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April 2018

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Associate Professor Sanjeeva Balasuriya
Senior Lecturer in Applied Mathematics

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Dr David Baraglia
ARC DECRA Fellow, APD Fellow

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Professor Nigel Bean
Chair of Applied Mathematics

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Associate Professor Nicholas Buchdahl
Reader in Pure Mathematics

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Associate Professor Gary Glonek
Associate Professor in Statistics

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Dr Ed Green
Lecturer in Applied Mathematics

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Dr Pedram Hekmati
Adjunct Senior Lecturer

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Professor Michael Murray
Chair of Pure Mathematics

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Associate Professor Joshua Ross
Senior Lecturer in Applied Mathematics

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Professor Patty Solomon
Professor of Statistical Bioinformatics

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Associate Professor Yvonne Stokes
Senior Lecturer in Applied Mathematics

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Professor Mathai Varghese
Elder Professor of Mathematics, Australian Laureate Fellow, Fellow of the Australian Academy of Scie

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Courses matching "Mathematical epidemiology with a focus on househol"

Mathematical Biology III

The application of mathematics to problems arising in the life sciences is a rapidly growing area yielding quantitative understanding of questions about such things as the spread of infectious diseases, population growth and interaction, organ (e.g. heart) function, cell signalling, nutrient supply, and more. This course will introduce students to the fascinating world of modelling biological systems. A variety of biological problems will be considered, in the context of which students will be exposed to a variety of mathematical techniques. No previous exposure to biology is necessary. Topics covered are: Scalar, discrete-time models, analysed using the mathematical tools of cobwebbing and linear stability analysis of fixed points; Linear stability analysis of systems of discrete-time equations; The theory of dynamical systems for models comprised of linear and nonlinear scalar and coupled ordinary differential equations, including vector fields, phase-plane analysis and elementary bifurcation theory; Reaction-advection-diffusion models, including equation derivation from the law of mass conservation and Fick's law. The 1D Fisher equation is examined in particular, a Hamiltonian function is introduced for analysis of the steady equation, while travelling wave solutions of the unsteady equation are obtained.

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Mathematical epidemiology: Stochastic models and their statistical calibration

Mathematical models are increasingly used to inform governmental policy-makers on issues that threaten human health or which have an adverse impact on the economy. It is this real-world success combined with the wide variety of interesting mathematical problems which arise that makes mathematical epidemiology one of the most exciting topics in applied mathematics. During the summer school, you will be introduced to mathematical epidemiology and some fundamental theory required for studying and parametrising stochastic models of infection dynamics, which will provide an ideal basis for addressing key research questions in this area; several such questions will be introduced and explored in this course. Topics: An introduction to mathematical epidemiology Discrete-time and continuous-time discrete-state stochastic infection models Numerical methods for studying stochastic infection models: EXPOKIT, transforms and their inversion Methods for simulating stochastic infection models: classical (Gillespie) algorithm, more efficient exact and approximate algorithms Methods for parameterising stochastic infection models: frequentist approaches, Bayesian approaches, approximate Bayesian computation Optimal observation of stochastic infection models

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Mathematical Statistics III

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

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Events matching "Mathematical epidemiology with a focus on househol"

00:00 Wed 30 Nov, -0001 :: Lower Napier LG14 :: A/Prof Jessica Purcell :: Monash University

00:00 Wed 30 Nov, -0001 :: Lower Napier LG14 :: A/Prof Jessica Purcell :: Monash University

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

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

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

For the past few decades, calculus and linear algebra have provided the basis for many university courses in mathematics, science or engineering. However there are other courses, which could be given to motivate the students, particularly those with only a passing love of mathematics. One possible course could show the essential features of how mathematicians solve problems using many different analytical, cerebral and computer skills. In this seminar I will describe such a one-semester course (2 lectures, 2 labs each week), which includes hands-on problem solving and students eventually creating their own problems. One or two exciting problems at first-year level will be developed in detail.
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 set-theoretic 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.
Mathematics of underground mining.
15:10 Fri 12 May, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Hyam Rubinstein

Underground mining infrastructure involves an interesting range of optimisation problems with geometric constraints. In particular, ramps, drives and tunnels have gradient within a certain prescribed range and turning circles (curvature) are also bounded. Finally obstacles have to be avoided, such as faults, ore bodies themselves and old workings. A group of mathematicians and engineers at Uni of Melb and Uni of SA have been working on this problem for a number of years. I will summarise what we have found and the challenges of working in the mining industry.
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 non-commutative 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.
Watching evolution in real time; problems and potential research areas.
15:10 Fri 26 May, 2006 :: G08. Mathematics Building University of Adelaide :: Prof Alan Cooper (Federation Fellow)

Recent studies (1) have indicated problems with our ability to use the genetic distances between species to estimate the time since their divergence (so called molecular clocks). An exponential decay curve has been detected in comparisons of closely related taxa in mammal and bird groups, and rough approximations suggest that molecular clock calculations may be problematic for the recent past (eg <1 million years). Unfortunately, this period encompasses a number of key evolutionary events where estimates of timing are critical such as modern human evolutionary history, the domestication of animals and plants, and most issues involved in conservation biology. A solution (formulated at UA) will be briefly outlined. A second area of active interest is the recent suggestion (2) that mitochondrial DNA diversity does not track population size in several groups, in contrast to standard thinking. This finding has been interpreted as showing that mtDNA may not be evolving neutrally, as has long been assumed.
Large ancient DNA datasets provide a means to examine these issues, by revealing evolutionary processes in real time (3). The data also provide a rich area for mathematical investigation as temporal information provides information about several parameters that are unknown in serial coalescent calculations (4).
  1. Ho SYW et al. Time dependency of molecular rate estimates and systematic overestimation of recent divergence times. Mol. Biol. Evol. 22, 1561-1568 (2005);
    Penny D, Nature 436, 183-184 (2005).
  2. Bazin E., et al. Population size does not influence mitochondrial genetic diversity in animals. Science 312, 570 (2006);
    Eyre-Walker A. Size does not matter for mitochondrial DNA, Science 312, 537 (2006).
  3. Shapiro B, et al. Rise and fall of the Beringian steppe bison. Science 306: 1561-1565 (2004);
    Chan et al. Bayesian estimation of the timing and severity of a population bottleneck from ancient DNA. PLoS Genetics, 2 e59 (2006).
  4. Drummond et al. Measurably evolving populations, Trends in Ecol. Evol. 18, 481-488 (2003);
    Drummond et al. Bayesian coalescent inference of past population dynamics from molecular sequences. Molecular Biology Evolution 22, 1185-92 (2005).
Maths and Movie Making
15:10 Fri 13 Oct, 2006 :: G08 Mathematics Building University of Adelaide :: Dr Michael Anderson

Mathematics underlies many of the techniques used in modern movie making. This talk will sketch out the movie visual effects pipeline, discussing how mathematics is used in the various stages and detailing some of the mathematical areas that are still being actively researched.
The talk will finish with an overview of the type of work the speaker is involved in, the steps that led him there and the opportunities for mathematicians in this new and exciting area.
Mathematical modelling of multidimensional tissue growth
16:10 Tue 24 Oct, 2006 :: Benham Lecture Theatre :: Prof John King

Some simple continuum-mechanics-based models for the growth of biological tissue will be formulated and their properties (particularly with regard to stability) described.
A Bivariate Zero-inflated Poisson Regression Model and application to some Dental Epidemiological data
14:10 Fri 27 Oct, 2006 :: G08 Mathematics Building University of Adelaide :: University Prof Sudhir Paul

Data in the form of paired (pre-treatment, post-treatment) counts arise in the study of the effects of several treatments after accounting for possible covariate effects. An example of such a data set comes from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Also, these data may show extra pairs of zeros than can be accounted for by a simpler model, such as, a bivariate Poisson regression model. In such situations we propose to use a zero-inflated bivariate Poisson regression (ZIBPR) model for the paired (pre-treatment, posttreatment) count data. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model and develop a procedure for testing treatment effects. The procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post-treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then compare our analysis, of the decayed, missing and filled teeth (DMFT) index data from the caries prevention study, based on the ZIBPR model with the analysis using a zero-inflated Poisson regression model in which the pre-treatment DMFT index is taken to be a covariate
Good and Bad Vibes
15:10 Fri 23 Feb, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Maurice Dodson

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 Schrödinger\'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 space-based gravity wave detector under construction.
Alberta Power Prices
15:10 Fri 9 Mar, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Robert Elliott

The pricing of electricity involves several interesting features. Apart from daily, weekly and seasonal fluctuations, power prices often exhibit large spikes. To some extent this is because electricity cannot be stored. We propose a model for power prices in the Alberta market. This involves a diffusion process modified by a factor related to a Markov chain which describes the number of large generators on line. The model is calibrated and future contracts priced.
Statistical convergence of sequences of complex numbers with application to Fourier series
15:10 Tue 27 Mar, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Ferenc Morics

The concept of statistical convergence was introduced by Henry Fast and Hugo Steinhaus in 1951. But in fact, it was Antoni Zygmund who first proved theorems on the statistical convergence of Fourier series, using the term \"almost convergence\". A sequence $\\{x_k : k=1,2\\ldots\\}$ of complex numbers is said to be statistically convergent to $\\xi$ if for every $\\varepsilon >0$ we have $$\\lim_{n\\to \\infty} n^{-1} |\\{1\\le k\\le n: |x_k-\\xi| > \\varepsilon\\}| = 0.$$ We present the basic properties of statistical convergence, and extend it to multiple sequences. We also discuss the convergence behavior of Fourier series.
Identifying the source of photographic images by analysis of JPEG quantization artifacts
15:10 Fri 27 Apr, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Matthew Sorell

In a forensic context, digital photographs are becoming more common as sources of evidence in criminal and civil matters. Questions that arise include identifying the make and model of a camera to assist in the gathering of physical evidence; matching photographs to a particular camera through the camera’s unique characteristics; and determining the integrity of a digital image, including whether the image contains steganographic information. From a digital file perspective, there is also the question of whether metadata has been deliberately modified to mislead the investigator, and in the case of multiple images, whether a timeline can be established from the various timestamps within the file, imposed by the operating system or determined by other image characteristics. This talk is concerned specifically with techniques to identify the make, model series and particular source camera model given a digital image. We exploit particular characteristics of the camera’s JPEG coder to demonstrate that such identification is possible, and that even when an image has subsequently been re-processed, there are often sufficient residual characteristics of the original coding to at least narrow down the possible camera models of interest.
A mathematical look at dripping honey
15:10 Fri 4 May, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Yvonne Stokes :: University of Adelaide

Honey dripping from an upturned spoon is an everyday example of a flow that extends and breaks up into drops. Such flows have been of interest for over 300 years, attracting the attention of Plateau and Rayleigh among others. Theoretical understanding has, however, lagged behind experimental investigation, with major progress being made only in the last two decades, driven by industrial applications including ink-jet printing, spinning of polymer and glass fibres, blow-moulding of containers, light bulbs and glass tubing, and rheological measurement by fibre extension. Albeit, the exact details of the final stages of breakup are yet to be fully resolved. An aspect that is relatively unexplored is the evolution of drop and filament from some initial configuration, and the influence of initial conditions on the final breakup. We will consider a drop of very viscous fluid hanging beneath a solid boundary, similar to honey dripping from an upturned spoon, using methods that allow examination of development and behaviour from early time, when a drop and filament begin to form, out to large times when the bulk of the fluid forms a drop at the bottom of a long thin filament which connects it with the upper boundary. The roles of gravity, inertia and surface tension will be examined.
Flooding in the Sundarbans
15:10 Fri 18 May, 2007 :: G08 Mathematics Building University of Adelaide :: Steve Need

The Sunderbans is a region of deltaic isles formed in the mouth of the Ganges River on the border between India and Bangladesh. As the largest mangrove forest in the world it is a world heritage site, however it is also home to several remote communities who have long inhabited some regions. Many of the inhabited islands are low-lying and are particularly vulnerable to flooding, a major hazard of living in the region. Determining suitable levels of protection to be provided to these communities relies upon accurate assessment of the flood risk facing these communities. Only recently the Indian Government commissioned a study into flood risk in the Sunderbans with a view to determine where flood protection needed to be upgraded.

Flooding due to rainfall is limited due to the relatively small catchment sizes, so the primary causes of flooding in the Sunderbans are unnaturally high tides, tropical cyclones (which regularly sweep through the bay of Bengal) or some combination of the two. Due to the link between tidal anomaly and drops in local barometric pressure, the two causes of flooding may be highly correlated. I propose stochastic methods for analysing the flood risk and present the early work of a case study which shows the direction of investigation. The strategy involves linking several components; a stochastic approximation to a hydraulic flood routing model, FARIMA and GARCH models for storm surge and a stochastic model for cyclone occurrence and tracking. The methods suggested are general and should have applications in other cyclone affected regions.

Learning to Satisfy Actuator and Camera Networks
15:10 Fri 25 May, 2007 :: G08 Mathematics Building University of Adelaide :: Assistant Prof Mark Coates

Wireless sensor and actuator networks (SANETs) represent an important extension of sensor networks, allowing nodes within the network to make autonomous decisions and perform actions (actuation) in response to sensor measurements and shared information. SANETS combine aspects of sensor networks and multi-robot systems, and the merger gives rise to an array of challenges absent from conventional sensor networks. SANETs are active systems that must use the sensed information to modify the environment in order to elicit a desired response. This involves the development of an actuation strategy, a set of decision rules that specify how the network responds to sensed conditions. In this talk, I will discuss the challenges involved in using distributed algorithms to learn suitable actuation strategies. I will draw connections with the class of learning satisfiability problems, which includes a range of learning tasks involving multiple constraints.
Modelling gene networks: the case of the quorum sensing network in bacteria.
15:10 Fri 1 Jun, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Adrian Koerber

The quorum sensing regulatory gene-network is employed by bacteria to provide a measure of their population-density and switch their behaviour accordingly. I will present an overview of quorum sensing in bacteria together with some of the modelling approaches I\'ve taken to describe this system. I will also discuss how this system relates to virulence and medical treatment, and the insights gained from the mathematics.
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 Gács, 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.
An Introduction to invariant differential pairings
14:10 Tue 24 Jul, 2007 :: Mathematics G08 :: Jens Kroeske

On homogeneous spaces G/P, where G is a semi-simple Lie group and P is a parabolic subgroup (the ordinary sphere or projective spaces being examples), invariant operators, that is operators between certain homogeneous bundles (functions, vector fields or forms being amongst the typical examples) that are invariant under the action of the group G, have been studied extensively. Especially on so called hermitian symmetric spaces which arise through a 1-grading of the Lie algebra of G there exists a complete classification of first order invariant linear differential operators even on more general manifolds (that allow a so called almost hermitian structure).

This talk will introduce the notion of an invariant bilinear differential pairing between sections of the aforementioned homogeneous bundles. Moreover we will discuss a classification (excluding certain totally degenerate cases) of all first order invariant bilinear differential pairings on manifolds with an almost hermitian symmetric structure. The similarities and connections with the linear operator classification will be highlighted and discussed.

Likelihood inference for a problem in particle physics
15:10 Fri 27 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Anthony Davison

The Large Hadron Collider (LHC), a particle accelerator located at CERN, near Geneva, is (currently!) expected to start operation in early 2008. It is located in an underground tunnel 27km in circumference, and when fully operational, will be the world's largest and highest energy particle accelerator. It is hoped that it will provide evidence for the existence of the Higgs boson, the last remaining particle of the so-called Standard Model of particle physics. The quantity of data that will be generated by the LHC is roughly equivalent to that of the European telecommunications network, but this will be boiled down to just a few numbers. After a brief introduction, this talk will outline elements of the statistical problem of detecting the presence of a particle, and then sketch how higher order likelihood asymptotics may be used for signal detection in this context. The work is joint with Nicola Sartori, of the Università Ca' Foscari, in Venice.
Likelihood inference for a problem in particle physics MATT
15:10 Fri 27 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Anthony Davison

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 well-known 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.
Insights into the development of the enteric nervous system and Hirschsprung's disease
15:10 Fri 24 Aug, 2007 :: G08 Mathematics building University of Adelaide :: Assoc. Prof. Kerry Landman :: Department of Mathematics and Statistics, University of Melbourne

During the development of the enteric nervous system, neural crest (NC) cells must first migrate into and colonise the entire gut from stomach to anal end. The migratory precursor NC cells change type and differentiate into neurons and glia cells. These cells form the enteric nervous system, which gives rise to normal gut function and peristaltic contraction. Failure of the NC cells to invade the whole gut results in a lack of neurons in a length of the terminal intestine. This potentially fatal condition, marked by intractable constipation, is called Hirschsprung's Disease. The interplay between cell migration, cell proliferation and embryonic gut growth are important to the success of the NC cell colonisation process. Multiscale models are needed in order to model the different spatiotemporal scales of the NC invasion. For example, the NC invasion wave moves into unoccupied regions of the gut with a wave speed of around 40 microns per hour. New time-lapse techniques have shown that there is a web-like network structure within the invasion wave. Furthermore, within this network, individual cell trajectories vary considerably. We have developed a population-scale model for basic rules governing NC cell invasive behaviour incorporating the important mechanisms. The model predictions were tested experimentally. Mathematical and experimental results agreed. The results provide an understanding of why many of the genes implicated in Hirschsprung's Disease influence NC population size. Our recently developed individual cell-based model also produces an invasion wave with a well-defined wave speed; however, in addition Individual cell trajectories within the invasion wave can be extracted. Further challenges in modeling the various scales of the developmental system will be discussed.
Riemann's Hypothesis
15:10 Fri 31 Aug, 2007 :: G08 Mathematics building University of Adelaide :: Emeritus Prof. E. O. Tuck

Riemann's hypothesis (that all non-trivial zeros of the zeta function have real part one-half) is the most famous currently unproved conjecture in mathematics, and a \\$1M prize awaits its proof. The mathematical statement of this problem is only at about second-year undergraduate level; after all, the zeta function is much like the trigonometric sine function, and all (?) second-year students know that all zeros of the sine function are (real) integer multiples of $\\pi$. Many of the steps apparently needed to make progress on the proof are also not much more complicated than that level. Some of these elementary steps, together with numerical explorations, will be described here. Nevertheless the Riemann hypothesis has defied proof so far, and very complicated and advanced abstract mathematics (that will NOT be described here) is often brought to bear on it. Does it need abstract mathematics, or just a flash of elementary inspiration?
Fermat's Last Theorem and modular elliptic curves
15:10 Wed 5 Sep, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Mark Kisin

I will give a historical talk, explaining the steps by which one can deduce Fermat's Last Theorem from a statement about modular forms and elliptic curves.
Regression: a backwards step?
13:10 Fri 7 Sep, 2007 :: Maths G08 :: Dr Gary Glonek

Most students of high school mathematics will have encountered the technique of fitting a line to data by least squares. Those who have taken a university statistics course will also have heard this method referred to as regression. However, it is not obvious from common dictionary definitions why this should be the case. For example, "reversion to an earlier or less advanced state or form". In this talk, the mathematical phenomenon that gave regression its name will be explained and will be shown to have implications in some unexpected contexts.
Queues with Advance Reservations
15:10 Fri 21 Sep, 2007 :: G04 Napier Building University of Adelaide :: Prof. Peter Taylor :: Department of Mathematics and Statistics, University of Melbourne

Queues where, on "arrival", customers make a reservation for service at some time in the future are endemic. However there is surprisingly little about them in the literature. Simulations illustrate some interesting implications of the facility to make such reservations. For example introducing independent and identically distributed reservation periods into an Erlang loss system can either increase or decrease the blocking probability from that given by Erlang's formula, despite the fact that the process of 'reserved arrivals' is still Poisson. In this talk we shall discuss a number of ways of looking at such queues. In particular, we shall obtain various transient and stationary distributions associated with the "bookings diary" for the infinite server system. However, this does not immediately answer the question of how to calculate the above-mentioned blocking probabilities. We shall conclude with a few suggestions as to how this calculation might be carried out.
The Linear Algebra of Internet Search Engines
15:10 Fri 5 Oct, 2007 :: G04 Napier Building University of Adelaide :: Dr Lesley Ward :: School of Mathematics and Statistics, University of South Australia

We often want to search the web for information on a given topic. Early web-search algorithms worked by counting up the number of times the words in a query topic appeared on each webpage. If the topic words appeared often on a given page, that page was ranked highly as a source of information on that topic. More recent algorithms rely on Link Analysis. People make judgments about how useful a given page is for a given topic, and they express these judgments through the hyperlinks they choose to put on their own webpages. Link-analysis algorithms aim to mine the collective wisdom encoded in the resulting network of links. I will discuss the linear algebra that forms the common underpinning of three link-analysis algorithms for web search. I will also present some work on refining one such algorithm, Kleinberg's HITS algorithm. This is joint work with Joel Miller, Greg Rae, Fred Schaefer, Ayman Farahat, Tom LoFaro, Tracy Powell, Estelle Basor, and Kent Morrison. It originated in a Mathematics Clinic project at Harvey Mudd College.
Statistical Critique of the International Panel on Climate Change's work on Climate Change.
18:00 Wed 17 Oct, 2007 :: Union Hall University of Adelaide :: Mr Dennis Trewin

Climate change is one of the most important issues facing us today. Many governments have introduced or are developing appropriate policy interventions to (a) reduce the growth of greenhouse gas emissions in order to mitigate future climate change, or (b) adapt to future climate change. This important work deserves a high quality statistical data base but there are statistical shortcomings in the work of the International Panel on Climate Change (IPCC). There has been very little involvement of qualified statisticians in the very important work of the IPCC which appears to be scientifically meritorious in most other ways. Mr Trewin will explain these shortcomings and outline his views on likely future climate change, taking into account the statistical deficiencies. His conclusions suggest climate change is still an important issue that needs to be addressed but the range of likely outcomes is a lot lower than has been suggested by the IPCC. This presentation will be based on an invited paper presented at the OECD World Forum.
Moderated Statistical Tests for Digital Gene Expression Technologies
15:10 Fri 19 Oct, 2007 :: G04 Napier Building University of Adelaide :: Dr Gordon Smyth :: Walter and Eliza Hall Institute of Medical Research in Melbourne, Australia

Digital gene expression (DGE) technologies measure gene expression by counting sequence tags. They are sensitive technologies for measuring gene expression on a genomic scale, without the need for prior knowledge of the genome sequence. As the cost of DNA sequencing decreases, the number of DGE datasets is expected to grow dramatically. Various tests of differential expression have been proposed for replicated DGE data using over-dispersed binomial or Poisson models for the counts, but none of the these are usable when the number of replicates is very small. We develop tests using the negative binomial distribution to model overdispersion relative to the Poisson, and use conditional weighted likelihood to moderate the level of overdispersion across genes. A heuristic empirical Bayes algorithm is developed which is applicable to very general likelihood estimation contexts. Not only is our strategy applicable even with the smallest number of replicates, but it also proves to be more powerful than previous strategies when more replicates are available. The methodology is applicable to other counting technologies, such as proteomic spectral counts.
Rubber Ballons -- Prototypes of Hysteresis
15:10 Fri 16 Nov, 2007 :: G04 Napier Building University of Adelaide :: Emeritus Prof. Ingo Muller :: Technical University Berlin

Rubber balloons are characterized by a non-monotone pressure-radius relation which presages interesting non-trivial stability problems. A stability criterion is developed and exploited in order to show that the balloon may be stabilized at any radius by loading it with a piston under an elastic spring, if only the spring is hard enough. If two connected balloons are subject to an inflation-deflation cycle, the pressure-radius curve exhibits a fairly simple hysteresis loop. More complex hysteresis loops appear when more balloons are all inflated together. And if many balloons are inflated and deflated at the same time, the hysteresis loop assumes the form reminiscent of pseudo-elasticity. Stability in those complex cases is determined by a simple suggestive argument. References: [1] W.Kitsche, I.Muller, P.Strehlow. Simulation of pseudo-elastic behaviour in a system of rubber balloons. In: Metastability and Incompletely Posed Problems, S.Antman, J.L.Ericksen, D.Kinderlehrer, I.Muller (eds.) IMA Volume No.3, Springer Verlag, New York (1987) [2] I.Muller, P.Strehlow, Rubber and Rubber Balloons, Springer Lecture Notes on Physics, Springer Verlag, Heidelberg (2004)
Similarity solutions for surface-tension driven flows
15:10 Fri 14 Mar, 2008 :: LG29 Napier Building University of Adelaide :: Prof John Lister :: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK

The breakup of a mass of fluid into drops is a ubiquitous phenomenon in daily life, the natural environment and technology, with common examples including a dripping tap, ocean spray and ink-jet printing. It is a feature of many generic industrial processes such as spraying, emulsification, aeration, mixing and atomisation, and is an undesirable feature in coating and fibre spinning. Surface-tension driven pinch-off and the subsequent recoil are examples of finite-time singularities in which the interfacial curvature becomes infinite at the point of disconnection. As a result, the flow near the point of disconnection becomes self-similar and independent of initial and far-field conditions. Similarity solutions will be presented for the cases of inviscid and very viscous flow, along with comparison to experiments. In each case, a boundary-integral representation can be used both to examine the time-dependent behaviour and as the basis of a modified Newton scheme for direct solution of the similarity equations.
Counting fish
13:10 Wed 19 Mar, 2008 :: Napier 210 :: Mr Jono Tuke

How often have you asked yourself: "I wonder how many fish are in that lake?" Probably never, but if you ever did, then this is the lecture for you. The solution is easy (Seuss, 1960), but raises the question of how good the answer is. I will answer this by looking at confidence intervals. In the lecture, I will discuss what a confidence interval is and how to calculate it using techniques for calculating probabilities in poker. I will also look at how these ideas have been used in epidemiology, the study of disease, to estimate the number of people with diabetes. [1] Seuss, Dr. (1960). "One Fish Two Fish Red Fish Blue Fish". Random House Books.
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 taxon-sequences. 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 near-minimal 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 edge-contraction during the reconstruction of the tree. We conclude by demonstrating how this technique is used to achieve adaptive fast convergence.

