; Penttila, T, Journal of Combinatorial Theory Series A 113 (273–290) 2006  Tduality for torus bundles with Hfluxes via noncommutative topology, II: the highdimensional case and the Tduality group Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 2006  The elliptic curves in gauge theory, string theory, and cohomology Sati, Hicham, The Journal of High Energy Physics (Print Edition) 3 (0–19) 2006  The many facets of Internet topology and traffic Alderson, D; Chang, H; Roughan, Matthew; Uhlig, S; Willinger, W, Networks and Heterogeneous Media 1 (569–600) 2006  YangMills theory for bundle gerbes Varghese, Mathai; Roberts, David, Journal of Physics A: Mathematical and Theoretical (Print Edition) 39 (6039–6044) 2006  Ktheory Varghese, Mathai, chapter in Encyclopedia of mathematical physics (Elsevier Academic Press) 246–254, 2006  Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in Ktheory Kordyukov, Y; Varghese, Mathai; Shubin, M, Journal fur die Reine und Angewandte Mathematik 581 (193–236) 2005  Hamiltonian dynamics and morse topology of humanoid robots Ivancevic, V; Pearce, Charles, Global Journal of Mathematics and Mathematical Sciences (GJMMS) 1 (9–19) 2005  Mtheory and characteristic classes Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (0201–0208) 2005  Risksensitive filtering and smoothing for continuoustime Markov processes Malcolm, William; Elliott, Robert; James, M, IEEE Transactions on Information Theory 51 (1731–1738) 2005  Tduality for torus bundles with Hfluxes via noncommutative topology Varghese, Mathai; Rosenberg, J, Communications in Mathematical Physics 253 (705–721) 2005  The index of projective families of elliptic operators Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 2005  Type II string theory and modularity Kriz, I; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (0381–03830) 2005  Type IIB string theory, Sduality, and generalized cohomology Kriz, I; Sati, Hicham, Nuclear Physics B 715 (639–664) 2005  Updating the parameters of a threshold scheme by minimal broadcast Barwick, Susan; Jackson, WenAi; Martin, K, IEEE Transactions on Information Theory 51 (620–633) 2005  A sufficient condition for the uniform exponential stability of timevarying systems with noise Grammel, G; Maizurna, Isna, Nonlinear AnalysisTheory Methods & Applications 56 (951–960) 2004  Geometrical contributions to secret sharing theory Jackson, WenAi; Martin, K; O'Keefe, Christine, Journal of Geometry 79 (102–133) 2004  Kirillov theory for a class of discrete nilpotent groups Tandra, Haryono; Moran, W, Canadian Journal of MathematicsJournal Canadien de Mathematiques 56 (883–896) 2004  Mtheory, type IIA superstrings, and elliptic cohomology Kriz, I; Sati, Hicham, Advances in Theoretical and Mathematical Physics 8 (345–394) 2004  Some relations between twisted Ktheory and E8 gauge theory Varghese, Mathai; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 22) 2004  Subquadrangles of order s of generalized quadrangles of order (s, s2), Part I Brown, Matthew; Thas, J, Journal of Combinatorial Theory Series A 106 (15–32) 2004  Subquadrangles of order s of generalized quadrangles of order (s, s2), Part II Brown, Matthew; Thas, J, Journal of Combinatorial Theory Series A 106 (33–48) 2004  Tduality: Topology change from Hflux Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Communications in Mathematical Physics 249 (383–415) 2004  Topology and Hflux of Tdual manifolds Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Physical Review Letters 92 (1816011–1816013) 2004  Measure Theory and Filtering: Introduction and Applications Aggoun, L; Elliott, Robert, (Cambridge University Press) 2004  Euler and his contribution to number theory Glen, Amy; Scott, Paul, Australian Mathematics Teacher 1 (2–5) 2004  Some relations between twisted Ktheory and E8 gauge theory Mathai, V; Sati, Hicham, The Journal of High Energy Physics (Online Editions) (WWW1–WWW22) 2004  A general fractional white noise theory and applications to finance Elliott, Robert; Van Der Hoek, John, Mathematical Finance 13 (301–330) 2003  Chern character in twisted Ktheory: Equivariant and holomorphic cases Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003  Edge of the wedge theory in hypoanalytic manifolds Eastwood, Michael; Graham, C, Communications in Partial Differential Equations 28 (2003–2028) 2003  Type1 Dbranes in an Hflux and twisted KOtheory Varghese, Mathai; Murray, Michael; Stevenson, Daniel, The Journal of High Energy Physics (Online Editions) 11 (www 1–www 22) 2003  Traffic matrices and network topology Roughan, Matthew, UCLA IPAM Workshop (2003: Lake Arrowhead, CA, USA), Los Angeles, CA, USA 28/09/03  On a convexity problem arising in queueing theory and electromagnetism Peake, M; Pearce, Charles, Sixth International Conference on Nonlinear Functional Analysis and Applications, Gyeongsang National University 01/09/00  Axial anomaly and topological charge in lattice gauge theory with overlap dirac operator Adams, Damian, Annals of Physics 296 (131–151) 2002  Families index theory for Overlap lattice Dirac operator. 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