Groundwater: using mathematics to solve our water crisis
13:10 Wed 9 Apr, 2008 :: Napier 210 :: Dr Michael Teubner

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

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

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

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

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

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

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

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

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

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

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

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

The 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 D-brane charges take values in the K-theory of spacetime, rather than in integral cohomology as one might have expected. I will also explore the mathematical consequences of a particular symmetry, called T-duality, in this context. I will give an intuitive introduction into D-branes and K-theory. No prior knowledge about either String Theory, D-branes or K-theory is required.
The limits of proof
13:10 Wed 21 May, 2008 :: Napier 210 :: A/Prof Finnur Larusson

The job of the mathematician is to discover new truths about mathematical objects and their relationships. Such truths are established by proving them. This raises a fundamental question. Can every mathematical truth be proved (by a sufficiently clever being) or are there truths that will forever lie beyond the reach of proof? Mathematics can be turned on itself to investigate this question. In this talk, we will see that under certain assumptions about proofs, there are truths that cannot be proved. You must decide for yourself whether you think these assumptions are valid!
Puzzle-based learning: Introduction to mathematics
15:10 Fri 23 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Zbigniew Michalewicz :: School of Computer Science, University of Adelaide

The talk addresses a gap in the educational curriculum for 1st year students by proposing a new course that aims at getting students to think about how to frame and solve unstructured problems. The idea is to increase the student's mathematical awareness and problem-solving skills by discussing a variety of puzzles. The talk makes an argument that this approach - called Puzzle-Based Learning - is very beneficial for introducing mathematics, critical thinking, and problem-solving skills.

The new course has been approved by the University of Adelaide for Faculty of Engineering, Computer Science, and Mathematics. Many other universities are in the process of introducing such a course. The course will be offered in two versions: (a) full-semester course and (b) a unit within general course (e.g. Introduction to Engineering). All teaching materials (power point slides, assignments, etc.) are being prepared. The new textbook (Puzzle-Based Learning: Introduction to Critical Thinking, Mathematics, and Problem Solving) will be available from June 2008. The talk provides additional information on this development.

For further information see

Computational Methods for Phase Response Analysis of Circadian Clocks
15:10 Fri 18 Jul, 2008 :: G04 Napier Building University of Adelaide. :: Prof. Linda Petzold :: Dept. of Mechanical and Environmental Engineering, University of California, Santa Barbara

Circadian clocks govern daily behaviors of organisms in all kingdoms of life. In mammals, the master clock resides in the suprachiasmatic nucleus (SCN) of the hypothalamus. It is composed of thousands of neurons, each of which contains a sloppy oscillator - a molecular clock governed by a transcriptional feedback network. Via intercellular signaling, the cell population synchronizes spontaneously, forming a coherent oscillation. This multi-oscillator is then entrained to its environment by the daily light/dark cycle.

Both at the cellular and tissular levels, the most important feature of the clock is its ability not simply to keep time, but to adjust its time, or phase, to signals. We present the parametric impulse phase response curve (pIPRC), an analytical analog to the phase response curve (PRC) used experimentally. We use the pIPRC to understand both the consequences of intercellular signaling and the light entrainment process. Further, we determine which model components determine the phase response behavior of a single oscillator by using a novel model reduction technique. We reduce the number of model components while preserving the pIPRC and then incorporate the resultant model into a couple SCN tissue model. Emergent properties, including the ability of the population to synchronize spontaneously are preserved in the reduction. Finally, we present some mathematical tools for the study of synchronization in a network of coupled, noisy oscillators.

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 (1823-1892) 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 (1831-1879) 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 diffusion-advection 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, Fokker-Plank-Kolmogorov-Feller 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 (advection-dispersion) 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 Jean-Luc 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 low-diffusivity 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 1-D 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.

Probabilistic models of human cognition
15:10 Fri 29 Aug, 2008 :: G03 Napier Building University of Adelaide :: Dr Daniel Navarro :: School of Psychology, University of Adelaide

Over the last 15 years a fairly substantial psychological literature has developed in which human reasoning and decision-making is viewed as the solution to a variety of statistical problems posed by the environments in which we operate. In this talk, I briefly outline the general approach to cognitive modelling that is adopted in this literature, which relies heavily on Bayesian statistics, and introduce a little of the current research in this field. In particular, I will discuss work by myself and others on the statistical basis of how people make simple inductive leaps and generalisations, and the links between these generalisations and how people acquire word meanings and learn new concepts. If time permits, the extensions of the work in which complex concepts may be characterised with the aid of nonparametric Bayesian tools such as Dirichlet processes will be briefly mentioned.
Free surface Stokes flows with surface tension
15:10 Fri 5 Sep, 2008 :: G03 Napier Building University of Adelaide :: Prof. Darren Crowdy :: Imperial College London

In this talk, we will survey a number of different free boundary problems involving slow viscous (Stokes) flows in which surface tension is active on the free boundary. Both steady and unsteady flows will be considered. Motivating applications range from industrial processes such as viscous sintering (where end-products are formed as a result of the surface-tension-driven densification of a compact of smaller particles that are heated in order that they coalesce) to biological phenomena such as understanding how organisms swim (i.e. propel themselves) at low Reynolds numbers. Common to our approach to all these problems will be an analytical/theoretical treatment of model problems via complex variable methods -- techniques well-known at infinite Reynolds numbers but used much less often in the Stokes regime. These model problems can give helpful insights into the behaviour of the true physical systems.
Mathematical modelling of blood flow in curved arteries
15:10 Fri 12 Sep, 2008 :: G03 Napier Building University of Adelaide :: Dr Jennifer Siggers :: Imperial College London

Atherosclerosis, characterised by plaques, is the most common arterial disease. Plaques tend to develop in regions of low mean wall shear stress, and regions where the wall shear stress changes direction during the course of the cardiac cycle. To investigate the effect of the arterial geometry and driving pressure gradient on the wall shear stress distribution we consider an idealised model of a curved artery with uniform curvature. We assume that the flow is fully-developed and seek solutions of the governing equations, finding the effect of the parameters on the flow and wall shear stress distribution. Most previous work assumes the curvature ratio is asymptotically small; however, many arteries have significant curvature (e.g. the aortic arch has curvature ratio approx 0.25), and in this work we consider in particular the effect of finite curvature.

We present an extensive analysis of curved-pipe flow driven by a steady and unsteady pressure gradients. Increasing the curvature causes the shear stress on the inside of the bend to rise, indicating that the risk of plaque development would be overestimated by considering only the weak curvature limit.

The Mechanics of Nanoscale Devices
15:10 Fri 10 Oct, 2008 :: G03 Napier Building University of Adelaide :: Associate Prof. John Sader :: Department of Mathematics and Statistics, The University of Melbourne

Nanomechanical sensors are often used to measure environmental changes with extreme sensitivity. Controlling the effects of surfaces and fluid dissipation presents significant challenges to achieving the ultimate sensitivity in these devices. In this talk, I will give an overview of theoretical/experimental work we are undertaking to explore the underlying physical processes in these systems. The talk will be general and aimed at introducing some recent developments in the field of nanomechanical sensors.
Assisted reproduction technology: how maths can contribute
13:10 Wed 22 Oct, 2008 :: Napier 210 :: Dr Yvonne Stokes

Most people will have heard of IVF (in vitro fertilisation), a technology for helping infertile couples have a baby. Although there are many IVF babies, many will also know that the success rate is still low for the cost and inconvenience involved. The fact that some women cannot make use of IVF because of life-threatening consequences is less well known but motivates research into other technologies, including IVM (in vitro maturation). What has all this to do with maths? Come along and find out how mathematical modelling is contributing to understanding and improvement in this important and interesting field.
Symmetry-breaking 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 low-energy 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 low-energy 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.
Oceanographic Research at the South Australian Research and Development Institute: opportunities for collaborative research
15:10 Fri 21 Nov, 2008 :: Napier G04 :: Associate Prof John Middleton :: South Australian Research and Development Institute

Increasing threats to S.A.'s fisheries and marine environment have underlined the increasing need for soundly based research into the ocean circulation and ecosystems (phyto/zooplankton) of the shelf and gulfs. With support of Marine Innovation SA, the Oceanography Program has within 2 years, grown to include 6 FTEs and a budget of over $4.8M. The program currently leads two major research projects, both of which involve numerical and applied mathematical modelling of oceanic flow and ecosystems as well as statistical techniques for the analysis of data. The first is the implementation of the Southern Australian Integrated Marine Observing System (SAIMOS) that is providing data to understand the dynamics of shelf boundary currents, monitor for climate change and understand the phyto/zooplankton ecosystems that under-pin SA's wild fisheries and aquaculture. SAIMOS involves the use of ship-based sampling, the deployment of underwater marine moorings, underwater gliders, HF Ocean RADAR, acoustic tracking of tagged fish and Autonomous Underwater vehicles.

The second major project involves measuring and modelling the ocean circulation and biological systems within Spencer Gulf and the impact on prawn larval dispersal and on the sustainability of existing and proposed aquaculture sites. The discussion will focus on opportunities for collaborative research with both faculty and students in this exciting growth area of S.A. science.

Key Predistribution in Grid-Based Wireless Sensor Networks
15:10 Fri 12 Dec, 2008 :: Napier G03 :: Dr Maura Paterson :: Information Security Group at Royal Holloway, University of London.

Wireless sensors are small, battery-powered devices that are deployed to measure quantities such as temperature within a given region, then form a wireless network to transmit and process the data they collect. We discuss the problem of distributing symmetric cryptographic keys to the nodes of a wireless sensor network in the case where the sensors are arranged in a square or hexagonal grid, and we propose a key predistribution scheme for such networks that is based on Costas arrays. We introduce more general structures known as distinct-difference configurations, and show that they provide a flexible choice of parameters in our scheme, leading to more efficient performance than that achieved by prior schemes from the literature.
Hunting Non-linear Mathematical Butterflies
15:10 Fri 23 Jan, 2009 :: Napier LG29 :: Prof Nalini Joshi :: University of Sydney

The utility of mathematical models relies on their ability to predict the future from a known set of initial states. But there are non-linear systems, like the weather, where future behaviours are unpredictable unless their initial state is known to infinite precision. This is the butterfly effect. I will show how to analyse functions to overcome this problem for the classical Painleve equations, differential equations that provide archetypical non-linear models of modern physics.
What on Earth is Computational Advertising?
15:10 Wed 28 Jan, 2009 :: Napier G03 :: Dr John Tomlin :: Yahoo! Research Labs

This talk will begin with a brief introduction to, and overview of, the topic we have come to call "computational advertising", by which we mean the algorithmic techniques useful for the optimal placement, scheduling and context of on-line advertisements. Such advertisements encompass a large and growing fraction of the advertising industry, and, in the forms of display advertising, content match, and search marketing, bring in a large fraction of the income derived from the web. In addition to the overview, we give two examples of optimization models applied to problems in sponsored search and display advertising.
On the Henstock-Kurzweil integral (along with concerns about general math education in Europe)
15:10 Fri 13 Feb, 2009 :: Napier LG28 :: Prof Jean-Pierre 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 Henstock-Kurzweil 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.).
Bursts and canards in a pituitary lactotroph model
15:10 Fri 6 Mar, 2009 :: Napier LG29 :: Dr Martin Wechselberger :: University of Sydney

Bursting oscillations in nerve cells have been the focus of a great deal of attention by mathematicians. These are typically studied by taking advantage of multiple time-scales in the system under study to perform a singular perturbation analysis. Bursting also occurs in hormone-secreting pituitary cells, but is characterized by fast bursts with small electrical impulses. Although the separation of time-scales is not as clear, singular perturbation analysis is still the key to understand the bursting mechanism. In particular, we will show that canards are responsible for the observed oscillatory behaviour.
Boltzmann's Equations for Suspension Flow in Porous Media and Correction of the Classical Model
15:10 Fri 13 Mar, 2009 :: Napier LG29 :: Prof Pavel Bedrikovetsky :: University of Adelaide

Suspension/colloid transport in porous media is a basic phenomenon in environmental, petroleum and chemical engineering. Suspension of particles moves through porous media and particles are captured by straining or attraction. We revise the classical equations for particle mass balance and particle capture kinetics and show its non-realistic behaviour in cases of large dispersion and of flow-free filtration. In order to resolve the paradoxes, the pore-scale model is derived. The model can be transformed to Boltzmann equation with particle distribution over pores. Introduction of sink-source terms into Boltzmann equation results in much more simple calculations if compared with the traditional Chapman-Enskog averaging procedure. Technique of projecting operators in Hilbert space of Fourier images is used. The projection subspace is constructed in a way to avoid dependency of averaged equations on sink-source terms. The averaging results in explicit expressions for particle flux and capture rate. The particle flux expression describes the effect of advective particle velocity decrease if compared with the carrier water velocity due to preferential capture of "slow" particles in small pores. The capture rate kinetics describes capture from either advective or diffusive fluxes. The equations derived exhibit positive advection velocity for any dispersion and particle capture in immobile fluid that resolves the above-mentioned paradox. Finally, we discuss validation of the model for propagation of contaminants in aquifers, for filtration, for potable water production by artesian wells, for formation damage in oilfields.
From histograms to multivariate polynomial histograms and shape estimation
12:10 Thu 19 Mar, 2009 :: Napier 210 :: A/Prof Inge Koch

Histograms are convenient and easy-to-use tools for estimating the shape of data, but they have serious problems which are magnified for multivariate data. We combine classic histograms with shape estimation by polynomials. The new relatives, `polynomial histograms', have surprisingly nice mathematical properties, which we will explore in this talk. We also show how they can be used for real data of 10-20 dimensions to analyse and understand the shape of these data.
Tummy troubles
12:10 Thu 9 Apr, 2009 :: Napier 210 :: Dr Ben Binder

Hirschsprung's disease is relatively common, affecting roughly 1 in 5000 newly born babies each year in Australia. The disease occurs when there is an incomplete formation of the nervous system in the gut. Mathematical models can help in determining the underlying mechanisms that cause the disease. Comparisons between theoretical predictions and experimental results will be made.
15:10 Thu 16 Apr, 2009 :: TBA :: Prof Jonathan Borwein :: University of Newcastle

Multi-scale tools for interpreting cell biology data
15:10 Fri 17 Apr, 2009 :: Napier LG29 :: Dr Matthew Simpson :: University of Melbourne

Trajectory data from observations of a random walk process are often used to characterize macroscopic transport coefficients and to infer motility mechanisms in cell biology. New continuum equations describing the average moments of the position of an individual agent in a population of interacting agents are derived and validated. Unlike standard noninteracting random walks, the new moment equations explicitly represent the interactions between agents as they are coupled to the macroscopic agent density. Key issues associated with the validity of the new continuum equations and the interpretation of experimental data will be explored.
Sloshing in tanks of liquefied natural gas (LNG) vessels
15:10 Wed 22 Apr, 2009 :: Napier LG29 :: Prof. Frederic Dias :: ENS, Cachan

The last scientific conversation I had with Ernie Tuck was on liquid impact. As a matter of fact, we discussed the paper by J.H. Milgram, Journal of Fluid Mechanics 37 (1969), entitled "The motion of a fluid in a cylindrical container with a free surface following vertical impact." Liquid impact is a key issue in sloshing and in particular in sloshing in tanks of LNG vessels. Numerical simulations of sloshing have been performed by various groups, using various types of numerical methods. In terms of the numerical results, the outcome is often impressive, but the question remains of how relevant these results are when it comes to determining impact pressures. The numerical models are too simplified to reproduce the high variability of the measured pressures. In fact, for the time being, it is not possible to simulate accurately both global and local effects. Unfortunately it appears that local effects predominate over global effects when the behaviour of pressures is considered. Having said this, it is important to point out that numerical studies can be quite useful to perform sensitivity analyses in idealized conditions such as a liquid mass falling under gravity on top of a horizontal wall and then spreading along the lateral sides. Simple analytical models inspired by numerical results on idealized problems can also be useful to predict trends. The talk is organized as follows: After a brief introduction on the sloshing problem and on scaling laws, it will be explained to what extent numerical studies can be used to improve our understanding of impact pressures. Results on a liquid mass hitting a wall obtained by a finite-volume code with interface reconstruction as well as results obtained by a simple analytical model will be shown to reproduce the trends of experiments on sloshing. This is joint work with L. Brosset (GazTransport & Technigaz), J.-M. Ghidaglia (ENS Cachan) and J.-P. Braeunig (INRIA).
Dynamics of Moving Average Rules in a Continuous-time Financial Market Model
15:10 Fri 8 May, 2009 :: LG29 :: Associate Prof (Tony) Xuezhong He :: University of Technology Sydney

Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used in discrete-time HAMs. Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and time delay are obtained. By focusing on the stabilizing role of the time delay, it is found that an increase in time delay not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize an otherwise unstable market price. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in financial markets.
Averaging reduction for stochastic PDEs
15:10 Fri 5 Jun, 2009 :: LG29 :: Dr Wei Wang :: University of Adelaide

In this talk, I introduce recent work on macroscopic reduction for stochastic PDEs by an averaging method. Furthermore by using a special coupling boundary conditions, a macroscopic discrete approximation model can be derived.
Quadrature domains, p-Laplacian growth, and bubbles contracting in Hele-Shaw cells with a power-law fluid.
15:10 Mon 15 Jun, 2009 :: Napier LG24 :: Dr Scott McCue :: Queensland University Technology

The classical Hele-Shaw flow problem is related to Laplacian growth and null-quadrature domains. A generalisation is constructed for power-law fluids, governed by the p-Laplace equation, and a number of results are established that are analogous to the classical case. Both fluid clearance and bubble extinction is considered, and by considering two extremes of extinction behaviour, a rather complete asymptotic description of possible behaviours is found.
Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations
15:10 Fri 19 Jun, 2009 :: LG29 :: Prof. Eckhard Platen :: University of Technology, Sydney

This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor-corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to overcome some of the numerical instabilities that are often experienced when using the explicit Euler method. This is of importance, for instance, in finance where martingale dynamics arise for solutions of SDEs with multiplicative diffusion coefficients. Numerical experiments demonstrate the improved asymptotic stability properties of the proposed symmetric predictor-corrector Euler methods.
Dispersing and settling populations in biology
15:10 Tue 23 Jun, 2009 :: Napier G03 :: Prof Kerry Landman :: University of Melbourne

Partial differential equations are used to model populations (such as cells, animals or molecules) consisting of individuals that undergo two important processes: dispersal and settling. I will describe some general characteristics of these systems, as well as some of our recent projects.
15:10 Thu 25 Jun, 2009 :: TBA :: Prof Arun Ram :: University of Melbourne

Unsolvable problems in mathematics
15:10 Fri 3 Jul, 2009 :: Badger Labs G13 Macbeth Lecture Theatre :: Prof Greg Hjorth :: University of Melbourne

In the 1900 International Congress of Mathematicians David Hilbert proposed a list of 23 landmark mathematical problems. The first of these problems was shown by Paul Cohen in 1963 to be undecidable—which is to say, in informal language, that it was in principle completely unsolvable. The tenth problem was shown by Yuri Matiyasevich to be unsolvable in 1970. These developments would very likely have been profoundly surprising, perhaps even disturbing, to Hilbert. I want to review some of the general history of unsolvable problems. As much as reasonably possible in the time allowed, I hope to give the audience a sense of why the appearance of unsolvable problems in mathematics was inevitable, and perhaps even desirable.
Quantum Billiards
15:10 Fri 7 Aug, 2009 :: Badger labs G13 Macbeth Lecture Theatre :: Prof Andrew Hassell :: Australian National University

By a "billiard" I mean a bounded plane domain D, with smooth (enough) boundary. Quantum billiards is the study of properties of eigenfunctions of the Laplacian on D, i.e. solutions of $\Delta u = Eu$, where $u$ is a function on D vanishing at the boundary, $\Delta$ is the Laplacian on D and $E$ is a real number, in the limit as $E \to \infty$. This large-E limit is the "classical limit" in which eigenfunctions exhibit behaviour related to the classical billiard system (a billiard ball moving around inside D, bouncing elastically off the boundary). I will talk about Quantum Ergodicity, which is the property that "most of" the eigenfunctions become uniformly distributed in D, asymptotically as $E \to \infty$, i.e. they are the same size, on average, in all parts of the domain D; and the stronger property of Quantum Unique Ergodicity, which is the same property with the words "most of" deleted.
Predicting turbulence
12:10 Wed 12 Aug, 2009 :: Napier 210 :: Dr Trent Mattner :: University of Adelaide

Turbulence is characterised by three-dimensional unsteady fluid motion over a wide range of spatial and temporal scales. It is important in many problems of technological and scientific interest, such as drag reduction, energy production and climate prediction. In this talk, I will explain why turbulent flows are difficult to predict and describe a modern mathematical model of turbulence based on a random collection of fluid vortices.
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 low-dimensional 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.
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 straight-pipe, 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 quasi-conformal 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.
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 2002-2003, Grigori Perelman gave a spectacular proof of the Poincare Conjecture (every smooth compact simply connected three-dimensional 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).
Contemporary frontiers in statistics
15:10 Mon 28 Sep, 2009 :: Badger Labs G31 Macbeth Lectrue :: Prof. Peter Hall :: University of Melbourne

The availability of powerful computing equipment has had a dramatic impact on statistical methods and thinking, changing forever the way data are analysed. New data types, larger quantities of data, and new classes of research problem are all motivating new statistical methods. We shall give examples of each of these issues, and discuss the current and future directions of frontier problems in statistics.
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.
Modelling and pricing for portfolio credit derivatives
15:10 Fri 16 Oct, 2009 :: MacBeth Lecture Theatre :: Dr Ben Hambly :: University of Oxford

The current financial crisis has been in part precipitated by the growth of complex credit derivatives and their mispricing. This talk will discuss some of the background to the `credit crunch', as well as the models and methods used currently. We will then develop an alternative view of large basket credit derivatives, as functions of a stochastic partial differential equation, which addresses some of the shortcomings.
Manifold destiny: a talk on water, fire and life
15:10 Fri 6 Nov, 2009 :: MacBeth Lecture Theatre :: Dr Sanjeeva Balasuriya :: University of Adelaide

Manifolds are important entities in dynamical systems, and organise space into regions in which different motions occur. For example, intersections between stable and unstable manifolds in discrete systems result in chaotic motion. This talk will focus on manifolds and their locations in continuous dynamical systems, and in particular on Melnikov's method and its adaptations for determining the effect of perturbations on manifolds. The relevance of such adaptations to a surprising range of applications will be shown, in addition to recent theoretical developments inspired by such problems. The applications addressed in this talk include understanding the motion of fluid near oceanic eddies and currents, optimising mixing in nano-fluidic devices in order to improve reactions, computing the speed of a flame front, and finding the spreading rate of bacterial colonies.
This talk has been cancelled
15:10 Fri 27 Nov, 2009 :: TBA :: Prof Ulrich Horst :: Humboldt-University, Berlin

A solution to the Gromov-Vaserstein problem
15:10 Fri 29 Jan, 2010 :: Engineering North N 158 Chapman Lecture Theatre :: Prof Frank Kutzschebauch :: University of Berne, Switzerland

Any matrix in $SL_n (\mathbb C)$ can be written as a product of elementary matrices using the Gauss elimination process. If instead of the field of complex numbers, the entries in the matrix are elements of a more general ring, this becomes a delicate question. In particular, rings of complex-valued functions on a space are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size $n$ of the matrix is at least 3. In the topological category, the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\mathbb C^m$, the problem was posed by Gromov in the 1980s. We report on a complete solution to Gromov's problem. A main tool is the Oka-Grauert-Gromov h-principle in complex analysis. Our main theorem can be formulated as follows: In the absence of obvious topological obstructions, the Gauss elimination process can be performed in a way that depends holomorphically on the matrix. This is joint work with Bj\"orn Ivarsson.
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 non-empty set (called an 'alphabet'). In mathematics, words naturally arise when one wants to represent elements from some set (e.g., integers, real numbers, p-adic 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 non-negative integers n. This is joint work with Jean-Paul Allouche (Universite Paris-Sud, France).

The exceptional Lie group G_2 and rolling balls
15:10 Fri 19 Feb, 2010 :: Napier LG28 :: Prof Pawel Nurowski :: University of Warsaw

In this talk, after a brief history of how the exceptional Lie group G_2 was discovered, I present various appearances of this group in mathematics. Its physical realisation as a symmetry group of a simple mechanical system will also be discussed.
Some unusual uses of usual symmetries and some usual uses of unusual symmetries
12:10 Wed 10 Mar, 2010 :: School board room :: Prof Phil Broadbridge :: La Trobe University

Ever since Sophus Lie around 1880, continuous groups of invariance transformations have been used to reduce variables and to construct special solutions of PDEs. I will outline the general ideas, then show some variations on the usual reduction algorithm that I have used to solve some practical nonlinear boundary value problems. Applications include soil-water flow, metal surface evolution and population genetics.
Nonlinear time series econometrics and financial econometrics: a personal overview
15:10 Fri 12 Mar, 2010 :: Napier G04 :: Prof Jiti Gao :: University of Adelaide

Through using ten examples, the talk focuses on the recent development on nonlinear time series econometrics and financial econometrics. Such examples cover the following models: 1. Nonlinear time series trend model; 2. Partially linear autoregressive model; 3. Nonlinear capital asset pricing model; 4. Additive capital asset pricing model; 5. Varying-coefficient capital asset pricing model; 6. Semiparametric error-term model; 7. Nonlinear and nonstationary model; 8. Partially linear ARCH model; 9. Continuous-time financial model; and 10. Stochastic volatility model.
Modelling of the Human Skin Equivalent
15:10 Fri 26 Mar, 2010 :: Napier 102 :: Prof Graeme Pettet :: Queensland University of Technology

A brief overview will be given of the development of a so called Human Skin Equivalent Construct. This laboratory grown construct can be used for studying growth, response and the repair of human skin subjected to wounding and/or treatment under strictly regulated conditions. Details will also be provided of a series of mathematical models we have developed that describe the dynamics of the Human Skin Equivalent Construct, which can be used to assist in the development of the experimental protocol, and to provide insight into the fundamental processes at play in the growth and development of the epidermis in both healthy and diseased states.
Exploratory experimentation and computation
15:10 Fri 16 Apr, 2010 :: Napier LG29 :: Prof Jonathan Borwein :: University of Newcastle

The mathematical research community is facing a great challenge to re-evaluate the role of proof in light of the growing power of current computer systems, of modern mathematical computing packages, and of the growing capacity to data-mine on the Internet. Add to that the enormous complexity of many modern capstone results such as the Poincare conjecture, Fermat's last theorem, and the Classification of finite simple groups. As the need and prospects for inductive mathematics blossom, the requirement to ensure the role of proof is properly founded remains undiminished. I shall look at the philosophical context with examples and then offer some of five bench-marking examples of the opportunities and challenges we face.
Mathematical epidemiology with a focus on households
15:10 Fri 23 Apr, 2010 :: Napier G04 :: Dr Joshua Ross :: University of Adelaide

Mathematical models are now used routinely to inform national and global policy-makers on issues that threaten human health or which have an adverse impact on the economy. In the first part of this talk I will provide an overview of mathematical epidemiology starting with the classical deterministic model and leading to some of the current challenges. I will then present some of my recently published work which provides computationally-efficient methods for studying a mathematical model incorporating household structure. We will conclude by briefly discussing some "work-in-progess" which utilises these methods to address the issues of inference, and mixing pattern and contact structure, for emerging infections.
Estimation of sparse Bayesian networks using a score-based approach
15:10 Fri 30 Apr, 2010 :: School Board Room :: Dr Jessica Kasza :: University of Copenhagen

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

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

Holonomy groups
15:10 Fri 7 May, 2010 :: Napier LG24 :: Dr Thomas Leistner :: University of Adelaide

In the first part of the talk I will illustrate some basic concepts of differential geometry that lead to the notion of a holonomy group. Then I will explain Berger's classification of Riemannian holonomy groups and discuss questions that arose from it. Finally, I will focus on holonomy groups of Lorentzian manifolds and indicate briefly why all this is of relevance to present-day theoretical physics.
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

High on a mathematician's to-do list is classifying objects and structures that arise in mathematics. We see patterns in things and want to know what other sorts of things behave similarly. This poses several problems. How can you tell when two seemingly different mathematical objects are the same? Can you even tell when two seemingly similar mathematical objects are the same? In fact, what does "the same" even mean? How can you tell if two things are the same when you can't even see them! In this talk, we will take a walk through some areas of maths known as algebraic topology and category theory and I will show you some of the ways mathematicians have devised to tell when two things are "the same".
Whole genome analysis of repetitive DNA
15:10 Fri 21 May, 2010 :: Napier 209 :: Prof David Adelson :: University of Adelaide

The interspersed repeat content of mammalian genomes has been best characterized in human, mouse and cow. We carried out de novo identification of repeated elements in the equine genome and identified previously unknown elements present at low copy number. The equine genome contains typical eutherian mammal repeats. We analysed both interspersed and simple sequence repeats (SSR) genome-wide, finding that some repeat classes are spatially correlated with each other as well as with G+C content and gene density. Based on these spatial correlations, we have confirmed recently-described ancestral vs clade-specific genome territories defined by repeat content. Territories enriched for ancestral repeats tended to be contiguous domains. To determine if these territories were evolutionarily conserved, we compared these results with a similar analysis of the human genome, and observed similar ancestral repeat enriched domains. These results indicate that ancestral, evolutionarily conserved mammalian genome territories can be identified on the basis of repeat content alone. Interspersed repeats of different ages appear to be analogous to geologic strata, allowing identification of ancient vs newly remodelled regions of mammalian genomes.
The mathematics of theoretical inference in cognitive psychology
15:10 Fri 11 Jun, 2010 :: Napier LG24 :: Prof John Dunn :: University of Adelaide

The aim of psychology in general, and of cognitive psychology in particular, is to construct theoretical accounts of mental processes based on observed changes in performance on one or more cognitive tasks. The fundamental problem faced by the researcher is that these mental processes are not directly observable but must be inferred from changes in performance between different experimental conditions. This inference is further complicated by the fact that performance measures may only be monotonically related to the underlying psychological constructs. State-trace analysis provides an approach to this problem which has gained increasing interest in recent years. In this talk, I explain state-trace analysis and discuss the set of mathematical issues that flow from it. Principal among these are the challenges of statistical inference and an unexpected connection to the mathematics of oriented matroids.
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 Khovanov-Lauda and Rouquier whose representation theory categorifies quantum groups of Kac-Moody 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.
Meteorological drivers of extreme bushfire events in southern Australia
15:10 Fri 2 Jul, 2010 :: Benham Lecture Theatre :: Prof Graham Mills :: Centre for Australian Weather and Climate Research, Melbourne

Bushfires occur regularly during summer in southern Australia, but only a few of these fires become iconic due to their effects, either in terms of loss of life or economic and social cost. Such events include Black Friday (1939), the Hobart fires (1967), Ash Wednesday (1983), the Canberra bushfires (2003), and most recently Black Saturday in February 2009. In most of these events the weather of the day was statistically extreme in terms of heat, (low) humidity, and wind speed, and in terms of antecedent drought. There are a number of reasons for conducting post-event analyses of the meteorology of these events. One is to identify any meteorological circulation systems or dynamic processes occurring on those days that might not be widely or hitherto recognised, to document these, and to develop new forecast or guidance products. The understanding and prediction of such features can be used in the short term to assist in effective management of fires and the safety of firefighters and in the medium range to assist preparedness for the onset of extreme conditions. The results of such studies can also be applied to simulations of future climates to assess the likely changes in frequency of the most extreme fire weather events, and their documentary records provide a resource that can be used for advanced training purposes. In addition, particularly for events further in the past, revisiting these events using reanalysis data sets and contemporary NWP models can also provide insights unavailable at the time of the events. Over the past few years the Bushfire CRC's Fire Weather and Fire Danger project in CAWCR has studied the mesoscale meteorology of a number of major fire events, including the days of Ash Wednesday 1983, the Dandenong Ranges fire in January 1997, the Canberra fires and the Alpine breakout fires in January 2003, the Lower Eyre Peninsula fires in January 2005 and the Boorabbin fire in December 2007-January 2008. Various aspects of these studies are described below, including the structures of dry cold frontal wind changes, the particular character of the cold fronts associated with the most damaging fires in southeastern Australia, and some aspects of how the vertical temperature and humidity structure of the atmosphere may affect the fire weather at the surface. These studies reveal much about these major events, but also suggest future research directions, and some of these will be discussed.
Adjoint methods for adaptive error control, optimization, and uncertainty quantification
15:10 Fri 16 Jul, 2010 :: Napier G03 :: Dr Varis Carey :: Colorado State University

We give an introduction to the use of adjoint equations (and solutions) for numerical error control and solution enhancement of PDEs. In addition, the same equations can be used for optimization routines and uncertainty quantification. We discuss the modification of these methods in the context of operator splitting and to non-variational (e.g. finite volume) methods. Finally, we conclude with an application of the method to the shallow water equations and discuss some of the hurdles that need to be overcome when extending adjoint methodologies to ocean and atmospheric modeling.
Mathematica Seminar
15:10 Wed 28 Jul, 2010 :: Engineering Annex 314 :: Kim Schriefer :: Wolfram Research

The Mathematica Seminars 2010 offer an opportunity to experience the applicability, ease-of-use, as well as the advancements of Mathematica 7 in education and academic research. These seminars will highlight the latest directions in technical computing with Mathematica, and the impact this technology has across a wide range of academic fields, from maths, physics and biology to finance, economics and business. Those not yet familiar with Mathematica will gain an overview of the system and discover the breadth of applications it can address, while experts will get firsthand experience with recent advances in Mathematica like parallel computing, digital image processing, point-and-click palettes, built-in curated data, as well as courseware examples.
Counting lattice points in polytopes and geometry
15:10 Fri 6 Aug, 2010 :: Napier G04 :: Dr Paul Norbury :: University of Melbourne

Counting lattice points in polytopes arises in many areas of pure and applied mathematics. A basic counting problem is this: how many different ways can one give change of 1 dollar into 5,10, 20 and 50 cent coins? This problem counts lattice points in a tetrahedron, and if there also must be exactly 10 coins then it counts lattice points in a triangle. The number of lattice points in polytopes can be used to measure the robustness of a computer network, or in statistics to test independence of characteristics of samples. I will describe the general structure of lattice point counts and the difficulty of calculations. I will then describe a particular lattice point count in which the structure simplifies considerably allowing one to calculate easily. I will spend a brief time at the end describing how this is related to the moduli space of Riemann surfaces.
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 non-technical terms of the topic described in the title, from first year linear algebra to von Neumann algebras.
A polyhedral model for boron nitride nanotubes
15:10 Fri 3 Sep, 2010 :: Napier G04 :: Dr Barry Cox :: University of Adelaide

The conventional rolled-up model of nanotubes does not apply to the very small radii tubes, for which curvature effects become significant. In this talk an existing geometric model for carbon nanotubes proposed by the authors, which accommodates this deficiency and which is based on the exact polyhedral cylindrical structure, is extended to a nanotube structure involving two species of atoms in equal proportion, and in particular boron nitride nanotubes. This generalisation allows the principle features to be included as the fundamental assumptions of the model, such as equal bond length but distinct bond angles and radii between the two species. The polyhedral model is based on the five simple geometric assumptions: (i) all bonds are of equal length, (ii) all bond angles for the boron atoms are equal, (iii) all boron atoms lie at an equal distance from the nanotube axis, (iv) all nitrogen atoms lie at an equal distance from the nanotube axis, and (v) there exists a fixed ratio of pyramidal height H, between the boron species compared with the corresponding height in a symmetric single species nanotube. Working from these postulates, expressions are derived for the various structural parameters such as radii and bond angles for the two species for specific values of the chiral vector numbers (n,m). The new model incorporates an additional constant of proportionality H, which we assume applies to all nanotubes comprising the same elements and is such that H = 1 for a single species nanotube. Comparison with `ab initio' studies suggest that this assumption is entirely reasonable, and in particular we determine the value H = 0.56\pm0.04 for boron nitride, based on computational results in the literature. This talk relates to work which is a couple of years old and given time at the end we will discuss some newer results in geometric models developed with our former student Richard Lee (now also at the University of Adelaide as a post doc) and some work-in-progress on carbon nanocones. Note: pyramidal height is our own terminology and will be explained in the talk.
Mathematical Sciences - Student and Industry Program
17:30 Mon 13 Sep, 2010 :: Rumours Cafe Level 6 Union House North Terrace Campus

Are you a professional who works within a relevant sector and wish to share your knowledge and experience with Students? Are you a current Student who is looking for the opportunity to talk to an Industry Professional? Then the Student and Industry Program is for you!

This event aims to provide current students with the opportunity to talk one-on-one with past graduates and industry professionals; gaining practical industry knowledge to help define their career goals. Students, industry and the University alike have the opportunity to benefit from the connections made through the program.

Admission is free, but places are limited, so get in early. Contact Maryanne Noon by Friday 3rd September 2010 with your name, Student ID number and program. e: p: 8313 0969

Other information Students are asked to arrive at 5:00pm sharp for a briefing prior to the function. Dress Code: Business Casual.

Contraction subgroups in locally compact groups
13:10 Fri 17 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Prof George Willis :: University of Newcastle

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

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

The sense of smell is important in nature, but the least well understood of our senses. A mathematical model of smell, which combines the transmission of volatile-organic-compound chemical signals (VOCs) on the wind, transduced by olfactory receptors in our noses into neural information, and assembled into our odour perception, is useful. Applications include regulations for odour nuisance, like German VDI protocols for calibrated noses, to the design of modern chemical sensors for extracting information from the environment and even for the perfume industry. This talk gives a broad overview of turbulent mixing in surface layers of the atmosphere, measurements of VOCs with PTR-MS (proton transfer reaction mass spectrometers), our noses, and integrated environmental models of the Alumina industry (a source of odour emissions) to help understand the science of smell.
Explicit numerical simulation of multiphase and confined flows
15:10 Fri 8 Oct, 2010 :: Napier G04 :: Prof Mark Biggs :: University of Adelaide

Simulations in which the system of interest is essentially mimicked are termed explicit numerical simulations (ENS). Direct numerical simulation (DNS) of turbulence is a well known and long-standing example of ENS. Such simulations provide a basis for elucidating fundamentals in a way that is impossible experimentally and formulating and parameterizing engineering models with reduced experimentation. In this presentation, I will first outline the concept of ENS. I will then report a number of ENS-based studies of various multiphase fluid systems and flows in porous media. In the first of these studies, which is concerned with flow of suspensions in porous media accompanied by deposition, ENS is used to demonstrate the significant inadequacies of the classical trajectory models typically used for the study of such problems. In the second study, which is concerned with elucidating the change in binary droplet collision behaviour with Capillary number (Ca) and Reynolds number (Re), a range of collision scenarios are revealed as a function of Ca and Re and it appears that the boundaries between these scenarios in the Ca-Re space are not distinct but, rather, smeared. In the final study, it is shown that ENS an be used to predict ab initio the hydrodynamic properties of single phase flow through porous media from the Darcy to the turbulent regimes.
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, high-dimensional low sample size problems), non-Gaussian 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.
Slippery issues in nano- and microscale fluid flows
11:10 Tue 30 Nov, 2010 :: Innova teaching suite B21 :: Dr Shaun C. Hendy :: Victoria University of Wellington

The no-slip boundary condition was considered to have been experimentally established for the flow of simple liquids over solid surfaces in the early 20th century. Nonetheless the refinement of a number of measurement techniques has recently led to the observation of nano- and microscale violations of the no-slip boundary condition by simple fluids flowing over non-wetting surfaces. However it is important to distinguish between intrinsic slip, which arises solely from the chemical interaction between the liquid and a homogeneous, atomically flat surface and effective slip, typically measured in macroscopic experiments, which emerges from the interaction of microscopic chemical heterogeneity, roughness and contaminants. Here we consider the role of both intrinsic and effective slip boundary conditions in nanoscale and microscale fluid flows using a theoretical approach, complemented by molecular dynamics simulations, and experimental evidence where available. Firstly, we consider nanoscale flows in small capillaries, including carbon nanotubes, where we have developed and solved a generalised Lucas-Washburn equation that incorporates slip to describe the uptake of droplets. We then consider the general problem of relating effective slip to microscopic intrinsic slip and roughness, and discuss several cases where we have been able to solve this problem analytically. Finally, we look at applications of these results to carbon nanotube growth, self-cleaning surfaces, catalysis, and putting insulation in your roof.
Arbitrage bounds for weighted variance swap prices
15:05 Fri 3 Dec, 2010 :: Napier LG28 :: Prof Mark Davis :: Imperial College London

This paper builds on earlier work by Davis and Hobson (Mathematical Finance, 2007) giving model-free---except for a 'frictionless markets' assumption--- necessary and sufficient conditions for absence of arbitrage given a set of current-time put and call options on some underlying asset. Here we suppose that the prices of a set of put options, all maturing at the same time, are given and satisfy the conditions for consistency with absence of arbitrage. We now add a path-dependent option, specifically a weighted variance swap, to the set of traded assets and ask what are the conditions on its time-0 price under which consistency with absence of arbitrage is maintained. In the present work, we work under the extra modelling assumption that the underlying asset price process has continuous paths. In general, we find that there is always a non- trivial lower bound to the range of arbitrage-free prices, but only in the case of a corridor swap do we obtain a finite upper bound. In the case of, say, the vanilla variance swap, a finite upper bound exists when there are additional traded European options which constrain the left wing of the volatility surface in appropriate ways.
O'week welcome lunch
12:00 Thu 24 Feb, 2011 :: 6.52 Ingkarni Wardli

This event gives an opportunity for new students in the School of Mathematical Sciences to meet the school's academic members and students already in the school.
Mathematical modelling in nanotechnology
15:10 Fri 4 Mar, 2011 :: 7.15 Ingkarni Wardli :: Prof Jim Hill :: University of Adelaide

In this talk we present an overview of the mathematical modelling contributions of the Nanomechanics Groups at the Universities of Adelaide and Wollongong. Fullerenes and carbon nanotubes have unique properties, such as low weight, high strength, flexibility, high thermal conductivity and chemical stability, and they have many potential applications in nano-devices. In this talk we first present some new results on the geometric structure of carbon nanotubes and on related nanostructures. One concept that has attracted much attention is the creation of nano-oscillators, to produce frequencies in the gigahertz range, for applications such as ultra-fast optical filters and nano-antennae. The sliding of an inner shell inside an outer shell of a multi-walled carbon nanotube can generate oscillatory frequencies up to several gigahertz, and the shorter the inner tube the higher the frequency. A C60-nanotube oscillator generates high frequencies by oscillating a C60 fullerene inside a single-walled carbon nanotube. Here we discuss the underlying mechanisms of nano-oscillators and using the Lennard-Jones potential together with the continuum approach, to mathematically model the C60-nanotube nano-oscillator. Finally, three illustrative examples of recent modelling in hydrogen storage, nanomedicine and nanocomputing are discussed.
Lattices in exotic groups
15:10 Fri 18 Mar, 2011 :: 7.15 Ingkarni Wardli :: Dr Anne Thomas :: University of Sydney

A lattice in a locally compact group G is a discrete subgroup of cofinite volume. Lattices in Lie groups are well-studied, but little is known about lattices in other, "exotic", locally compact groups. Examples of exotic groups include isometry groups of trees, buildings, polyhedral complexes and CAT(0) spaces, and Kac-Moody groups. We will survey known results, which include both rigidity and surprising examples of flexibility, and discuss the wide range of tools used to investigate lattices in these non-classical settings.
To which extent the model of Black-Scholes can be applied in the financial market?
12:10 Mon 21 Mar, 2011 :: 5.57 Ingkarni Wardli :: Ahmed Hamada :: University of Adelaide

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

I hope we don't have to wait until oil and coal run out before we tackle that." - Thomas Edison, 1931. In a bid to resolve energy issues consistent with Thomas Edison's worries, scientists have been looking at other clean and sustainable sources of energy such as natural gas - methane. In this talk, the interaction between a methane molecule and carbon nanotubes is investigated mathematically, using two different models - first discrete and second, continuous. These models are analyzed to determine the dimensions of the particular nanotubes which will readily suck-up methane molecules. The results determine the minimum and maximum interaction energies required for methane encapsulation in different tube sizes, and establish the second model of the methane molecule as a simple and elegant model which might be exploited for other problems.
Nanotechnology: The mathematics of gas storage in metal-organic frameworks.
12:10 Mon 28 Mar, 2011 :: 5.57 Ingkarni Wardli :: Wei Xian Lim :: University of Adelaide

Have you thought about what sort of car you would be driving in the future? Would it be a hybrid, solar, hydrogen or electric car? I would like to be driving a hydrogen car because my field of research may aid in their development! In my presentation I will introduce you to the world of metal-organic frameworks, which are an exciting new class of materials that have great potential in applications such as hydrogen gas storage. I will also discuss about the mathematical model that I am using to model the performance of metal-organic frameworks based on beryllium.
Algebraic hypersurfaces arising from Gorenstein algebras
15:10 Fri 8 Apr, 2011 :: 7.15 Ingkarni Wardli :: Associate Prof Alexander Isaev :: Australian National University

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 CR-geometry. 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 Value-at-Risk and conditional Value-at-Risk as measures. However, these measures are not time consistent and Value-at-Risk can penalize diversification. A modern theory of risk measures is being developed which is related to solutions of backward stochastic differential equations in continuous time and stochastic difference equations in discrete time. I first review risk measures used in mathematical finance, including static and dynamic risk measures. I recall results relating to backward stochastic difference equations (BSDEs) associated with a single jump process. Then I evaluate some numerical examples of the solutions of the backward stochastic difference equations and related risk measures. These concepts are new. I hope the examples will indicate how they might be used.
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

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.
On parameter estimation in population models
15:10 Fri 6 May, 2011 :: 715 Ingkarni Wardli :: Dr Joshua Ross :: The University of Adelaide

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

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 two-dimensions and discuss advantages and limitations of the proposal.
Statistical challenges in molecular phylogenetics
15:10 Fri 20 May, 2011 :: Mawson Lab G19 lecture theatre :: Dr Barbara Holland :: University of Tasmania

This talk will give an introduction to the ways that mathematics and statistics gets used in the inference of evolutionary (phylogenetic) trees. Taking a model-based approach to estimating the relationships between species has proven to be an enormously effective, however, there are some tricky statistical challenges that remain. The increasingly plentiful amount of DNA sequence data is a boon, but it is also throwing a spotlight on some of the shortcomings of current best practice particularly in how we (1) assess the reliability of our phylogenetic estimates, and (2) how we choose appropriate models. This talk will aim to give a general introduction this area of research and will also highlight some results from two of my recent PhD students.
Permeability of heterogeneous porous media - experiments, mathematics and computations
15:10 Fri 27 May, 2011 :: B.21 Ingkarni Wardli :: Prof Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University

Permeability is a key parameter important to a variety of applications in geological engineering and in the environmental geosciences. The conventional definition of Darcy flow enables the estimation of permeability at different levels of detail. This lecture will focus on the measurement of surface permeability characteristics of a large cuboidal block of Indiana Limestone, using a surface permeameter. The paper discusses the theoretical developments, the solution of the resulting triple integral equations and associated computational treatments that enable the mapping of the near surface permeability of the cuboidal region. This data combined with a kriging procedure is used to develop results for the permeability distribution at the interior of the cuboidal region. Upon verification of the absence of dominant pathways for fluid flow through the cuboidal region, estimates are obtained for the "Effective Permeability" of the cuboid using estimates proposed by Wiener, Landau and Lifschitz, King, Matheron, Journel et al., Dagan and others. The results of these estimates are compared with the geometric mean, derived form the computational estimates.
Optimal experimental design for stochastic population models
15:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Dan Pagendam :: CSIRO, Brisbane

Markov population processes are popular models for studying a wide range of phenomena including the spread of disease, the evolution of chemical reactions and the movements of organisms in population networks (metapopulations). Our ability to use these models effectively can be limited by our knowledge about parameters, such as disease transmission and recovery rates in an epidemic. Recently, there has been interest in devising optimal experimental designs for stochastic models, so that practitioners can collect data in a manner that maximises the precision of maximum likelihood estimates of the parameters for these models. I will discuss some recent work on optimal design for a variety of population models, beginning with some simple one-parameter models where the optimal design can be obtained analytically and moving on to more complicated multi-parameter models in epidemiology that involve latent states and non-exponentially distributed infectious periods. For these more complex models, the optimal design must be arrived at using computational methods and we rely on a Gaussian diffusion approximation to obtain analytical expressions for Fisher's information matrix, which is at the heart of most optimality criteria in experimental design. I will outline a simple cross-entropy algorithm that can be used for obtaining optimal designs for these models. We will also explore the improvements in experimental efficiency when using the optimal design over some simpler designs, such as the design where observations are spaced equidistantly in time.
From group action to Kontsevich's Swiss-Cheese conjecture through categorification
15:10 Fri 3 Jun, 2011 :: Mawson Lab G19 :: Dr Michael Batanin :: Macquarie University

The Kontsevich Swiss-Cheese 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 Swiss-Cheese 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).
Probability density estimation by diffusion
15:10 Fri 10 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Dirk Kroese :: University of Queensland

One of the beautiful aspects of Mathematics is that seemingly disparate areas can often have deep connections. This talk is about the fundamental connection between probability density estimation, diffusion processes, and partial differential equations. Specifically, we show how to obtain efficient probability density estimators by solving partial differential equations related to diffusion processes. This new perspective leads, in combination with Fast Fourier techniques, to very fast and accurate algorithms for density estimation. Moreover, the diffusion formulation unifies most of the existing adaptive smoothing algorithms and provides a natural solution to the boundary bias of classical kernel density estimators. This talk covers topics in Statistics, Probability, Applied Mathematics, and Numerical Mathematics, with a surprise appearance of the theta function. This is joint work with Zdravko Botev and Joe Grotowski.
Stochastic models of reaction diffusion
15:10 Fri 17 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Jon Chapman :: Oxford University

We consider two different position jump processes: (i) a random walk on a lattice (ii) the Euler scheme for the Smoluchowski differential equation. Both of these reduce to the diffusion equation as the time step and size of the jump tend to zero. We consider the problem of adding chemical reactions to these processes, both at a surface and in the bulk. We show how the "microscopic" parameters should be chosen to achieve the correct "macroscopic" reaction rate. This choice is found to depend on which stochastic model for diffusion is used.
Routing in equilibrium
15:10 Tue 21 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Timothy Griffin :: University of Cambridge

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 non-distributive algebras using algorithms in the Bellman-Ford 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 non-distributive structures. This provides the first polynomial time algorithm for computing locally optimal solutions to path problems.
Object oriented data analysis
14:10 Thu 30 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Steve Marron :: The University of North Carolina at Chapel Hill

Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie Groups and Symmetric Spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for Object Oriented Data Analysis create several potentially large new interfaces between mathematics and statistics. Even in situations where Euclidean analysis makes sense, there are statistical challenges because of the High Dimension Low Sample Size problem, which motivates a new type of asymptotics leading to non-standard mathematical statistics.
The (dual) local cyclic homology valued Chern-Connes character for some infinite dimensional spaces
13:10 Fri 29 Jul, 2011 :: B.19 Ingkarni Wardli :: Dr Snigdhayan Mahanta :: School of Mathematical Sciences

I will explain how to construct a bivariant Chern-Connes character on the category of sigma-C*-algebras taking values in Puschnigg's local cyclic homology. Roughly, setting the first (resp. the second) variable to complex numbers one obtains the K-theoretic (resp. dual K-homological) Chern-Connes character in one variable. We shall focus on the dual K-homological Chern-Connes character and investigate it in the example of SU(infty).
The Selberg integral
15:10 Fri 5 Aug, 2011 :: 7.15 Ingkarni Wardli :: Prof Ole Warnaar :: University of Queensland

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

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 number-theoretically, 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.
Dealing with the GC-content bias in second-generation DNA sequence data
15:10 Fri 12 Aug, 2011 :: Horace Lamb :: Prof Terry Speed :: Walter and Eliza Hall Institute

The field of genomics is currently dealing with an explosion of data from so-called second-generation DNA sequencing machines. This is creating many challenges and opportunities for statisticians interested in the area. In this talk I will outline the technology and the data flood, and move on to one particular problem where the technology is used: copy-number analysis. There we find a novel bias, which, if not dealt with properly, can dominate the signal of interest. I will describe how we think about and summarize it, and go on to identify a plausible source of this bias, leading up to a way of removing it. Our approach makes use of the total variation metric on discrete measures, but apart from this, is largely descriptive.
Comparing Einstein to Newton via the post-Newtonian expansions
15:10 Fri 19 Aug, 2011 :: 7.15 Ingkarni Wardli :: Dr Todd Oliynyk :: Monash University

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 post-Newtonian expansions.
Configuration spaces in topology and geometry
15:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne

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.
Mathematical modelling of lobster populations in South Australia
12:10 Mon 12 Sep, 2011 :: 5.57 Ingkarni Wardli :: Mr John Feenstra :: University of Adelaide

Just how many lobsters are there hanging around the South Australian coastline? How is this number changing over time? What is the demographic breakdown of this number? And what does it matter? Find out the answers to these questions in my upcoming talk. I will provide a brief flavour of the kinds of quantitative methods involved, showcasing relevant applications of regression, population modelling, estimation, as well as simulation. A product of these analyses are biological performance indicators which are used by government to help decide on fishery controls such as yearly total allowable catch quotas. This assists in maintaining the sustainability of the fishery and hence benefits both the fishers and the lobsters they catch.
Graph C*-algebras
15:10 Fri 16 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Aidan Sims :: University of Wollongong

In the late 1990's, Kumjian-Pask-Raeburn-Renault introduced the class of graph C*-algebras, building on previous work of Cuntz-Krieger and of Enomoto-Watatani in the early 1980's. Since then these C*-algebras have been very intensively studied because they are on the one hand very general, and yet on the other hand extremely tractable. In this talk I shall give an overview of what a graph C*-algebra is, and of some of the remarkable results about these intriguing objects proved by many mathematicians over the last 15 years. We will not assume any specific background, and all are very welcome to attend.
Statistical analysis of metagenomic data from the microbial community involved in industrial bioleaching
12:10 Mon 19 Sep, 2011 :: 5.57 Ingkarni Wardli :: Ms Susana Soto-Rojo :: University of Adelaide

In the last two decades heap bioleaching has become established as a successful commercial option for recovering copper from low-grade secondary sulfide ores. Genetics-based approaches have recently been employed in the task of characterizing mineral processing bacteria. Data analysis is a key issue and thus the implementation of adequate mathematical and statistical tools is of fundamental importance to draw reliable conclusions. In this talk I will give a recount of two specific problems that we have been working on. The first regarding experimental design and the latter on modeling composition and activity of the microbial consortium.
Estimating transmission parameters for the swine flu pandemic
15:10 Fri 23 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Kathryn Glass :: Australian National University

Following the onset of a new strain of influenza with pandemic potential, policy makers need specific advice on how fast the disease is spreading, who is at risk, and what interventions are appropriate for slowing transmission. Mathematical models play a key role in comparing interventions and identifying the best response, but models are only as good as the data that inform them. In the early stages of the 2009 swine flu outbreak, many researchers estimated transmission parameters - particularly the reproduction number - from outbreak data. These estimates varied, and were often biased by data collection methods, misclassification of imported cases or as a result of early stochasticity in case numbers. I will discuss a number of the pitfalls in achieving good quality parameter estimates from early outbreak data, and outline how best to avoid them. One of the early indications from swine flu data was that children were disproportionately responsible for disease spread. I will introduce a new method for estimating age-specific transmission parameters from both outbreak and seroprevalence data. This approach allows us to take account of empirical data on human contact patterns, and highlights the need to allow for asymmetric mixing matrices in modelling disease transmission between age groups. Applied to swine flu data from a number of different countries, it presents a consistent picture of higher transmission from children.
Statistical analysis of school-based student performance data
12:10 Mon 10 Oct, 2011 :: 5.57 Ingkarni Wardli :: Ms Jessica Tan :: University of Adelaide

Join me in the journey of being a statistician for 15 minutes of your day (if you are not already one) and experience the task of data cleaning without having to get your own hands dirty. Most of you may have sat the Basic Skills Tests when at school or know someone who currently has to do the NAPLAN (National Assessment Program - Literacy and Numeracy) tests. Tests like these assess student progress and can be used to accurately measure school performance. In trying to answer the research question: "what conclusions about student progress and school performance can be drawn from NAPLAN data or data of a similar nature, using mathematical and statistical modelling and analysis techniques?", I have uncovered some interesting results about the data in my initial data analysis which I shall explain in this talk.
On the role of mixture distributions in the modelling of heterogeneous data
15:10 Fri 14 Oct, 2011 :: 7.15 Ingkarni Wardli :: Prof Geoff McLachlan :: University of Queensland

We consider the role that finite mixture distributions have played in the modelling of heterogeneous data, in particular for clustering continuous data via mixtures of normal distributions. A very brief history is given starting with the seminal papers by Day and Wolfe in the sixties before the appearance of the EM algorithm. It was the publication in 1977 of the latter algorithm by Dempster, Laird, and Rubin that greatly stimulated interest in the use of finite mixture distributions to model heterogeneous data. This is because the fitting of mixture models by maximum likelihood is a classic example of a problem that is simplified considerably by the EM's conceptual unification of maximum likelihood estimation from data that can be viewed as being incomplete. In recent times there has been a proliferation of applications in which the number of experimental units n is comparatively small but the underlying dimension p is extremely large as, for example, in microarray-based genomics and other high-throughput experimental approaches. Hence there has been increasing attention given not only in bioinformatics and machine learning, but also in mainstream statistics, to the analysis of complex data in this situation where n is small relative to p. The latter part of the talk shall focus on the modelling of such high-dimensional data using mixture distributions.
Likelihood-free Bayesian inference: modelling drug resistance in Mycobacterium tuberculosis
15:10 Fri 21 Oct, 2011 :: 7.15 Ingkarni Wardli :: Dr Scott Sisson :: University of New South Wales

A central pillar of Bayesian statistical inference is Monte Carlo integration, which is based on obtaining random samples from the posterior distribution. There are a number of standard ways to obtain these samples, provided that the likelihood function can be numerically evaluated. In the last 10 years, there has been a substantial push to develop methods that permit Bayesian inference in the presence of computationally intractable likelihood functions. These methods, termed ``likelihood-free'' or approximate Bayesian computation (ABC), are now being applied extensively across many disciplines. In this talk, I'll present a brief, non-technical overview of the ideas behind likelihood-free methods. I'll motivate and illustrate these ideas through an analysis of the epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
Mathematical opportunities in molecular space
15:10 Fri 28 Oct, 2011 :: B.18 Ingkarni Wardli :: Dr Aaron Thornton :: CSIRO

The study of molecular motion, interaction and space at the nanoscale has become a powerful tool in the area of gas separation, storage and conversion for efficient energy solutions. Modeling in this field has typically involved highly iterative computational algorithms such as molecular dynamics, Monte Carlo and quantum mechanics. Mathematical formulae in the form of analytical solutions to this field offer a range of useful and insightful advantages including optimization, bifurcation analysis and standardization. Here we present a few case scenarios where mathematics has provided insight and opportunities for further investigation.
Quasimodo's Cipher
15:10 Fri 4 Nov, 2011 :: Room change: Horace Lamb lecture theatre :: Dr Burkard Polster :: Monash University

I thought to see the fairies in the fields, but I saw only the evil elephants with their black backs. Woe! How that sight awed me! The elves danced all around and about while I heard voices calling clearly.... Puzzled? Curious? Come and join in the chase for the key to this cipher message, learn about the beautiful mathematics underlying the ancient art of ringing the changes, and find out what all this has to do with juggling.
Fluid flows in microstructured optical fibre fabrication
15:10 Fri 25 Nov, 2011 :: B.17 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide

Optical fibres are used extensively in modern telecommunications as they allow the transmission of information at high speeds. Microstructured optical fibres are a relatively new fibre design in which a waveguide for light is created by a series of air channels running along the length of the material. The flexibility of this design allows optical fibres to be created with adaptable (and previously unrealised) optical properties. However, the fluid flows that arise during fabrication can greatly distort the geometry, which can reduce the effectiveness of a fibre or render it useless. I will present an overview of the manufacturing process and highlight the difficulties. I will then focus on surface-tension driven deformation of the macroscopic version of the fibre extruded from a reservoir of molten glass, occurring during fabrication, which will be treated as a two-dimensional Stokes flow problem. I will outline two different complex-variable numerical techniques for solving this problem along with comparisons of the results, both to other models and to experimental data.
Mixing, dynamics, and probability
15:10 Fri 2 Mar, 2012 :: B.21 Ingkarni Wardli :: A/Prof Gary Froyland :: University of New South Wales

Many interesting natural phenomena are hard to predict. When modelled as a dynamical system, this unpredictability is often the result of rapid separation of nearby trajectories. Viewing the dynamics as acting on a probability measure, the mixing property states that two measurements (or random variables), evaluated at increasingly separated times, become independent in the time-separation limit. Thus, the later measurement becomes increasingly difficult to predict, given the outcome of the earlier measurement. If this approach to independence occurs exponentially quickly in time, one can profitably use linear operator tools to analyse the dynamics. I will give an overview of these techniques and show how they can be applied to answer mathematical questions, describe observed behaviour in fluid mixing, and analyse models of the ocean and atmosphere.
IGA Workshop: The mathematical implications of gauge-string dualities
09:30 Mon 5 Mar, 2012 :: 7.15 Ingkarni Wardli :: Prof Rajesh Gopakumar :: Harish-Chandra Research Institute

Lecture series by Rajesh Gopakumar (Harish-Chandra Research Institute). The lectures will be supplemented by talks by other invited speakers.
String Theory and the Quest for Quantum Spacetime
15:10 Fri 9 Mar, 2012 :: Ligertwood 333 Law Lecture Theatre 2 :: Prof Rajesh Gopakumar :: Harish-Chandra Research Institute

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.
Forecasting electricity demand distributions using a semiparametric additive model
15:10 Fri 16 Mar, 2012 :: B.21 Ingkarni Wardli :: Prof Rob Hyndman :: Monash University

Electricity demand forecasting plays an important role in short-term load allocation and long-term planning for future generation facilities and transmission augmentation. Planners must adopt a probabilistic view of potential peak demand levels, therefore density forecasts (providing estimates of the full probability distributions of the possible future values of the demand) are more helpful than point forecasts, and are necessary for utilities to evaluate and hedge the financial risk accrued by demand variability and forecasting uncertainty. Electricity demand in a given season is subject to a range of uncertainties, including underlying population growth, changing technology, economic conditions, prevailing weather conditions (and the timing of those conditions), as well as the general randomness inherent in individual usage. It is also subject to some known calendar effects due to the time of day, day of week, time of year, and public holidays. I will describe a comprehensive forecasting solution designed to take all the available information into account, and to provide forecast distributions from a few hours ahead to a few decades ahead. We use semi-parametric additive models to estimate the relationships between demand and the covariates, including temperatures, calendar effects and some demographic and economic variables. Then we forecast the demand distributions using a mixture of temperature simulation, assumed future economic scenarios, and residual bootstrapping. The temperature simulation is implemented through a new seasonal bootstrapping method with variable blocks. The model is being used by the state energy market operators and some electricity supply companies to forecast the probability distribution of electricity demand in various regions of Australia. It also underpinned the Victorian Vision 2030 energy strategy.
The entropy of an overlapping dynamical system
15:10 Fri 23 Mar, 2012 :: Napier G03 :: Prof Michael Barnsley :: Australian National University

The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence between these two classes of objects is used to: 1. find a necessary and sufficient condition for a fractal transformation from the attractor of one overlapping IFS to the attractor of another overlapping IFS to be a homeomorphism and 2. find a formula for the topological entropy of the dynamical system associated with an overlapping function. These results suggest a new method for analysing clocks, weather systems and prime numbers.
The mechanics of plant root growth
15:10 Fri 30 Mar, 2012 :: B.21 Ingkarni Wardli :: Dr Rosemary Dyson :: University of Birmingham

Growing plant cells undergo rapid axial elongation with negligible radial expansion: high internal turgor pressure causes viscous stretching of the cell wall. We represent the cell wall as a thin fibre-reinforced viscous sheet, providing insight into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and showing how either dynamical changes in material properties, achieved through changes in the cell-wall microstructure, or passive fibre reorientation may suppress cell elongation. We then investigate how the action of enzymes on the cell wall microstructure can lead to the required dynamic changes in macroscale wall material properties, and thus demonstrate a mechanism by which hormones may regulate plant growth.
What is a self-similar group?
15:10 Fri 20 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Murray Elder :: University of Newcastle

I will give a brief introduction to the theory of self-similar groups, focusing on a couple of pertinent examples: Grigorchuk's group of intermediate growth, and the basilica group.
Spatial-point data sets and the Polya distribution
15:10 Fri 27 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Benjamin Binder :: The University of Adelaide

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

In this talk, methane (CH4) adsorption is investigated on both graphite and in the region between two aligned single-walled carbon nanotubes, which we refer to as the groove site. The Lennard–Jones potential function and the continuous approximation is exploited to determine surface binding energies between a single CH4 molecule and graphite and between a single CH4 and two aligned single-walled carbon nanotubes. The modelling indicates that for a CH4 molecule interacting with graphite, the binding energy of the system is minimized when the CH4 carbon is 3.83 angstroms above the surface of the graphitic carbon, while the binding energy of the CH4–groove site system is minimized when the CH4 carbon is 5.17 angstroms away from the common axis shared by the two aligned single-walled carbon nanotubes. These results confirm the current view that for larger groove sites, CH4 molecules in grooves are likely to move towards the outer surfaces of one of the single-walled carbon nanotubes. The results presented in this talk are computationally efficient and are in good agreement with experiments and molecular dynamics simulations, and show that CH4 adsorption on graphite and groove surfaces is more favourable at lower temperatures and higher pressures.
Multiscale models of collective cell behaviour: Linear or nonlinear diffusion?
15:10 Fri 4 May, 2012 :: B.21 Ingkarni Wardli :: Dr Matthew Simpson :: Queensland University of Technology

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. There is no guidance available in the mathematical biology literature with regard to which approach is more appropriate. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. We provide a link between individual-based and continuum models using a multiscale approach in which we analyse the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is a nonlinear diffusion equation related to the porous media equation. We show that there are several reasonable approaches for dealing with agent size effects, and that these different approaches are related mathematically through the concept of mean action time. We extend our results to consider proliferation and travelling waves where greater care must be taken to ensure that the continuum model replicates the discrete process. This is joint work with Dr Ruth Baker (Oxford) and Dr Scott McCue (QUT).
Index type invariants for twisted signature complexes
13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide

Atiyah-Patodi-Singer proved an index theorem for non-local boundary conditions in the 1970's that has been widely used in mathematics and mathematical physics. A key application of their theory gives the index theorem for signature operators on oriented manifolds with boundary. As a consequence, they defined certain secondary invariants that were metric independent. I will discuss some recent work with Benameur where we extend the APS theory to signature operators twisted by an odd degree closed differential form, and study the corresponding secondary invariants.
Modelling protective anti-tumour immunity using a hybrid agent-based and delay differential equation approach
15:10 Fri 11 May, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Kim :: University of Sydney

Although cancers seem to consistently evade current medical treatments, the body's immune defences seem quite effective at controlling incipient tumours. Understanding how our immune systems provide such protection against early-stage tumours and how this protection could be lost will provide insight into designing next-generation immune therapies against cancer. To engage this problem, we formulate a mathematical model of the immune response against small, incipient tumours. The model considers the initial stimulation of the immune response in lymph nodes and the resulting immune attack on the tumour and is formulated as a hybrid agent-based and delay differential equation model.
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

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 3-dimensional 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.
P or NP: this is the question
13:10 Tue 22 May, 2012 :: 7.15 Ingkarni Wardli :: Dr Ali Eshragh :: School of Mathematical Sciences

Up to early 70's, the main concentration of mathematicians was the design of algorithms. However, the advent of computers changed this focus from not just the design of an algorithm but also to the most efficient algorithm. This created a new field of research, namely the complexity of algorithms, and the associated problem "Is P equal to NP?" was born. The latter question has been unknown for more than four decades and is one of the most famous open problems of the 21st century. Any person who can solve this problem will be awarded US$1,000,000 by the Clay Institute. In this talk, we are going to introduce this problem through simple examples and explain one of the intriguing approaches that may help to solve it.
Enhancing the Jordan canonical form
15:10 Fri 1 Jun, 2012 :: B.21 Ingkarni Wardli :: A/Prof Anthony Henderson :: The University of Sydney

In undergraduate linear algebra, we teach the Jordan canonical form theorem: that every similarity class of n x n complex matrices contains a special matrix which is block-diagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal, ones on the super-diagonal, and zeroes elsewhere). This is of course very useful for matrix calculations. After explaining some of the general context of this result, I will focus on a case which, despite its close proximity to the Jordan canonical form theorem, has only recently been worked out: the classification of pairs of a vector and a matrix.
A brief introduction to Support Vector Machines
12:30 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide

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

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

A series of four 2-hour lectures by Dr. Ittay Weiss. The theory of dendroidal sets was introduced by Moerdijk and Weiss in 2007 in the study of homotopy operads in algebraic topology. In the five years that have past since then several fundamental and highly non-trivial results were established. For instance, it was established that dendroidal sets provide models for homotopy operads in a way that extends the Joyal-Lurie approach to homotopy categories. It can be shown that dendroidal sets provide new models in the study of n-fold loop spaces. And it is very recently shown that dendroidal sets model all connective spectra in a way that extends the modeling of certain spectra by Picard groupoids. The aim of the lecture series will be to introduce the concepts mentioned above, present the elementary theory, and understand the scope of the results mentioned as well as discuss the potential for further applications. Sources for the course will include the article "From Operads to Dendroidal Sets" (in the AMS volume on mathematical foundations of quantum field theory (also on the arXiv)) and the lecture notes by Ieke Moerdijk "simplicial methods for operads and algebraic geometry" which resulted from an advanced course given in Barcelona 3 years ago. No prior knowledge of operads will be assumed nor any knowledge of homotopy theory that is more advanced then what is required for the definition of the fundamental group. The basics of the language of presheaf categories will be recalled quickly and used freely.
Notions of non-commutative metric spaces; why and how
15:10 Fri 15 Jun, 2012 :: B.21 Ingkarni Wardli :: Dr Ittay Weiss :: The University of the South Pacific

The classical notion of metric space includes the axiom of symmetry: d(x,y)=d(y,x). Some applications of metric techniques to problems in computer graphics, concurrency, and physics (to mention a few) are seriously stressing the limitations imposed by symmetry, resulting in various relaxations of it. I will review some of the motivating problems that seem to require non-symmetry and then review some of the suggested models to deal with the problem. My review will be critical to the topological implications (which are often unpleasant) of some of the models and I will present metric 1-spaces, a new notion of generalized metric spaces.
Three Minute Thesis
14:00 Mon 2 Jul, 2012 :: B.21 Ingkarni Wardli

This session will feature the The School of Mathematical Sciences Three Minute Thesis competition. Each postgraduate participating will have three minutes to explain their thesis at a level appropriate for a non-specialist audience. The competition is open to all postgraduates within the School. All staff are welcome to attend.
Inquiry-based learning: yesterday and today
15:30 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Prof Ron Douglas :: Texas A&M University

The speaker will report on a project to develop and promote approaches to mathematics instruction closely related to the Moore method -- methods which are called inquiry-based learning -- as well as on his personal experience of the Moore method. For background, see the speaker's article in the May 2012 issue of the Notices of the American Mathematical Society. To download the article, click on "Media" above.
2012 AMSI-SSAI Lecture: Approximate Bayesian computation (ABC): advances and limitations
11:00 Fri 13 Jul, 2012 :: Engineering South S112 :: Prof Christian Robert :: Universite Paris-Dauphine

The lack of closed form likelihoods has been the bane of Bayesian computation for many years and, prior to the introduction of MCMC methods, a strong impediment to the propagation of the Bayesian paradigm. We are now facing models where an MCMC completion of the model towards closed-form likelihoods seems unachievable and where a further degree of approximation appears unavoidable. In this talk, I will present the motivation for approximative Bayesian computation (ABC) methods, the consistency results already available, the various Monte Carlo implementations found in the current literature, as well as the inferential, rather than computational, challenges set by these methods. A recent advance based on empirical likelihood will also be discussed.
Geometry - algebraic to arithmetic to absolute
15:10 Fri 3 Aug, 2012 :: B.21 Ingkarni Wardli :: Dr James Borger :: Australian National University

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, lambda-algebraic geometry, allows one to do just this and why one might care.
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

Let V = C^n, and let (-,-) be a non-degenerate bilinear form on V , which is either symmetric or anti-symmetric. 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 non-semisimplicity 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 surfaces---trying to fill in a gap in the Enriques-Kodaira classification. Attempting to classify some collection of mathematical objects is a very common activity for pure mathematicians, and there are many well-known examples of successful classification schemes; for example, the classification of finite simple groups, and the classification of simply connected topological 4-manifolds. The aim of this talk will be to illustrate how techniques from differential geometry can be used to classify compact surfaces. The level of the talk will be very elementary, and the material is all very well known, but it is sometimes instructive to look back over simple cases of a general problem with the benefit of experience to gain greater insight into the more general and difficult cases.
Continuous random walk models for solute transport in porous media
15:10 Fri 17 Aug, 2012 :: B.21 Ingkarni Wardli :: Prof Pavel Bedrikovetski :: The University of Adelaide

The classical diffusion (thermal conductivity) equation was derived from the Master random walk equation and is parabolic. The main assumption was a probabilistic distribution of the jump length while the jump time is constant. Distribution of the jump time along with the jump length adds the second time derivative into the averaged equations, but the equation becomes ... elliptic! Where from to take an extra initial condition? We discuss how to pose the well-posed flow problem, exact 1d solution and numerous engineering applications. This is joint work with A. Shapiro and H. Yuan.
Infectious diseases modelling: from biology to public health policy
15:10 Fri 24 Aug, 2012 :: B.20 Ingkarni Wardli :: Dr James McCaw :: The University of Melbourne

The mathematical study of human-to-human transmissible pathogens has established itself as a complementary methodology to the traditional epidemiological approach. The classic susceptible--infectious--recovered model paradigm has been used to great effect to gain insight into the epidemiology of endemic diseases such as influenza and pertussis, and the emergence of novel pathogens such as SARS and pandemic influenza. The modelling paradigm has also been taken within the host and used to explain the within-host dynamics of viral (or bacterial or parasite) infections, with implications for our understanding of infection, emergence of drug resistance and optimal drug-interventions. In this presentation I will provide an overview of the mathematical paradigm used to investigate both biological and epidemiological infectious diseases systems, drawing on case studies from influenza, malaria and pertussis research. I will conclude with a summary of how infectious diseases modelling has assisted the Australian government in developing its pandemic preparedness and response strategies.
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

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 store-and-forward, all-port and full-duplex 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 all-to-all 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.
Geometric quantisation in the noncompact setting
13:10 Fri 14 Sep, 2012 :: Engineering North 218 :: Dr Peter Hochs :: Leibniz University, Hannover

Traditionally, the geometric quantisation of an action by a compact Lie group on a compact symplectic manifold is defined as the equivariant index of a certain Dirac operator. This index is a well-defined formal difference of finite-dimensional representations, since the Dirac operator is elliptic and the manifold and the group in question are compact. From a mathematical and physical point of view however, it is very desirable to extend geometric quantisation to noncompact groups and manifolds. Defining a suitable index is much harder in the noncompact setting, but several interesting results in this direction have been obtained. I will review the difficulties connected to noncompact geometric quantisation, and some of the solutions that have been proposed so far, mainly in connection to the "quantisation commutes with reduction" principle. (An introduction to this principle will be given in my talk at the Colloquium on the same day.)
Quantisation commutes with reduction
15:10 Fri 14 Sep, 2012 :: B.20 Ingkarni Wardli :: Dr Peter Hochs :: Leibniz University Hannover

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

Many problems within applied mathematics require the solution of a linear system of equations. For instance, models of arterial umbilical blood flow are obtained through a finite element approximation, resulting in a linear, n x n system. For small systems the solution is (almost) trivial, but what happens when n is large? Say, n ~ 10^6? In this case matrix inversion is expensive (read: completely impractical) and we seek approximate solutions in a reasonable time. In this talk I will discuss the basic theory underlying Krylov subspace methods; a class of non-stationary iterative methods which are currently the methods-of-choice for large, sparse, linear systems. In particular I will focus on the method of Generalised Minimum RESiduals (GMRes), which is of the most popular for nonsymmetric systems. It is hoped that through this presentation I will convince you that a) solving linear systems is not necessarily trivial, and that b) my lack of any tangible results is not (entirely) a result of my own incompetence.
Towards understanding fundamental interactions for nanotechnology
15:10 Fri 5 Oct, 2012 :: B.20 Ingkarni Wardli :: Dr Doreen Mollenhauer :: MacDiarmid Institute for Advanced Materials and Nanotechnology, Wellington

Multiple simultaneous interactions show unique collective properties that are qualitatively different from properties displayed by their monovalent constituents. Multivalent interactions play an important role for the self-organization of matter, recognition processes and signal transduction. A broad understanding of these interactions is therefore crucial in order to answer central questions and make new developments in the field of biotechnology and material science. In the framework of a joint experimental and theoretical project we study the electronic effects in monovalent and multivalent interactions by doing quantum chemical calculations. The particular interest of our investigations is in organic molecules interacting with gold nanoparticles or graphene. The main purpose is to analyze the nature of multivalent bonding in comparison to monovalent interaction.
Complex analysis in low Reynolds number hydrodynamics
15:10 Fri 12 Oct, 2012 :: B.20 Ingkarni Wardli :: Prof Darren Crowdy :: Imperial College London

It is a well-known fact that the methods of complex analysis provide great advantage in studying physical problems involving a harmonic field satisfying Laplace's equation. One example is in ideal fluid mechanics (infinite Reynolds number) where the absence of viscosity, and the assumption of zero vorticity, mean that it is possible to introduce a so-called complex potential -- an analytic function from which all physical quantities of interest can be inferred. In the opposite limit of zero Reynolds number flows which are slow and viscous and the governing fields are not harmonic it is much less common to employ the methods of complex analysis even though they continue to be relevant in certain circumstances. This talk will give an overview of a variety of problems involving slow viscous Stokes flows where complex analysis can be usefully employed to gain theoretical insights. A number of example problems will be considered including the locomotion of low-Reynolds-number micro-organisms and micro-robots, the friction properties of superhydrophobic surfaces in microfluidics and problems of viscous sintering and the manufacture of microstructured optic fibres (MOFs).
Multi-scale models of evolutionary epidemiology: where is HIV going?
14:00 Fri 19 Oct, 2012 :: Napier 205 :: Dr Lorenzo Pellis :: The University of Warwick

An important component of pathogen evolution at the population level is evolution within hosts, which can alter the composition of genotypes available for transmission as infection progresses. I will present a deterministic multi-scale model, linking the within-host competition dynamics with the transmission dynamics at a population level. I will take HIV as an example of how this framework can help clarify the conflicting evolutionary pressure an infectious disease might be subject to.
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

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.
Epidemic models in socially structured populations: when are simple models too simple?
14:00 Thu 25 Oct, 2012 :: 5.56 Ingkarni Wardli :: Dr Lorenzo Pellis :: The University of Warwick

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

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

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.
Interaction of double-stranded DNA inside single-walled carbon nanotubes
12:10 Mon 5 Nov, 2012 :: B.21 Ingkarni Wardli :: Mr Mansoor Alshehri :: University of Adelaide

Here we investigate the interaction of deoxyribonucleic acid (DNA) inside single walled carbon nanotubes (SWCNTs). Using classical applied mathematical modeling, we derive explicit analytical expressions for the encapsulation of DNA inside single-walled carbon nanotubes. We adopt the 6-12 Lennard-Jones potential function together with the continuous approach to determine the preferred minimum energy position of the dsDNA molecule inside a single-walled carbon nanotube, so as to predict its location with reference to the cross- section of the carbon nanotube. An analytical expression is obtained in terms of hypergeometric functions, which provides a computationally rapid procedure to determine critical numerical values.
Modern trends in dynamo theory
15:10 Fri 16 Nov, 2012 :: B.20 Ingkarni Wardli :: Prof Michael Proctor :: University of Cambridge

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 mean-field 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 mean-field 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.
Asymptotic independence of (simple) two-dimensional Markov processes
15:10 Fri 1 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Guy Latouche :: Universite Libre de Bruxelles

The one-dimensional birth-and death model is one of the basic processes in applied probability but difficulties appear as one moves to higher dimensions. In the positive recurrent case, the situation is singularly simplified if the stationary distribution has product-form. We investigate the conditions under which this property holds, and we show how to use the knowledge to find product-form approximations for otherwise unmanageable random walks. This is joint work with Masakiyo Miyazawa and Peter Taylor.
Twistor theory and the harmonic hull
15:10 Fri 8 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Michael Eastwood :: Australian National University

Harmonic functions are real-analytic 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.
A multiscale approach to reaction-diffusion processes in domains with microstructure
15:10 Fri 15 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Malte Peter :: University of Augsburg

Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multi-scale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation. The talk will give an introduction to multi-scale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, a few aspects of solving the resulting systems of equations numerically will also be discussed.
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

We derive extended Lorentz transformations between inertial frames for relative velocities greater than the speed of light, and which are complementary to the Lorentz transformation giving rise to the Einstein special theory of relativity. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions.
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

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).
A stability theorem for elliptic Harnack inequalities
15:10 Fri 5 Apr, 2013 :: B.18 Ingkarni Wardli :: Prof Richard Bass :: University of Connecticut

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.
A glimpse at the Langlands program
15:10 Fri 12 Apr, 2013 :: B.18 Ingkarni Wardli :: Dr Masoud Kamgarpour :: University of Queensland

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 high-profile international research program known as the Langlands program. Many fundamental problems, including the Shimura-Taniyama-Weil 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.
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

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.
Models of cell-extracellular matrix interactions in tissue engineering
15:10 Fri 3 May, 2013 :: B.18 Ingkarni Wardli :: Dr Ed Green :: University of Adelaide

Tissue engineers hope in future to be able to grow functional tissues in vitro to replace those that are damaged by injury, disease, or simple wear and tear. They use cell culture methods, such as seeding cells within collagen gels, that are designed to mimic the cells' environment in vivo. Amongst other factors, it is clear that mechanical interactions between cells and the extracellular matrix (ECM) in which they reside play an important role in tissue development. However, the mechanics of the ECM is complex, and at present, its role is only partly understood. In this talk, I will present mathematical models of some simple cell-ECM interaction problems, and show how they can be used to gain more insight into the processes that regulate tissue development.
Filtering Theory in Modelling the Electricity Market
12:10 Mon 6 May, 2013 :: B.19 Ingkarni Wardli :: Ahmed Hamada :: University of Adelaide

In mathematical finance, as in many other fields where applied mathematics is a powerful tool, we assume that a model is good enough when it captures different sources of randomness affecting the quantity of interests, which in this case is the electricity prices. The power market is very different from other markets in terms of the randomness sources that can be observed in the prices feature and evolution. We start from suggesting a new model that simulates the electricity prices, this new model is constructed by adding a periodicity term, a jumps terms and a positives mean reverting term. The later term is driven by a non-observable Markov process. So in order to prices some financial product, we have to use some of the filtering theory to deal with the non-observable process, these techniques are gaining very much of interest from practitioners and researchers in the field of financial mathematics.
Neuronal excitability and canards
15:10 Fri 10 May, 2013 :: B.18 Ingkarni Wardli :: A/Prof Martin Wechselberger :: University of Sydney

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 FitzHugh-Nagumo/Morris-Lecar type neural model and to a more complicated neural model that describes paradoxical excitation due to propofol anesthesia.
Progress in the prediction of buoyancy-affected turbulence
15:10 Fri 17 May, 2013 :: B.18 Ingkarni Wardli :: Dr Daniel Chung :: University of Melbourne

Buoyancy-affected turbulence represents a significant challenge to our understanding, yet it dominates many important flows that occur in the ocean and atmosphere. The presentation will highlight some recent progress in the characterisation, modelling and prediction of buoyancy-affected turbulence using direct and large-eddy simulations, along with implications for the characterisation of mixing in the ocean and the low-cloud feedback in the atmosphere. Specifically, direct numerical simulation data of stratified turbulence will be employed to highlight the importance of boundaries in the characterisation of turbulent mixing in the ocean. Then, a subgrid-scale model that captures the anisotropic character of stratified mixing will be developed for large-eddy simulation of buoyancy-affected turbulence. Finally, the subgrid-scale model is utilised to perform a systematic large-eddy simulation investigation of the archetypal low-cloud regimes, from which the link between the lower-tropospheric stability criterion and the cloud fraction interpreted.
Heat kernel estimates on non-compact Riemannian manifolds: why and how?
15:10 Fri 7 Jun, 2013 :: B.18 Ingkarni Wardli :: Prof Thierry Coulhon :: Australian National University

We will describe what is known and remains to be known about the connection between the large scale geometry of non-compact Riemannian manifolds (and more general metric measure spaces) and large time estimates of their heat kernel. We will show how some of these estimates can be characterised in terms of Sobolev inequalities and give applications to the boundedness of Riesz transforms.
Invariant Theory: The 19th Century and Beyond
15:10 Fri 21 Jun, 2013 :: B.18 Ingkarni Wardli :: Dr Jarod Alper :: Australian National University

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.
Quantization, Representations and the Orbit Philosophy
15:10 Fri 5 Jul, 2013 :: B.18 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University

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 Hamiltonian Cycle Problem and Markov Decision Processes
15:10 Fri 2 Aug, 2013 :: B.18 Ingkarni Wardli :: Prof Jerzy Filar :: Flinders University

We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider a moving object on a graph G where, at each vertex, a controller may select an arc emanating from that vertex according to a probabilistic decision rule. A stationary policy is simply a control where these decision rules are time invariant. Such a policy induces a Markov chain on the vertices of the graph. Therefore, HCP is equivalent to a search for a stationary policy that induces a 0-1 probability transition matrix whose non-zero entries trace out a Hamiltonian cycle in the graph. A consequence of this embedding is that we may consider the problem over a number of, alternative, convex - rather than discrete - domains. These include: (a) the space of stationary policies, (b) the more restricted but, very natural, space of doubly stochastic matrices induced by the graph, and (c) the associated spaces of so-called "occupational measures". This approach to the HCP has led to both theoretical and algorithmic approaches to the underlying HCP problem. In this presentation, we outline a selection of results generated by this line of research.
Shannon entropy as a diagnostic tool for PDEs in conservation form
15:10 Fri 16 Aug, 2013 :: B.18 Ingkarni Wardli :: Prof Philip Broadbridge :: La Trobe University

After normalization, an evolving real non-negative function may be viewed as a probability density. From this we may derive the corresponding evolution law for Shannon entropy. Parabolic equations, hyperbolic equations and fourth-order diffusion equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a self-consistent manner and at an elementary level by reference to some simple evolution equations such as the linear heat equation. It is easily seen that the 2nd law of thermodynamics is equivalent to loss of Shannon information when temperature obeys a general nonlinear 2nd order diffusion equation. With fourth order diffusion terms, new problems arise. We know from applications such as thin film flow and surface diffusion, that fourth order diffusion terms may generate ripples and they do not satisfy the Second Law. Despite this, we can identify the class of fourth order quasilinear diffusion equations that increase the Shannon entropy.
Knots and Quantum Computation
15:10 Fri 6 Sep, 2013 :: B.18 Ingkarni Wardli :: Dr Scott Morrison :: Australian National University

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.
Thin-film flow in helical channels
12:10 Mon 9 Sep, 2013 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide

Spiral particle separators are used in the mineral processing industry to refine ores. A slurry, formed by mixing crushed ore with a fluid, is run down a helical channel and at the end of the channel, the particles end up sorted in different sections of the channel. Design of such devices is largely experimentally based, and mathematical modelling of flow in helical channels is relatively limited. In this talk, I will outline some of the work that I have been doing on thin-film flow in helical channels.
Symmetry gaps for geometric structures
15:10 Fri 20 Sep, 2013 :: B.18 Ingkarni Wardli :: Dr Dennis The :: Australian National University

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 well-known 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 example-based 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 Francis-Staite :: University of Adelaide

The torus is very common example of a surface in R^3, but it's a lot more interesting than just a donut! I will introduce some standard mathematical descriptions of the torus, a bit of number theory, and finally what the irrational line on the torus is. Why is this interesting? Well despite donuts being yummy to eat, the irrational line on the torus gives a range of pathological counter-examples. In Differential Geometry, it is an example of a manifold that is a subset of another manifold, but not a submanifold. In Lie theory, it is an example of a subgroup of a Lie group which is not a Lie subgroup. If that wasn't enough of a mouthful, I may also provide some sweet incentives to come along! Does anyone know the location of a good donut store?
How to stack oranges in three dimensions, 24 dimensions and beyond
18:00 Thu 26 Sep, 2013 :: Horace Lamb Lecture Theatre :: Prof Akshay Venkatesh :: Stanford University

How can we pack balls as tightly as possible? In other words: to squeeze as many balls as possible into a limited space, what's the best way of arranging the balls? It's not hard to guess what the answer should be - but it's very hard to be sure that it really is the answer! I'll tell the interesting story of this problem, going back to the astronomer Kepler, and ending almost four hundred years later with Thomas Hales. I will then talk about stacking 24-dimensional oranges: what this means, how it relates to the Voyager spacecraft, and the many things we don't know beyond this.
Dynamics and the geometry of numbers
14:10 Fri 27 Sep, 2013 :: Horace Lamb Lecture Theatre :: Prof Akshay Venkatesh :: Stanford University

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.
Gravitational slingshot and space mission design
15:10 Fri 11 Oct, 2013 :: B.18 Ingkarni Wardli :: Prof Pawel Nurowski :: Polish Academy of Sciences

When planning a space mission the weight of the spacecraft is the main issue. Every gram sent into the outer space costs a lot. A considerable part of the overall weight of the spaceship consists of a fuel needed to control it. I will explain how space agencies reduce the amount of fuel needed to go to a given place in the Solar System by using gravity of celestial bodies encountered along the trip. I will start with the explanation of an old trick called `gravitational slingshot', and end up with a modern technique which is based on the analysis of a 3-body problem appearing in Newtonian mechanics.
How the leopard got his spots
14:10 Mon 14 Oct, 2013 :: 7.15 Ingkarni Wardli :: Dr Ed Green :: School of Mathematical Sciences

Patterns are everywhere in nature, whether they be the spots and stripes on animals' coats, or the intricate arrangement of different cell types in a tissue. But how do these patterns arise? Whilst every cell contains a plan of the organism in its genes, the cells need to organise themselves so that each knows what it should do to achieve this plan. Mathematics can help biologists explore how different types of signals might be used to control the patterning process. In this talk, I will introduce two simple mathematical theories of biological pattern formation: Turing patterns where, surprisingly, the essential ingredient for producing the pattern is diffusion, which usually tends to make things more uniform; and the Keller-Segel model, which provides a simple mechanism for the formation of multicellular structures from isolated single cells. These mathematical models can be used to explain how tissues develop, and why there are many spotted animals with a stripy tail, but no stripy animals with a spotted tail.
Classification Using Censored Functional Data
15:10 Fri 18 Oct, 2013 :: B.18 Ingkarni Wardli :: A/Prof Aurore Delaigle :: University of Melbourne

We consider classification of functional data. This problem has received a lot of attention in the literature in the case where the curves are all observed on the same interval. A difficulty in applications is that the functional curves can be supported on quite different intervals, in which case standard methods of analysis cannot be used. We are interested in constructing classifiers for curves of this type. More precisely, we consider classification of functions supported on a compact interval, in cases where the training sample consists of functions observed on other intervals, which may differ among the training curves. We propose several methods, depending on whether or not the observable intervals overlap by a significant amount. In the case where these intervals differ a lot, our procedure involves extending the curves outside the interval where they were observed. We suggest a new nonparametric approach for doing this. We also introduce flexible ways of combining potential differences in shapes of the curves from different populations, and potential differences between the endpoints of the intervals where the curves from each population are observed.
Interaction of double-stranded DNA inside single-walled carbon nanotubes
12:35 Mon 28 Oct, 2013 :: B.19 Ingkarni Wardli :: Mansoor Alshehri :: University of Adelaide

Here we investigate the interaction of deoxyribonucleic acid (DNA) inside single walled carbon nanotubes (SWCNTs). Using classical applied mathematical modeling, we derive explicit analytical expressions for the encapsulation of DNA inside single-walled carbon nanotubes. We adopt the 6-12 Lennard-Jones potential function together with the continuous approach to determine the preferred minimum energy position of the dsDNA molecule inside a single-walled carbon nanotube, so as to predict its location with reference to the cross- section of the carbon nanotube. An analytical expression is obtained in terms of hypergeometric functions, which provides a computationally rapid procedure to determine critical numerical values.
The geometry of rolling surfaces and non-holonomic mechanics
15:10 Fri 1 Nov, 2013 :: B.18 Ingkarni Wardli :: Prof Robert Bryant :: Duke University

In mechanics, the system of a sphere rolling over a plane without slipping or twisting is a fundamental example of what is called a non-holonomic 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.
A gentle introduction to bubble evolution in Hele-Shaw flows
15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT

A Hele-Shaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a Hele-Shaw cell that is otherwise filled with viscous fluid, we can observe a bubble of air growing in size. The process is highly unstable, and the bubble boundary expands in an uneven fashion, leading to striking fingering patterns (look up Hele-Shaw cell or Saffman-Taylor instability on YouTube). From a mathematical perspective, modelling these Hele-Shaw flows is interesting because the governing equations are sufficiently ``simple'' that a considerable amount of analytical progress is possible. Indeed, there is no other context in which (genuinely) two-dimensional moving boundary problems are so tractable. More generally, Hele-Shaw flows are important as they serve as prototypes for more complicated (and important) physical processes such as crystal growth and diffusion limited aggregation. I will give an introduction to some of the main ideas and summarise some of my present research in this area.
A few flavours of optimal control of Markov chains
11:00 Thu 12 Dec, 2013 :: B18 :: Dr Sam Cohen :: Oxford University

In this talk we will outline a general view of optimal control of a continuous-time 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 infinite-horizon value functions, and with finite and infinitely many states. Examples will be drawn from finance, networks and electronic engineering.
Weak Stochastic Maximum Principle (SMP) and Applications
15:10 Thu 12 Dec, 2013 :: B.21 Ingkarni Wardli :: Dr Harry Zheng :: Imperial College, London

In this talk we discuss a weak necessary and sufficient SMP for Markov modulated optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke's generalized gradient of the Hamiltonian and Clarke's normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian the necessary condition becomes sufficient. We give examples to demonstrate the weak SMP and its applications in quadratic loss minimization.
The effects of pre-existing immunity
15:10 Fri 7 Mar, 2014 :: B.18 Ingkarni Wardli :: Associate Professor Jane Heffernan :: York University, Canada

Immune system memory, also called immunity, is gained as a result of primary infection or vaccination, and can be boosted after vaccination or secondary infections. Immunity is developed so that the immune system is primed to react and fight a pathogen earlier and more effectively in secondary infections. The effects of memory, however, on pathogen propagation in an individual host (in-host) and a population (epidemiology) are not well understood. Mathematical models of infectious diseases, employing dynamical systems, computer simulation and bifurcation analysis, can provide projections of pathogen propagation, show outcomes of infection and help inform public health interventions. In the Modelling Infection and Immunity (MI^2) lab, we develop and study biologically informed mathematical models of infectious diseases at both levels of infection, and combine these models into comprehensive multi-scale models so that the effects of individual immunity in a population can be determined. In this talk we will discuss some of the interesting mathematical phenomenon that arise in our models, and show how our results are directly applicable to what is known about the persistence of infectious diseases.
Viscoelastic fluids: mathematical challenges in determining their relaxation spectra
15:10 Mon 17 Mar, 2014 :: 5.58 Ingkarni Wardli :: Professor Russell Davies :: Cardiff University

Determining the relaxation spectrum of a viscoelastic fluid is a crucial step before a linear or nonlinear constitutive model can be applied. Information about the relaxation spectrum is obtained from simple flow experiments such as creep or oscillatory shear. However, the determination process involves the solution of one or more highly ill-posed inverse problems. The availability of only discrete data, the presence of noise in the data, as well as incomplete data, collectively make the problem very hard to solve. In this talk I will illustrate the mathematical challenges inherent in determining relaxation spectra, and also introduce the method of wavelet regularization which enables the representation of a continuous relaxation spectrum by a set of hyperbolic scaling functions.
A model for the BitCoin block chain that takes propagation delays into account
15:10 Fri 28 Mar, 2014 :: B.21 Ingkarni Wardli :: Professor Peter Taylor :: The University of Melbourne

Unlike cash transactions, most electronic transactions require the presence of a trusted authority to verify that the payer has sufficient funding to be able to make the transaction and to adjust the account balances of the payer and payee. In recent years BitCoin has been proposed as an "electronic equivalent of cash". The general idea is that transactions are verified in a coded form in a block chain, which is maintained by the community of participants. Problems can arise when the block chain splits: that is different participants have different versions of the block chain, something which can happen only when there are propagation delays, at least if all participants are behaving according to the protocol. In this talk I shall present a preliminary model for the splitting behaviour of the block chain. I shall then go on to perform a similar analysis for a situation where a group of participants has adopted a recently-proposed strategy for gaining a greater advantage from BitCoin processing than its combined computer power should be able to control.
The limits of proof
14:10 Wed 2 Apr, 2014 :: Hughes Lecture Room 322 :: Assoc. Prof. Finnur Larusson :: School of Mathematical Sciences

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

Eigenfunctions of Hamiltonians arise naturally in the theory of quantum mechanics as stationary states of quantum systems. Their eigenvalues have an interpretation as the square root of E, where E is the energy of the system. We wish to better understand the high energy limit which defines the boundary between quantum and classical mechanics. In this talk I will focus on results regarding the restriction of eigenfunctions to lower dimensional subspaces, in particular to hypersurfaces. A convenient way to study such problems is to reframe them as problems in semiclassical analysis.
Flow barriers and flux in unsteady flows
15:10 Fri 4 Apr, 2014 :: B.21 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: The University of Adelaide

How does one define the boundary of the ozone hole, an oceanic eddy, or Jupiter's Great Red Spot? These occur in flows which are unsteady (nonautonomous), that is, which change with time, and therefore any boundary must as well. In steady (autonomous) flows, defining flow boundaries is straightforward: one first finds fixed points of the flow, and then determines entities in space which are attracted to or repelled from these points as time progresses. These are respectively the stable and unstable manifolds of the fixed points, and can be shown to partition space into regions of different types of flow. This talk will focus on the required modifications to this idea for determining flow barriers in the more realistic unsteady context. An application to maximising mixing in microfluidic devices will also be presented.
Network-based approaches to classification and biomarker identification in metastatic melanoma
15:10 Fri 2 May, 2014 :: B.21 Ingkarni Wardli :: Associate Professor Jean Yee Hwa Yang :: The University of Sydney

Finding prognostic markers has been a central question in much of current research in medicine and biology. In the last decade, approaches to prognostic prediction within a genomics setting are primarily based on changes in individual genes / protein. Very recently, however, network based approaches to prognostic prediction have begun to emerge which utilize interaction information between genes. This is based on the believe that large-scale molecular interaction networks are dynamic in nature and changes in these networks, rather than changes in individual genes/proteins, are often drivers of complex diseases such as cancer. In this talk, I use data from stage III melanoma patients provided by Prof. Mann from Melanoma Institute of Australia to discuss how network information can be utilize in the analysis of gene expression analysis to aid in biological interpretation. Here, we explore a number of novel and previously published network-based prediction methods, which we will then compare to the common single-gene and gene-set methods with the aim of identifying more biologically interpretable biomarkers in the form of networks.
The Mandelbrot Set
12:10 Mon 5 May, 2014 :: B.19 Ingkarni Wardli :: David Bowman :: University of Adelaide

The Mandelbrot set is an icon of modern mathematics, an image which fires the popular imagination when accompanied by the words 'chaos' and 'fractal'. However, few could give even a vague definition of this mysterious set and fewer still know the mathematical meaning behind it. In this talk we will be looking at the role that the Mandelbrot set plays in complex dynamics, the study of iterated complex valued functions. We shall discuss attracting and repelling cycles and how they are related to the different components of the Mandelbrot set.
Ergodicity and loss of capacity: a stochastic horseshoe?
15:10 Fri 9 May, 2014 :: B.21 Ingkarni Wardli :: Professor Ami Radunskaya :: Pomona College, the United States of America

Random fluctuations of an environment are common in ecological and economical settings. The resulting processes can be described by a stochastic dynamical system, where a family of maps parametrized by an independent, identically distributed random variable forms the basis for a Markov chain on a continuous state space. Random dynamical systems are a beautiful combination of deterministic and random processes, and they have received considerable interest since von Neuman and Ulam's seminal work in the 1940's. Key questions in the study of a stochastic dynamical system are: does the system have a well-defined average, i.e. is it ergodic? How does this long-term behavior compare to that of the state variable in a constant environment with the averaged parameter? In this talk we answer these questions for a family of maps on the unit interval that model self-limiting growth. The techniques used can be extended to study other families of concave maps, and so we conjecture the existence of a "stochastic horseshoe".
Ice floe collisions in the Marginal Ice Zone
12:10 Mon 12 May, 2014 :: B.19 Ingkarni Wardli :: Lucas Yiew :: University of Adelaide

In an era of climate change, it is becoming increasingly important to model the dynamics of sea-ice cover in the polar regions. The Marginal Ice Zone represents a vast region of ice cover strongly influenced by the effects of ocean waves. As ocean waves penetrate this region, wave energy is progressively dispersed through energy dissipative mechanisms such as collisions between ice floes (discrete chunks of ice). In this talk I will discuss the mathematical models required to build a collision model, and the validation of these models with experimental results.
Stochastic models of evolution: Trees and beyond
15:10 Fri 16 May, 2014 :: B.18 Ingkarni Wardli :: Dr Barbara Holland :: The University of Tasmania

In the first part of the talk I will give a general introduction to phylogenetics, and discuss some of the mathematical and statistical issues that arise in trying to infer evolutionary trees. In particular, I will discuss how we model the evolution of DNA along a phylogenetic tree using a continuous time Markov process. In the second part of the talk I will discuss how to express the two-state continuous-time Markov model on phylogenetic trees in such a way that allows its extension to more general models. In this framework we can model convergence of species as well as divergence (speciation). I will discuss the identifiability (or otherwise) of the models that arise in some simple cases. Use of a statistical framework means that we can use established techniques such as the AIC or likelihood ratio tests to decide if datasets show evidence of convergent evolution.
Computing with groups
15:10 Fri 30 May, 2014 :: B.21 Ingkarni Wardli :: Dr Heiko Dietrich :: Monash University

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 well-established methods for permutation group; we will then discuss some recent progress for matrix groups.
Optimal transportation and Monge-Ampere type equation
15:10 Fri 13 Jun, 2014 :: B.21 Ingkarni Wardli :: Professor Xu-Jia Wang :: Centre for Mathematics and its Applications, Australian National University

The optimal transportation is to find an optimal mapping of transferring one mass density to another one such that the total cost is minimised. This problem was first introduced by Monge in 1781. Monge's cost function is propositional to the distance the mass is transferred, namely c(x,y)=|x-y|, but more general costs are allowed. The optimal transportation has found a variety of applications and has been extensively studied since then. In 1940s Kantorovich introduced a dual functional, by which one can determine the optimal mapping through the associated potential function, for a large class of cost functions. The potential function satisfies a Monge-Ampere type equation, which is a fully nonlinear partial differential equation arising also in geometric problems related to the Gauss curvature, and has been studied by Aleksandrov, Calabi, Nirenberg, Pogorelov, Cheng-Yau, and Caffarelli, among many others. In this talk we will first introduce the optimal transportation and review the existence of optimal mappings. We then focus on the regularity of the optimal mappings. By studying the associated Monge-Ampere equation, sharp conditions on the cost function have been found by the speaker and his collaborators. For Monge's cost function |x-y|, which does not satisfy the sharp conditions, we have also obtained the existence of optimal mappings, and established interesting regularity and singularity results for the mapping.
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

I will describe a new method for numerically computing eigenfunctions and eigenvalues on certain plane domains, derived from the so-called "scaling method" of Vergini and Saraceno. It is based on properties of the Dirichlet-to-Neumann 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).
The Dirichlet problem for the prescribed Ricci curvature equation
12:10 Fri 15 Aug, 2014 :: Ingkarni Wardli B20 :: Artem Pulemotov :: University of Queensland

We will discuss the following question: is it possible to find a Riemannian metric whose Ricci curvature is equal to a given tensor on a manifold M? To answer this question, one must analyze a weakly elliptic second-order geometric PDE. In the first part of the talk, we will review the history of the subject and state several classical theorems. After that, our focus will be on new results concerning the case where M has nonempty boundary.
Boundary-value problems for the Ricci flow
15:10 Fri 15 Aug, 2014 :: B.18 Ingkarni Wardli :: Dr Artem Pulemotov :: The University of Queensland

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.
Neural Development of the Visual System: a laminar approach
15:10 Fri 29 Aug, 2014 :: N132 Engineering North :: Dr Andrew Oster :: Eastern Washington University

In this talk, we will introduce the architecture of the visual system in higher order primates and cats. Through activity-dependent plasticity mechanisms, the left and right eye streams segregate in the cortex in a stripe-like manner, resulting in a pattern called an ocular dominance map. We introduce a mathematical model to study how such a neural wiring pattern emerges. We go on to consider the joint development of the ocular dominance map with another feature of the visual system, the cytochrome oxidase blobs, which appear in the center of the ocular dominance stripes. Since cortex is in fact comprised of layers, we introduce a simple laminar model and perform a stability analysis of the wiring pattern. This intricate biological structure (ocular dominance stripes with "blobs" periodically distributed in their centers) can be understood as occurring due to two Turing instabilities combined with the leading-order dynamics of the system.
Neural Development of the Visual System: a laminar approach
15:10 Fri 29 Aug, 2014 :: This talk will now be given as a School Colloquium :: Dr Andrew Oster :: Eastern Washington University

In this talk, we will introduce the architecture of the visual system in higher order primates and cats. Through activity-dependent plasticity mechanisms, the left and right eye streams segregate in the cortex in a stripe-like manner, resulting in a pattern called an ocular dominance map. We introduce a mathematical model to study how such a neural wiring pattern emerges. We go on to consider the joint development of the ocular dominance map with another feature of the visual system, the cytochrome oxidase blobs, which appear in the center of the ocular dominance stripes. Since cortex is in fact comprised of layers, we introduce a simple laminar model and perform a stability analysis of the wiring pattern. This intricate biological structure (ocular dominance stripes with 'blobs' periodically distributed in their centers) can be understood as occurring due to two Turing instabilities combined with the leading-order dynamics of the system.
Problems in pandemic preparedness
15:10 Fri 12 Sep, 2014 :: N132 Engineering North :: Dr Joshua Ross :: The University of Adelaide

The emergence of novel strains of viruses pose an ever-present threat to our health and well-being. In this talk, I will provide an overview of work I have done, or am doing, in collaboration with colleagues and students on two topics related to pandemic preparedness: the first being antiviral usage for pre- and post-exposure prophylaxis; and the second being estimating transmissibility and severity from First Few Hundred (FF100) studies.
Visualising the diversity of benchmark instances and generating new test instances to elicit insights into algorithm performance
15:10 Fri 10 Oct, 2014 :: Napier 102 :: Professor Kate Smith-Miles :: Monash University

Objective assessment of optimization algorithm performance is notoriously difficult, with conclusions often inadvertently biased towards the chosen test instances. Rather than reporting average performance of algorithms across a set of chosen instances, we discuss a new methodology to enable the strengths and weaknesses of different optimization algorithms to be compared across a broader instance space. Results will be presented on timetabling, graph colouring and the TSP to demonstrate: (i) how pockets of the instance space can be found where algorithm performance varies significantly from the average performance of an algorithm; (ii) how the properties of the instances can be used to predict algorithm performance on previously unseen instances with high accuracy; (iii) how the relative strengths and weaknesses of each algorithm can be visualized and measured objectively; and (iv) how new test instances can be generated to fill the instance space and provide desired insights into algorithmic power.
Micro Magnetofluidics - Wireless Manipulation for Microfluidics
15:10 Fri 24 Oct, 2014 :: N.132 Engineering North :: Professor Nam-Trung Nguyen :: Griffith University

Microfluidics is rich in multi-physics phenomena, which offer fundamentally new capabilities in the manipulation and detection of biological particles. Most current microfluidic applications are based on hydrodynamic, electrokinetic, acoustic and optic actuation. Implementing these concepts requires bulky external pumping/valving systems and energy supplies. The required wires and connectors make their fabrication and handling difficult. Most of the conventional approaches induce heat that may affect sensitive bio particles such as cells. There is a need for a technology for fluid handling in microfluidic devices that is of low-cost, simple, wireless, free of induced heat and independent of pH level or ion concentration. The use of magnetism would provide a wireless solution for this need. Micro magnetofluidics is a newly established research field that links magnetism and microfluidics to gain new capabilities. Magnetism provides a convenient and wireless way for control and manipulation of fluid flow in the microscale. Investigation of magnetism-induced phenomena in a microfluidic device has the advantage of well-defined experimental condition such as temperature and magnetic field because of the system size. This talk presents recent interesting phenomena in both continuous-flow and digital micro magnetofluidics.
Happiness and social information flow: Computational social science through data.
15:10 Fri 7 Nov, 2014 :: EM G06 (Engineering & Maths Bldg) :: Dr Lewis Mitchell :: University of Adelaide

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

The recent explosion in big data coming from online social networks has led to an increasing interest in bringing quantitative methods to bear on questions in social science. A recent high-profile example is the study of emotional contagion, which has led to significant challenges and controversy. This talk will focus on two issues related to emotional contagion, namely remote-sensing of population-level wellbeing and the problem of information flow across a social network. We discuss some of the challenges in working with massive online data sets, and present a simple tool for measuring large-scale happiness from such data. By combining over 10 million geolocated messages collected from Twitter with traditional census data we uncover geographies of happiness at the scale of states and cities, and discuss how these patterns may be related to traditional wellbeing measures and public health outcomes. Using tools from information theory we also study information flow between individuals and how this may relate to the concept of predictability for human behaviour.
Predicting pressure drops in pipelines due to pump trip events
12:10 Mon 2 Mar, 2015 :: Napier LG29 :: David Arnold :: University of Adelaide

Sunwater is a Queensland company that designs, builds and manages large-scale water infrastructure such as dams, weirs and pipelines. In this talk, I will discuss one of the aspects that is crucial in the design stage of long pipelines, the pipelines ability to withstand large pressure disturbances caused by pump trip events. A pump trip is a sudden, unplanned shutdown of a pump, which causes potentially destructive pressure waves to propagate through the pipe network. Accurate simulation of such events is time consuming and costly, so rules of thumb and intuition are used during initial planning and design of a pipeline project. I will discuss some simple mathematical models for pump trip events, show some results, and discuss how they could be used in the initial design process.
Multiscale modelling of multicellular biological systems: mechanics, development and disease
03:10 Fri 6 Mar, 2015 :: Lower Napier LG24 :: Dr James Osborne :: University of Melbourne

When investigating the development and function of multicellular biological systems it is not enough to only consider the behaviour of individual cells in isolation. For example when studying tissue development, how individual cells interact, both mechanically and biochemically, influences the resulting tissues form and function. In this talk we present a multiscale modelling framework for simulating the development and function of multicellular biological systems (in particular tissues). Utilising the natural structural unit of the cell, the framework consists of three main scales: the tissue level (macro-scale); the cell level (meso-scale); and the sub-cellular level (micro-scale), with multiple interactions occurring between all scales. The cell level is central to the framework and cells are modelled as discrete interacting entities using one of a number of possible modelling paradigms, including lattice based models (cellular automata and cellular Potts) and off-lattice based models (cell centre and vertex based representations). The sub-cellular level concerns numerous metabolic and biochemical processes represented by interaction networks rendered stochastically or into ODEs. The outputs from such systems influence the behaviour of the cell level affecting properties such as adhesion and also influencing cell mitosis and apoptosis. At the tissue level we consider factors or restraints that influence the cells, for example the distribution of a nutrient or messenger molecule, which is represented by field equations, on a growing domain, with individual cells functioning as sinks and/or sources. The modular approach taken within the framework enables more realistic behaviour to be considered at each scale. This framework is implemented within the Open Source Chaste library (Cancer Heart and Soft Tissue Environment, ( and has been used to model biochemical and biomechanical interactions in various biological systems. In this talk we present the key ideas of the framework along with applications within the fields of development and disease.
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.
The Mathematics behind the Ingkarni Wardli Quincunx
12:10 Mon 23 Mar, 2015 :: Napier LG29 :: Andrew Pfeiffer :: University of Adelaide

The quincunx is a fun machine on the ground floor of Ingkarni Wardli. Hopefully you've had a chance to play with it at some point. Perhaps you were waiting for your coffee, or just procrastinating. However, you may have no idea what I'm talking about. If so, read on. To operate the quincunx, you turn a handle and push balls into a sea of needles. The needles then pseudo-randomly direct each ball into one of eight bins. On the quincunx, there is a page of instructions that makes some mathematical claims. For example, it claims that the balls should look roughly like a normal distribution. In this talk, I will discuss some of the mathematics behind the quincunx. I will also seek to make the claims of the quincunx more precise.
Topological matter and its K-theory
11:10 Thu 2 Apr, 2015 :: Ingkarni Wardli B18 :: Guo Chuan Thiang :: University of Adelaide

The notion of fundamental particles, as well as phases of condensed matter, evolves as new mathematical tools become available to the physicist. I will explain how K-theory provides a powerful language for describing quantum mechanical symmetries, homotopies of their realisations, and topological insulators. Real K-theory is crucial in this framework, and its rich structure is still being explored both physically and mathematically.
IGA Workshop on Symmetries and Spinors: Interactions Between Geometry and Physics
09:30 Mon 13 Apr, 2015 :: Conference Room 7.15 on Level 7 of the Ingkarni Wardli building :: J. Figueroa-O'Farrill (University of Edinburgh), M. Zabzine (Uppsala University), et al

The interplay between physics and geometry has lead to stunning advances and enriched the internal structure of each field. This is vividly exemplified in the theory of supergravity, which is a supersymmetric extension of Einstein's relativity theory to the small scales governed by the laws of quantum physics. Sophisticated mathematics is being employed for finding solutions to the generalised Einstein equations and in return, they provide a rich source for new exotic geometries. This workshop brings together world-leading scientists from both, geometry and mathematical physics, as well as young researchers and students, to meet and learn about each others work.
Spherical T-duality: the non-principal case
12:10 Fri 1 May, 2015 :: Napier 144 :: Mathai Varghese :: University of Adelaide

Spherical T-duality is related to M-theory and was introduced in recent joint work with Bouwknegt and Evslin. I will begin by briefly reviewing the case of principal SU(2)-bundles with degree 7 flux, and then focus on the non-principal case for most of the talk, ending with the relation to SUGRA/M-theory.
Multivariate regression in quantitative finance: sparsity, structure, and robustness
15:10 Fri 1 May, 2015 :: Engineering North N132 :: A/Prof Mark Coates :: McGill University

Many quantitative hedge funds around the world strive to predict future equity and futures returns based on many sources of information, including historical returns and economic data. This leads to a multivariate regression problem. Compared to many regression problems, the signal-to-noise ratio is extremely low, and profits can be realized if even a small fraction of the future returns can be accurately predicted. The returns generally have heavy-tailed distributions, further complicating the regression procedure.

In this talk, I will describe how we can impose structure into the regression problem in order to make detection and estimation of the very weak signals feasible. Some of this structure consists of an assumption of sparsity; some of it involves identification of common factors to reduce the dimension of the problem. I will also describe how we can formulate alternative regression problems that lead to more robust solutions that better match the performance metrics of interest in the finance setting.

Haven't I seen you before? Accounting for partnership duration in infectious disease modeling
15:10 Fri 8 May, 2015 :: Level 7 Conference Room Ingkarni Wardli :: Dr Joel Miller :: Monash University


Our ability to accurately predict and explain the spread of an infectious disease is a significant factor in our ability to implement effective interventions. Our ability to accurately model disease spread depends on how accurately we capture the various effects. This is complicated by the fact that infectious disease spread involves a number of time scales. Four that are particularly relevant are: duration of infection in an individual, duration of partnerships between individuals, the time required for an epidemic to spread through the population, and the time required for the population structure to change (demographic or otherwise).

Mathematically simple models of disease spread usually make the implicit assumption that the duration of partnerships is by far the shortest time scale in the system. Thus they miss out on the tendency for infected individuals to deplete their local pool of susceptibles. Depending on the details of the disease in question, this effect may be significant.

I will discuss work done to reduce these assumptions for "SIR" (Susceptible-Infected-Recovered) diseases, which allows us to interpolate between populations which are static and populations which change partners rapidly in closed populations (no entry/exit). I will then discuss early results in applying these methods to diseases such as HIV in which the population time scales are relevant.

The twistor equation on Lorentzian Spin^c manifolds
12:10 Fri 15 May, 2015 :: Napier 144 :: Andree Lischewski :: University of Adelaide

In this talk I consider a conformally covariant spinor field equation, called the twistor equation, which can be formulated on any Lorentzian Spin^c manifold. Its solutions have become of importance in the study of supersymmetric field theories in recent years and were named "charged conformal Killing spinors". After a short review of conformal Spin^c geometry in Lorentzian signature, I will briefly discuss the emergence of charged conformal Killing spinors in supergravity. I will then focus on special geometric structures related to the twistor equation and use charged conformal Killing spinors in order to establish a link between conformal and CR geometry.
Can mathematics help save energy in computing?
15:10 Fri 22 May, 2015 :: Engineering North N132 :: Prof Markus Hegland :: ANU


Recent development of computational hardware is characterised by two trends: 1. High levels of duplication of computational capabilities in multicore, parallel and GPU processing, and, 2. Substantially faster development of the speed of computational technology compared to communication technology

A consequence of these two trends is that energy costs of modern computing devices from mobile phones to supercomputers are increasingly dominated by communication costs. In order to save energy one would thus need to reduce the amount of data movement within the computer. This can be achieved by recomputing results instead of communicating them. The resulting increase in computational redundancy may also be used to make the computations more robust against hardware faults. Paradoxically, by doing more (computations) we do use less (energy).

This talk will first discuss for a simple example how a mathematical understanding can be applied to improve computational results using extrapolation. Then the problem of energy consumption in computational hardware will be considered. Finally some recent work will be discussed which shows how redundant computing is used to mitigate computational faults and thus to save energy.

Big things are weird
12:10 Mon 25 May, 2015 :: Napier LG29 :: Luke Keating-Hughes :: University of Adelaide

The pyramids of Giza, the depths of the Mariana trench, the massive Einstein Cross Quasar; all of these things are big and weird. Big weird things aren't just apparent in the physical world though, they appear in mathematics too! In this talk I will try to motivate a mathematical big thing and then show that it is weird. In particular, we will introduce the necessary topology and homotopy theory in order to show that although all finite dimensional spheres are (almost canonically) non-contractible spaces - an infinite dimensional sphere IS contractible! This result's significance will then be explained in the context of Kuiper's Theorem if time permits.
Complex Systems, Chaotic Dynamics and Infectious Diseases
15:10 Fri 5 Jun, 2015 :: Engineering North N132 :: Prof Michael Small :: UWA

In complex systems, the interconnection between the components of the system determine the dynamics. The system is described by a very large and random mathematical graph and it is the topological structure of that graph which is important for understanding of the dynamical behaviour of the system. I will talk about two specific examples - (1) spread of infectious disease (where the connection between the agents in a population, rather than epidemic parameters, determine the endemic state); and, (2) a transformation to represent a dynamical system as a graph (such that the "statistical mechanics" of the graph characterise the dynamics).
Instantons and Geometric Representation Theory
12:10 Thu 23 Jul, 2015 :: Engineering and Maths EM212 :: Professor Richard Szabo :: Heriot-Watt University

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


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.

Mathematical Modeling and Analysis of Active Suspensions
14:10 Mon 3 Aug, 2015 :: Napier 209 :: Professor Michael Shelley :: Courant Institute of Mathematical Sciences, New York University

Complex fluids that have a 'bio-active' microstructure, like suspensions of swimming bacteria or assemblies of immersed biopolymers and motor-proteins, are important examples of so-called active matter. These internally driven fluids can have strange mechanical properties, and show persistent activity-driven flows and self-organization. I will show how first-principles PDE models are derived through reciprocal coupling of the 'active stresses' generated by collective microscopic activity to the fluid's macroscopic flows. These PDEs have an interesting analytic structures and dynamics that agree qualitatively with experimental observations: they predict the transitions to flow instability and persistent mixing observed in bacterial suspensions, and for microtubule assemblies show the generation, propagation, and annihilation of disclination defects. I'll discuss how these models might be used to study yet more complex biophysical systems.
Non-crossing quantiles
15:10 Fri 14 Aug, 2015 :: Ingkarni Wardli B21 :: Dr Yanan Fan :: UNSW

Quantile regression has received increased attention in the statistics community in recent years. However, since the quantile regression curves are estimated separately, the curves can cross, leading to invalid response distribution. Many authors have proposed remedies for this in the context of frequentist estimation. In this talk, I will explain some of the existing approaches, and then describe a new Bayesian semi-parametric approach for fitting non-crossing quantile regression models simultaneously.
The Calderon Problem: From the Past to the Present
15:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B21 :: Dr Leo Tzou :: University of Sydney

The problem of determining the electrical conductivity of a body by making voltage and current measurements on the object's surface has various applications in fields such as oil exploration and early detection of malignant breast tumour. This classical problem posed by Calderon remained open until the late '80s when it was finally solved in a breakthrough paper by Sylvester-Uhlmann.

In the recent years, geometry has played an important role in this problem. The unexpected connection of this subject to fields such as dynamical systems, symplectic geometry, and Riemannian geometry has led to some interesting progress. This talk will be an overview of some of the recent results and an outline of the techniques used to treat this problem.

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

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

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

Finally, customers who are served by the same server can also be looked at as players who form a grand coalition, now inflicting damage on each other in the form of additional waiting time. We show how cooperative game theory, specifically the Aumann-Shapley prices, leads to a way in which this damage can be attributed to individual customers or groups of customers.
Analytic complexity of bivariate holomorphic functions and cluster trees
12:10 Fri 2 Oct, 2015 :: Ingkarni Wardli B17 :: Timur Sadykov :: Plekhanov University, Moscow

The Kolmogorov-Arnold theorem yields a representation of a multivariate continuous function in terms of a composition of functions which depend on at most two variables. In the analytic case, understanding the complexity of such a representation naturally leads to the notion of the analytic complexity of (a germ of) a bivariate multi-valued analytic function. According to Beloshapka's local definition, the order of complexity of any univariate function is equal to zero while the n-th complexity class is defined recursively to consist of functions of the form a(b(x,y)+c(x,y)), where a is a univariate analytic function and b and c belong to the (n-1)-th complexity class. Such a represenation is meant to be valid for suitable germs of multi-valued holomorphic functions. A randomly chosen bivariate analytic functions will most likely have infinite analytic complexity. However, for a number of important families of special functions of mathematical physics their complexity is finite and can be computed or estimated. Using this, we introduce the notion of the analytic complexity of a binary tree, in particular, a cluster tree, and investigate its properties.
The Mathematics of Crime
15:10 Fri 23 Oct, 2015 :: Ingkarni Wardli B21 :: Prof Andrea Bertozzi :: UCLA

Law enforcement agencies across the US have discovered that partnering with a team of mathematicians and social scientists from UCLA can help them determine where crime is likely to occur. Dr. Bertozzi will talk about the fascinating story behind her participation on the UCLA team that developed a “predictive policing” computer program that zeros-in on areas that have the highest probability of crime. In addition, the use of mathematics in studying gang crimes and other criminal activities will also be discussed. Commercial use of the "predictive-policing" program allows communities to put police officers in the right place at the right time, stopping crime before it happens.
Use of epidemic models in optimal decision making
15:00 Thu 19 Nov, 2015 :: Ingkarni Wardli 5.57 :: Tim Kinyanjui :: School of Mathematics, The University of Manchester

Epidemic models have proved useful in a number of applications in epidemiology. In this work, I will present two areas that we have used modelling to make informed decisions. Firstly, we have used an age structured mathematical model to describe the transmission of Respiratory Syncytial Virus in a developed country setting and to explore different vaccination strategies. We found that delayed infant vaccination has significant potential in reducing the number of hospitalisations in the most vulnerable group and that most of the reduction is due to indirect protection. It also suggests that marked public health benefit could be achieved through RSV vaccine delivered to age groups not seen as most at risk of severe disease. The second application is in the optimal design of studies aimed at collection of household-stratified infection data. A design decision involves making a trade-off between the number of households to enrol and the sampling frequency. Two commonly used study designs are considered: cross-sectional and cohort. The search for an optimal design uses Bayesian methods to explore the joint parameter-design space combined with Shannon entropy of the posteriors to estimate the amount of information for each design. We found that for the cross-sectional designs, the amount of information increases with the sampling intensity while the cohort design often exhibits a trade-off between the number of households sampled and the intensity of follow-up. Our results broadly support the choices made in existing data collection studies.
Chaos in dimensions 2 and 3
15:10 Fri 18 Mar, 2016 :: Engineering South S112 :: Dr Andy Hammerlindl :: Monash University

I will talk about known models of chaotic dynamical systems in dimensions two and three, and results which classify the types of chaotic dynamics that are robust under perturbation. I will also talk about my own work towards understanding chaotic dynamics for discrete-time systems in dimension three. This is joint work with C. Bonatti, A. Gogolev, and R. Potrie.
Connecting within-host and between-host dynamics to understand how pathogens evolve
15:10 Fri 1 Apr, 2016 :: Engineering South S112 :: A/Prof Mark Tanaka :: University of New South Wales

Modern molecular technologies enable a detailed examination of the extent of genetic variation among isolates of bacteria and viruses. Mathematical models can help make inferences about pathogen evolution from such data. Because the evolution of pathogens ultimately occurs within hosts, it is influenced by dynamics within hosts including interactions between pathogens and hosts. Most models of pathogen evolution focus on either the within-host or the between-host level. Here I describe steps towards bridging the two scales. First, I present a model of influenza virus evolution that incorporates within-host dynamics to obtain the between-host rate of molecular substitution as a function of the mutation rate, the within-host reproduction number and other factors. Second, I discuss a model of viral evolution in which some hosts are immunocompromised, thereby extending opportunities for within-host virus evolution which then affects population-level evolution. Finally, I describe a model of Mycobacterium tuberculosis in which multi-drug resistance evolves within hosts and spreads by transmission between hosts.
Sard Theorem for the endpoint map in sub-Riemannian manifolds
12:10 Fri 29 Apr, 2016 :: Eng & Maths EM205 :: Alessandro Ottazzi :: University of New South Wales

Sub-Riemannian geometries occur in several areas of pure and applied mathematics, including harmonic analysis, PDEs, control theory, metric geometry, geometric group theory, and neurobiology. We introduce sub-Riemannian manifolds and give some examples. Therefore we discuss some of the open problems, and in particular we focus on the Sard Theorem for the endpoint map, which is related to the study of length minimizers. Finally, we consider some recent results obtained in collaboration with E. Le Donne, R. Montgomery, P. Pansu and D. Vittone.
Extreme eigenvalues
15:10 Fri 29 Apr, 2016 :: Engineering South S112 :: Dr Julie Clutterbuck :: Monash University

Each bounded domain has a sequence of eigenvalues attached to it. These are determined by the geometry of the domain, but do not completely encode the geometry. A natural question is to ask: which domains optimise the eigenvalues? For example, which domains have the smallest or largest first eigenvalue, or have the largest gap between eigenvalues? This is a rather old problem, with connections to the isoperimetric problem. I will describe some old and new results.
Mathematical modelling of the immune response to influenza
15:00 Thu 12 May, 2016 :: Ingkarni Wardli B20 :: Ada Yan :: University of Melbourne

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

We have constructed a model of the immune response to influenza based on data from viral interference experiments, where ferrets were exposed to two influenza strains within a short time period. The changes in viral kinetics of the second virus due to the first virus depend on the strains used as well as the interval between exposures, enabling inference of the timing of innate and adaptive immune response components and the role of cross-reactivity in resolving infection. Our model provides a mechanistic explanation for the observed variation in viruses' abilities to protect against subsequent infection at short inter-exposure intervals, either by delaying the second infection or inducing stochastic extinction of the second virus. It also explains the decrease in recovery time for the second infection when the two strains elicit cross-reactive cellular adaptive immune responses. To account for inter-subject as well as inter-virus variation, the model is formulated using a hierarchical framework. We will fit the model to experimental data using Markov Chain Monte Carlo methods; quantification of the model will enable a deeper understanding of the effects of potential new treatments.
Harmonic Analysis in Rough Contexts
15:10 Fri 13 May, 2016 :: Engineering South S112 :: Dr Pierre Portal :: Australian National University

In recent years, perspectives on what constitutes the ``natural" framework within which to conduct various forms of mathematical analysis have shifted substantially. The common theme of these shifts can be described as a move towards roughness, i.e. the elimination of smoothness assumptions that had previously been considered fundamental. Examples include partial differential equations on domains with a boundary that is merely Lipschitz continuous, geometric analysis on metric measure spaces that do not have a smooth structure, and stochastic analysis of dynamical systems that have nowhere differentiable trajectories. In this talk, aimed at a general mathematical audience, I describe some of these shifts towards roughness, placing an emphasis on harmonic analysis, and on my own contributions. This includes the development of heat kernel methods in situations where such a kernel is merely a distribution, and applications to deterministic and stochastic partial differential equations.
Some free boundary value problems in mean curvature flow and fully nonlinear curvature flows
12:10 Fri 27 May, 2016 :: Eng & Maths EM205 :: Valentina Wheeler :: University of Wollongong

In this talk we present an overview of the current research in mean curvature flow and fully nonlinear curvature flows with free boundaries, with particular focus on our own results. Firstly we consider the scenario of a mean curvature flow solution with a ninety-degree angle condition on a fixed hypersurface in Euclidean space, that we call the contact hypersurface. We prove that under restrictions on either the initial hypersurface (such as rotational symmetry) or restrictions on the contact hypersurface the flow exists for all times and converges to a self-similar solution. We also discuss the possibility of a curvature singularity appearing on the free boundary contained in the contact hypersurface. We extend some of these results to the setting of a hypersurface evolving in its normal direction with speed given by a fully nonlinear functional of the principal curvatures.
Time series analysis of paleo-climate proxies (a mathematical perspective)
15:10 Fri 27 May, 2016 :: Engineering South S112 :: Dr Thomas Stemler :: University of Western Australia

In this talk I will present the work my colleagues from the School of Earth and Environment (UWA), the "trans disciplinary methods" group of the Potsdam Institute for Climate Impact Research, Germany, and I did to explain the dynamics of the Australian-South East Asian monsoon system during the last couple of thousand years. From a time series perspective paleo-climate proxy series are more or less the monsters moving under your bed that wake you up in the middle of the night. The data is clearly non-stationary, non-uniform sampled in time and the influence of stochastic forcing or the level of measurement noise are more or less unknown. Given these undesirable properties almost all traditional time series analysis methods fail. I will highlight two methods that allow us to draw useful conclusions from the data sets. The first one uses Gaussian kernel methods to reconstruct climate networks from multiple proxies. The coupling relationships in these networks change over time and therefore can be used to infer which areas of the monsoon system dominate the complex dynamics of the whole system. Secondly I will introduce the transformation cost time series method, which allows us to detect changes in the dynamics of a non-uniform sampled time series. Unlike the frequently used interpolation approach, our new method does not corrupt the data and therefore avoids biases in any subsequence analysis. While I will again focus on paleo-climate proxies, the method can be used in other applied areas, where regular sampling is not possible.
Student Performance Issues in First Year University Calculus
15:10 Fri 10 Jun, 2016 :: Engineering South S112 :: Dr Christine Mangelsdorf :: University of Melbourne

MAST10006 Calculus 2 is the largest subject in the School of Mathematics and Statistics at the University of Melbourne, accounting for about 2200 out of 7400 first year enrolments. Despite excellent and consistent feedback from students on lectures, tutorials and teaching materials, scaled failure rates in Calculus 2 averaged an unacceptably high 29.4% (with raw failure rates reaching 40%) by the end of 2014. To understand the issues behind the poor student performance, we studied the exam papers of students with grades of 40-49% over a three-year period. In this presentation, I will present data on areas of poor performance in the final exam, show samples of student work, and identify possible causes for their errors. Many of the performance issues are found to relate to basic weaknesses in the students’ secondary school mathematical skills that inhibit their ability to successfully complete Calculus 2. Since 2015, we have employed a number of approaches to support students’ learning that significantly improved student performance in assessment. I will discuss the changes made to assessment practices and extra support materials provided online and in person, that are driving the improvement.
Multi-scale modeling in biofluids and particle aggregation
15:10 Fri 17 Jun, 2016 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide

In today's seminar I will give 2 examples in mathematical biology which describes the multi-scale organization at 2 levels: the meso/micro level and the continuum/macro level. I will then detail suitable tools in statistical mechanics to link these different scales. The first problem arises in mathematical physiology: swelling-de-swelling mechanism of mucus, an ionic gel. Mucus is packaged inside cells at high concentration (volume fraction) and when released into the extracellular environment, it expands in volume by two orders of magnitude in a matter of seconds. This rapid expansion is due to the rapid exchange of calcium and sodium that changes the cross-linked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a two-phase, polymer/solvent mixture theory (in the continuum level description), together with the chemistry of the polymer, its nearest neighbor interaction and its binding with the dissolved ionic species (in the micro-scale description). The problem is posed as a free-boundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibrium-states of the ionic gels are analyzed. In the second example, we numerically study the adhesion fragmentation dynamics of rigid, round particles clusters subject to a homogeneous shear flow. In the macro level we describe the dynamics of the number density of these cluster. The description in the micro-scale includes (a) binding/unbinding of the bonds attached on the particle surface, (b) bond torsion, (c) surface potential due to ionic medium, and (d) flow hydrodynamics due to shear flow.
Probabilistic Meshless Methods for Bayesian Inverse Problems
15:10 Fri 5 Aug, 2016 :: Engineering South S112 :: Dr Chris Oates :: University of Technology Sydney

This talk deals with statistical inverse problems that involve partial differential equations (PDEs) with unknown parameters. Our goal is to account, in a rigorous way, for the impact of discretisation error that is introduced at each evaluation of the likelihood due to numerical solution of the PDE. In the context of meshless methods, the proposed, model-based approach to discretisation error encourages statistical inferences to be more conservative in the presence of significant solver error. In addition, (i) a principled learning-theoretic approach to minimise the impact of solver error is developed, and (ii) the challenge of non-linear PDEs is considered. The method is applied to parameter inference problems in which non-negligible solver error must be accounted for in order to draw valid statistical conclusions.
Approaches to modelling cells and remodelling biological tissues
14:10 Wed 10 Aug, 2016 :: Ingkarni Wardli 5.57 :: Professor Helen Byrne :: University of Oxford

Biological tissues are complex structures, whose evolution is characterised by multiple biophysical processes that act across diverse space and time scales. For example, during normal wound healing, fibroblast cells located around the wound margin exert contractile forces to close the wound while those located in the surrounding tissue synthesise new tissue in response to local growth factors and mechanical stress created by wound contraction. In this talk I will illustrate how mathematical modelling can provide insight into such complex processes, taking my inspiration from recent studies of cell migration, vasculogenesis and wound healing.
Mathematical modelling of social spreading processes
15:10 Fri 19 Aug, 2016 :: Napier G03 :: Prof Hans De Sterck :: Monash University

Social spreading processes are intriguing manifestations of how humans interact and shape each others' lives. There is great interest in improving our understanding of these processes, and the increasing availability of empirical information in the era of big data and online social networks, combined with mathematical and computational modelling techniques, offer compelling new ways to study these processes. I will first discuss mathematical models for the spread of political revolutions on social networks. The influence of online social networks and social media on the dynamics of the Arab Spring revolutions of 2011 are of particular interest in our work. I will describe a hierarchy of models, starting from agent-based models realized on empirical social networks, and ending up with population-level models that summarize the dynamical behaviour of the spreading process. We seek to understand quantitatively how political revolutions may be facilitated by the modern online social networks of social media. The second part of the talk will describe a population-level model for the social dynamics that cause cigarette smoking to spread in a population. Our model predicts that more individualistic societies will show faster adoption and cessation of smoking. Evidence from a newly composed century-long composite data set on smoking prevalence in 25 countries supports the model, with potential implications for public health interventions around the world. Throughout the talk, I will argue that important aspects of social spreading processes can be revealed and understood via quantitative mathematical and computational models matched to empirical data. This talk describes joint work with John Lang and Danny Abrams.
Predicting turbulence
14:10 Tue 30 Aug, 2016 :: Napier 209 :: Dr Trent Mattner :: School of Mathematical Sciences

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

The elusive Weyl fermion was recently realised as quasiparticle excitations of a topological semimetal. I will explain what a semi-metal is, and the precise mathematical sense in which they can be "topological", in the sense of the general theory of topological insulators. This involves understanding vector bundles with singularities, with the aid of Mayer-Vietoris principles, gerbes, and generalised degree theory.
Modelling evolution of post-menopausal human longevity: The Grandmother Hypothesis
15:10 Fri 2 Sep, 2016 :: Napier G03 :: Dr Peter Kim :: University of Sydney

Human post-menopausal longevity makes us unique among primates, but how did it evolve? One explanation, the Grandmother Hypothesis, proposes that as grasslands spread in ancient Africa displacing foods ancestral youngsters could effectively exploit, older females whose fertility was declining left more descendants by subsidizing grandchildren and allowing mothers to have new babies sooner. As more robust elders could help more descendants, selection favoured increased longevity while maintaining the ancestral end of female fertility. We develop a probabilistic agent-based model that incorporates two sexes and mating, fertility-longevity tradeoffs, and the possibility of grandmother help. Using this model, we show how the grandmother effect could have driven the evolution of human longevity. Simulations reveal two stable life-histories, one human-like and the other like our nearest cousins, the great apes. The probabilistic formulation shows how stochastic effects can slow down and prevent escape from the ancestral condition, and it allows us to investigate the effect of mutation rates on the trajectory of evolution.
The mystery of colony collapse: Mathematics and honey bee loss
15:10 Fri 16 Sep, 2016 :: Napier G03 :: Prof Mary Myerscough :: University of Sydney

Honey bees are vital to the production of many foods which need to be pollinated by insects. Yet in many parts of the world honey bee colonies are in decline. A crucial contributor to hive well-being is the health, productivity and longevity of its foragers. When forager numbers are depleted due to stressors in the colony (such as disease or malnutrition) or in the environment (such as pesticides) there is a significant effect, not only on the amount of food (nectar and pollen) that can be collected but also on the colony's capacity to raise brood (eggs, larvae and pupae) to produce new adult bees to replace lost or aged bees. We use a set of differential equation models to explore the effect on the hive of high forager death rates. In particular we examine what happens when bees become foragers at a comparatively young age and how this can lead to a sudden rapid decline of adult bees and the death of the colony.
A principled experimental design approach to big data analysis
15:10 Fri 23 Sep, 2016 :: Napier G03 :: Prof Kerrie Mengersen :: Queensland University of Technology

Big Datasets are endemic, but they are often notoriously difficult to analyse because of their size, complexity, history and quality. The purpose of this paper is to open a discourse on the use of modern experimental design methods to analyse Big Data in order to answer particular questions of interest. By appeal to a range of examples, it is suggested that this perspective on Big Data modelling and analysis has wide generality and advantageous inferential and computational properties. In particular, the principled experimental design approach is shown to provide a flexible framework for analysis that, for certain classes of objectives and utility functions, delivers equivalent answers compared with analyses of the full dataset. It can also provide a formalised method for iterative parameter estimation, model checking, identification of data gaps and evaluation of data quality. Finally it has the potential to add value to other Big Data sampling algorithms, in particular divide-and-conquer strategies, by determining efficient sub-samples.
Transmission Dynamics of Visceral Leishmaniasis: designing a test and treat control strategy
12:10 Thu 29 Sep, 2016 :: EM218 :: Graham Medley :: London School of Hygiene & Tropical Medicine

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

Medley, G.F., Hollingsworth, T.D., Olliaro, P.L. & Adams, E.R. (2015) Health-seeking, diagnostics and transmission in the control of visceral leishmaniasis. Nature 528, S102-S108 (3 December 2015), DOI: 10.1038/nature16042
Symmetric functions and quantum integrability
15:10 Fri 30 Sep, 2016 :: Napier G03 :: Dr Paul Zinn-Justin :: University of Melbourne/Universite Pierre et Marie Curie

We'll discuss an approach to studying families of symmetric polynomials which is based on ''quantum integrability'', that is, on the use of exactly solvable two-dimensional lattice models. We'll first explain the general strategy on the simplest case, namely Schur polynomials, with the introduction of a model of lattice paths (a.k.a. five-vertex model). We'll then discuss recent work (in collaboration with M. Wheeler) that extends this approach to Hall--Littlewood polynomials and Grothendieck polynomials, and some applications of it.
On the Willmore energy
15:10 Fri 7 Oct, 2016 :: Napier G03 :: Dr Yann Bernard :: Monash University

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.
Measuring and mapping carbon dioxide from remote sensing satellite data
15:10 Fri 21 Oct, 2016 :: Napier G03 :: Prof Noel Cressie :: University of Wollongong

This talk is about environmental statistics for global remote sensing of atmospheric carbon dioxide, a leading greenhouse gas. An important compartment of the carbon cycle is atmospheric carbon dioxide (CO2), where it (and other gases) contribute to climate change through a greenhouse effect. There are a number of CO2 observational programs where measurements are made around the globe at a small number of ground-based locations at somewhat regular time intervals. In contrast, satellite-based programs are spatially global but give up some of the temporal richness. The most recent satellite launched to measure CO2 was NASA's Orbiting Carbon Observatory-2 (OCO-2), whose principal objective is to retrieve a geographical distribution of CO2 sources and sinks. OCO-2's measurement of column-averaged mole fraction, XCO2, is designed to achieve this, through a data-assimilation procedure that is statistical at its basis. Consequently, uncertainty quantification is key, starting with the spectral radiances from an individual sounding to borrowing of strength through spatial-statistical modelling.
Introduction to Lorentz Geometry: Riemann vs Lorentz
12:10 Fri 18 Nov, 2016 :: Engineering North N132 :: Abdelghani Zeghib :: Ecole Normale Superieure de Lyon

The goal is to compare Riemannian and Lorentzian geometries and see what one loses and wins when going from the Riemann to Lorentz. Essentially, one loses compactness and ellipticity, but wins causality structure and mathematical and physical situations when natural Lorentzian metrics emerge.
Collective and aneural foraging in biological systems
15:10 Fri 3 Mar, 2017 :: Lower Napier LG14 :: Dr Jerome Buhl and Dr David Vogel :: The University of Adelaide

The field of collective behaviour uses concepts originally adapted from statistical physics to study how complex collective phenomena such as mass movement or swarm intelligence emerge from relatively simple interactions between individuals. Here we will focus on two applications of this framework. First we will have look at new insights into the evolution of sociality brought by combining models of nutrition and social interactions to explore phenomena such as collective foraging decisions, emergence of social organisation and social immunity. Second, we will look at the networks built by slime molds under exploration and foraging context.
Fast approximate inference for arbitrarily large statistical models via message passing
15:10 Fri 17 Mar, 2017 :: Engineering South S111 :: Prof Matt Wand :: University of Technology Sydney

We explain how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian statistical models. In particular, this approach is amenable to handling arbitrarily large models of particular types once a set of primitive operations is established. The approach is founded upon a message passing formulation of mean field variational Bayes that utilizes factor graph representations of statistical models. The notion of factor graph fragments is introduced and is shown to facilitate compartmentalization of the required algebra and coding.
Geometric structures on moduli spaces
12:10 Fri 31 Mar, 2017 :: Napier 209 :: Nicholas Buchdahl :: University of Adelaide

Moduli spaces are used to classify various kinds of objects, often arising from solutions of certain differential equations on manifolds; for example, the complex structures on a compact surface or the anti-self-dual Yang-Mills equations on an oriented smooth 4-manifold. Sometimes these moduli spaces carry important information about the underlying manifold, manifested most clearly in the results of Donaldson and others on the topology of smooth 4-manifolds. It is also the case that these moduli spaces themselves carry interesting geometric structures; for example, the Weil-Petersson metric on moduli spaces of compact Riemann surfaces, exploited to great effect by Maryam Mirzakhani. In this talk, I shall elaborate on the theme of geometric structures on moduli spaces, with particular focus on some recent-ish work done in conjunction with Georg Schumacher.
One-layer liquid films loaded with self-propelled particles and two-layer films under vibration
15:10 Fri 31 Mar, 2017 :: Engineering South S111 :: Dr Andriy Pototskyy :: Swinburne University of Technology

In the first part, we consider a colony of self-propelled particles (swimmers) in a thin liquid film resting on a solid plate with deformable liquid-gas interface. The local surface tension of the liquid-gas interface is altered by the local density of swimmers due to the soluto-Marangoni effect. Linear stability of the flat film and nonlinear time evolution is analyzed in case of the swarming interaction between the swimmers. In the second part, we study the Faraday instability and nonlinear patterns in vibrated two-layer liquid films. For gravitationally stable two-layer films with a lighter fluid on top of the heavier fluid, we find squares, hexagons, quasiperiodic patterns with eightfold symmetry as well as localized states in the form of large scale depletion regions or finite depth holes, occurring at the interface and surface. For a Rayleigh-Taylor unstable combination (heavier fluid above the light one) we show that external vibration increases the lifetime of the film by delaying or completely suppressing the film rupture.
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 well-understood. Conjectured connections have applications to quantum topology and physics, 3-manifold 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.
What are operator algebras and what are they good for?
15:10 Fri 12 May, 2017 :: Engineering South S111 :: Prof Aidan Sims :: University of Wollongong

Back in the early 1900s when people were first grappling with the new ideas of quantum mechanics and looking for mathematical techniques to study them, they found themselves, unavoidably, dealing with what have now become known as operator algebras. As a research area, operator algebras has come a very long way since then, and has spread out to touch on many other areas of mathematics, as well as maintaining its links with mathematical physics. I'll try to convey roughly what operator algebras are, and describe some of the highlights of their career thus far, particularly the more recent ones.
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 non-optimal 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.
Exact coherent structures in high speed flows
15:10 Fri 28 Jul, 2017 :: Ingkarni Wardli B17 :: Prof Philip Hall :: Monash University

In recent years, there has been much interest in the relevance of nonlinear solutions of the Navier-Stokes equations to fully turbulent flows. The solutions must be calculated numerically at moderate Reynolds numbers but in the limit of high Reynolds numbers asymptotic methods can be used to greatly simplify the computational task and to uncover the key physical processes sustaining the nonlinear states. In particular, in confined flows exact coherent structures defining the boundary between the laminar and turbulent attractors can be constructed. In addition, structures which capture the essential physical properties of fully turbulent flows can be found. The extension of the ideas to boundary layer flows and current work attempting to explain the law of the wall will be discussed.
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 long-standing 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 well-defined universal modules (or "motifs"), connected together. The existence of these newly-discovered modules has important implications for evolutionary biology, embryology and development, cancer research, and drug development.
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 long-standing 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 well-defined universal modules (or “motifs”), connected together. The existence of these newly-discovered modules has important implications for evolutionary biology, embryology and development, cancer research, and drug development.
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 Kashiwara-Vergne (KV) problem (first solved in 2006 by Alekseev-Meinrenken). I will explain how this relationship illuminates the intricate algebra of the KV problem.
On the fundamental of Rayleigh-Taylor instability and interfacial mixing
15:10 Fri 15 Sep, 2017 :: Ingkarni Wardli B17 :: Prof Snezhana Abarzhi :: University of Western Australia

Rayleigh-Taylor instability (RTI) develops when fluids of different densities are accelerated against their density gradient. Extensive interfacial mixing of the fluids ensues with time. Rayleigh-Taylor (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 light-material 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 non-equilibrium processes in nature and technology. Traditionally, it was presumed that RTI leads to uncontrolled growth of small-scale imperfections, single-scale 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 multi-scale and has significant degree of order. This talk presents a physics-based 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.
Measuring the World's Biggest Bubble
13:10 Tue 19 Sep, 2017 :: Napier LG23 :: Prof Matt Roughan :: School of Mathematical Sciences

Recently I had a bit of fun helping Graeme Denton measure his Guinness World Record (GWR) Largest (Indoor) Soap Bubble. It was a lot harder than I initially thought it would be. Soap films are interesting mathematically -- in principle they form minimal surfaces, and have constant curvature. So it should have been fairly easy. But really big bubbles aren't ideal, so measuring the GWR bubble required a mix of maths and pragmatism. It's a good example of mathematical modeling in general, so I thought it was worth a few words. I'll tell you what we did, and how we estimated how big the bubble actually was. Some links:
Understanding burn injuries and first aid treatment using simple mathematical models
15:10 Fri 13 Oct, 2017 :: Ingkarni Wardli B17 :: Prof Mat Simpson :: Queensland University of Technology

Scald burns from accidental exposure to hot liquids are the most common cause of burn injury in children. Over 2000 children are treated for accidental burn injuries in Australia each year. Despite the frequency of these injuries, basic questions about the physics of heat transfer in living tissues remain unanswered. For example, skin thickness varies with age and anatomical location, yet our understanding of how tissue damage from thermal injury is influenced by skin thickness is surprisingly limited. In this presentation we will consider a series of porcine experiments to study heat transfer in living tissues. We consider burning the living tissue, as well as applying various first aid treatment strategies to cool the living tissue after injury. By calibrating solutions of simple mathematical models to match the experimental data we provide insight into how thermal energy propagates through living tissues, as well as exploring different first aid strategies. We conclude by outlining some of our current work that aims to produce more realistic mathematical models.
How oligomerisation impacts steady state gradient in a morphogen-receptor system
15:10 Fri 20 Oct, 2017 :: Ingkarni Wardli 5.57 :: Mr Phillip Brown :: University of Adelaide

In developmental biology an important process is cell fate determination, where cells start to differentiate their form and function. This is an element of the broader concept of morphogenesis. It has long been held that cell differentiation can occur by a chemical signal providing positional information to 'undecided' cells. This chemical produces a gradient of concentration that indicates to a cell what path it should develop along. More recently it has been shown that in a particular system of this type, the chemical (protein) does not exist purely as individual molecules, but can exist in multi-protein complexes known as oligomers. Mathematical modelling has been performed on systems of oligomers to determine if this concept can produce useful gradients of concentration. However, there are wide range of possibilities when it comes to how oligomer systems can be modelled and most of them have not been explored. In this talk I will introduce a new monomer system and analyse it, before extending this model to include oligomers. A number of oligomer models are proposed based on the assumption that proteins are only produced in their oligomer form and can only break apart once they have left the producing cell. It will be shown that when oligomers are present under these conditions, but only monomers are permitted to bind with receptors, then the system can produce robust, biologically useful gradients for a significantly larger range of model parameters (for instance, degradation, production and binding rates) compared to the monomer system. We will also show that when oligomers are permitted to bind with receptors there is negligible difference compared to the monomer system.
The Markovian binary tree applied to demography and conservation biology
15:10 Fri 27 Oct, 2017 :: Ingkarni Wardli B17 :: Dr Sophie Hautphenne :: University of Melbourne

Markovian binary trees form a general and tractable class of continuous-time branching processes, which makes them well-suited for real-world applications. Thanks to their appealing probabilistic and computational features, these processes have proven to be an excellent modelling tool for applications in population biology. Typical performance measures of these models include the extinction probability of a population, the distribution of the population size at a given time, the total progeny size until extinction, and the asymptotic population composition. Besides giving an overview of the main performance measures and the techniques involved to compute them, we discuss recently developed statistical methods to estimate the model parameters, depending on the accuracy of the available data. We illustrate our results in human demography and in conservation biology.
A multiscale approximation of a Cahn-Larche system with phase separation on the microscale
15:10 Thu 22 Feb, 2018 :: Ingkarni Wardli 5.57 :: Ms Lisa Reischmann :: University of Augsberg

We consider the process of phase separation of a binary system under the influence of mechanical deformation and we derive a mathematical multiscale model, which describes the evolving microstructure taking into account the elastic properties of the involved materials. Motivated by phase-separation processes observed in lipid monolayers in film-balance experiments, the starting point of the model is the Cahn-Hilliard equation coupled with the equations of linear elasticity, the so-called Cahn-Larche system. Owing to the fact that the mechanical deformation takes place on a macrosopic scale whereas the phase separation happens on a microscopic level, a multiscale approach is imperative. We assume the pattern of the evolving microstructure to have an intrinsic length scale associated with it, which, after nondimensionalisation, leads to a scaled model involving a small parameter epsilon>0, which is suitable for periodic-homogenisation techniques. For the full nonlinear problem the so-called homogenised problem is then obtained by letting epsilon tend to zero using the method of asymptotic expansion. Furthermore, we present a linearised Cahn-Larche system and use the method of two-scale convergence to obtain the associated limit problem, which turns out to have the same structure as in the nonlinear case, in a mathematically rigorous way. Properties of the limit model will be discussed.
Calculating optimal limits for transacting credit card customers
15:10 Fri 2 Mar, 2018 :: Horace Lamb 1022 :: Prof Peter Taylor :: University of Melbourne

Credit card users can roughly be divided into `transactors', who pay off their balance each month, and `revolvers', who maintain an outstanding balance, on which they pay substantial interest. In this talk, we focus on modelling the behaviour of an individual transactor customer. Our motivation is to calculate an optimal credit limit from the bank's point of view. This requires an expression for the expected outstanding balance at the end of a payment period. We establish a connection with the classical newsvendor model. Furthermore, we derive the Laplace transform of the outstanding balance, assuming that purchases are made according to a marked point process and that there is a simplified balance control policy which prevents all purchases in the rest of the payment period when the credit limit is exceeded. We then use the newsvendor model and our modified model to calculate bounds on the optimal credit limit for the more realistic balance control policy that accepts all purchases that do not exceed the limit. We illustrate our analysis using a compound Poisson process example and show that the optimal limit scales with the distribution of the purchasing process, while the probability of exceeding the optimal limit remains constant. Finally, we apply our model to some real credit card purchase data.
Models, machine learning, and robotics: understanding biological networks
15:10 Fri 16 Mar, 2018 :: Horace Lamb 1022 :: Prof Steve Oliver :: University of Cambridge

The availability of complete genome sequences has enabled the construction of computer models of metabolic networks that may be used to predict the impact of genetic mutations on growth and survival. Both logical and constraint-based models of the metabolic network of the model eukaryote, the ale yeast Saccharomyces cerevisiae, have been available for some time and are continually being improved by the research community. While such models are very successful at predicting the impact of deleting single genes, the prediction of the impact of higher order genetic interactions is a greater challenge. Initial studies of limited gene sets provided encouraging results. However, the availability of comprehensive experimental data for the interactions between genes involved in metabolism demonstrated that, while the models were able to predict the general properties of the genetic interaction network, their ability to predict interactions between specific pairs of metabolic genes was poor. I will examine the reasons for this poor performance and demonstrate ways of improving the accuracy of the models by exploiting the techniques of machine learning and robotics. The utility of these metabolic models rests on the firm foundations of genome sequencing data. However, there are two major problems with these kinds of network models - there is no dynamics, and they do not deal with the uncertain and incomplete nature of much biological data. To deal with these problems, we have developed the Flexible Nets (FNs) modelling formalism. FNs were inspired by Petri Nets and can deal with missing or uncertain data, incorporate both dynamics and regulation, and also have the potential for model predictive control of biotechnological processes.
Complexity of 3-Manifolds
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 3-manifolds and explain the connections between combinatorics, algebra, geometry, and topology that arise in its study. The complexity of a 3-manifold 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 3-manifolds, but they also lead to a structure theory of minimal triangulations of 3-manifolds.
15:10 Fri 4 May, 2018 :: Horace Lamb 1022 :: Dr Anthony Licata :: Australian National University

15:10 Fri 18 May, 2018 :: Horace Lamb 1022 :: Dr Robby Marangell :: University of Sydney

15:10 Fri 25 May, 2018 :: Horace Lamb 1022 :: Dr Ngamta (Natalie) Thamwattana :: University of Wollongong

15:10 Fri 1 Jun, 2018 :: Horace Lamb 1022 :: A/Prof Eduardo Altmann :: University of Sydney

News matching "Mathematical epidemiology with a focus on househol"

Summer Research Scholarship Applications NOW OPEN
Applications for AMSI Vacation Scholarships and Adelaide Summer Research Scholarships are now OPEN. AMSI Vacation Scholarships: Closing date Friday 16th September. University of Adelaide Summer Research Scholarships: Closing date Friday 7th October. Please submit all Adelaide applications to the School of Mathematical Sciences. Posted Wed 30 Nov -1.

More information...

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.

2008-2010: $645,000

Prof RJ Elliott: Dynamic risk measures. (Australian Professorial Fellowship)

2008-2012: $897,000

Dr MD Finn: Topological Optimisation of Fluid Mixing.

2008-2010: $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.

2008-2010: $240,000

The latter grant is held through the ANU Posted Wed 26 Sep 07.

New Professor of Statistical Bioinformatics
Associate Professor Patty Solomon will take up the Chair of Statistical Bioinformatics within the School of Mathematical Sciences effective from 29th of October, 2007. Posted Mon 29 Oct 07.
Mathematics Building to be demolished
The existing mathematics building will be demolished to make way for a new 8-storey, 6-star building. The new building, which is expected to be completed for the start of semester 1, 2010, will house the Schools of Electrical and Electronic Engineering, Computer Science and Mathematical Sciences. The demolition will begin on 10th December 2007. See the Building Life Impact web-site for more details. Posted Mon 12 Nov 07.
School of Mathematical Sciences has a new home.
From the 10th of December the School of Mathematical Sciences will be located on levels 3 and 4 of 10 Pulteney Street. The School office is located on level 3 and is open from 10:00 am to 3:00 pm, Monday to Friday. Posted Sun 9 Dec 07.
School to move to new accommodation
In anticipation of the demolition of the existing Mathematics building, the School of Mathematical Sciences will be moving to new temporary accommodation. As from 10th December 2007 we can be found on level 3 (School Office) and 4 of 10 Pulteney Street. Posted Mon 10 Dec 07.
Success in Learning and Teaching Grants
The School of Mathematical Sciences has been awarded two Faculty L&T awards. Congratulations to Dr David Green for his successful grant "One Simulation Modelling Instruction Module" and to Drs Adrian Koerber, Paul McCann and Jim Denier for their successful grant "Graphics Calculators and beyond". Posted Tue 11 Mar 08.
Teaching Fellow Position

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

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

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

Please see the University web site for further details.

Posted Wed 17 Sep 08.
Mini Winter School on Geometry and Physics
The Institute for Geometry and its Applications will host a Winter School on Geometry and Physics on 20-22 July 2009. There will be three days of expository lectures aimed at 3rd year and honours students interested in postgraduate studies in pure mathematics or mathematical physics. Posted Wed 24 Jun 09.

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Three post-doc positions advertised
The School of Mathematical Sciences is seeking to appoint three post-doctoral research associates. These positions have now closed. Posted Wed 29 Jul 09.
Adelaide becomes full member of the Australian Mathematical Sciences Institute
The University of Adelaide, through the School of Mathematical Sciences, has recently become a full member of the Australian Mathematical Sciences Institute. AMSI undertakes wide ranging activities to support the Mathematical Sciences within Australia. Full details of AMSI and their activities can be found on their website Posted Wed 29 Jul 09.
Prizegiving photographs now available
Congratulations again to all of the 2008 School of Mathematical Sciences student prizewinners. A selection of photographs from the prizegiving evening at the Museum of South Australia is now available. Posted Wed 26 Aug 09.

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Sam Cohen wins prize for best student talk at Aust MS 2009
Congratulations to Mr Sam Cohen, a PhD student within the School, who was awarded the B. H. Neumann Prize for the best student paper at the 2009 meeting of the Australian Mathematical Society for his talk on Dynamic Risk Measures and Nonlinear Expectations with Markov Chain noise. Posted Tue 6 Oct 09.
Welcome to Dr Joshua Ross
We welcome Dr Joshua Ross as a new lecturer in the School of Mathematical Sciences. Joshua has moved over to Adelaide from the University of Cambridge. His research interests are mathematical modelling (especially mathematical biology) and operations research. Posted Mon 15 Mar 10.

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Maths by Email has arrived
Maths by Email is an initiative of CSIRO and the Australian Mathematical Sciences Institute. It is a free fortnightly email newsletter featuring maths news and events. To find out more, including how to subscribe, go to the Maths by Email website. Posted Thu 8 Apr 10.

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We're in Innova 21
The School of Mathematical Sciences has moved to Floors 6 and 7 of the new Innova 21 building. The School Reception is located on Floor 6. Posted Sun 18 Jul 10.
Prize Giving Dinner
The School of Mathematical Sciences Prize Giving Dinner was held on 29th of July in the Pacific Cultures Gallery of the South Australian Museum. Photos from the evening can be found here. Posted Thu 29 Jul 10.
IGA Lecture Series by Professor Dan Freed
The School of Mathematical Sciences will host a series of lectures by Professor Dan Freed (University of Texas, Austin) as part of an upcoming IGA/AMSI workshop, October 18-22, 2010. Details of the workshop can be found here. Posted Tue 5 Oct 10.
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 traffic-matrix 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 matrix-analytic 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 Mathai-Quillen formalism in topological field theory.". Posted Tue 30 Nov 10.
ARC Grant successes
The School of Mathematical Sciences has again been successful in securing funding through the ARCs Linkage Project Scheme. Congratulations to Tong Roberts for his success in the ARCs Linkage Projects scheme: Prof Pavel Bedrikovetski, Prof Anthony J Roberts, A/Prof Andrei G Kotooussov, Prof Mark JBiggs, Prof Sheik S Rahman, Dr Yildiray Cinar, Dr Mark R Tingay, Dr Manouchehr Haghighi, A/Prof Phillip Pendleton, Dr John D Codrington, Mr Jose T Rodrigues, Mr Imran Abbasy, Novel technology for enhanced coal seam gas production utilising mechanisms of stimulated cleat permeability through graded particle injection $360,000 over three years. Posted Wed 1 Jun 11.
Inaugural winner of the Alf van der Poorten Travelling Fellowship
Congratulations to Dr Ray Vozzo who has been awarded the inaugural Alf van der Poorten Travelling Fellowship from the Australian Mathematical Society. Ray will use the fellowship to attend a meeting in Potsdam and visit colleagues in the United Kingdom. Posted Wed 20 Jul 11.
First Australian-New Zealand Rotating Flows Workshop
The first Australian-New Zealand Rotating Flow Workshop will be held from 9th to 11th of January 2012. The workshop, organised by the School of Mathematical Sciences at the University of Adelaide and the Department of Engineering Science at the University of Auckland, will bring together world leading researchers in the broad field of rotating flows. The workshop is sponsored by AMSI, the School of Mathematical Sciences, the University of Auckland and the Royal Society of New Zealand. Please visit the workshop website for further details. Posted Sat 24 Sep 11.
Best paper prize at Membrane Symposium
Congratulations to Wei Xian Lim who was awarded the prize for the best student presentation at the Membrane Society of Australasia 2011 ECR Membrane Symposium for her talk on "Mathematical modelling of gas capture in porous materials". Xian is working on her PhD with Jim Hill and Barry Cox. Posted Mon 28 Nov 11.
The mathematical implications of gauge-string dualities
Between Monday 5 and Friday 9 March 2012, the Institute for Geometry and its Applications will host a lecture series by Rajesh Gopakumar from the Harish-Chandra Research Institute. These lectures will be supplemented by talks by other invited speakers. Posted Tue 6 Dec 11.

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Top-up scholarship available
A PhD opportunity is available to help in mathematical modelling of the interaction of ocean waves and sea ice. For information, see this advertisement. Posted Thu 1 Nov 12.
Summer Research Student Thomas Brown wins the AMSI/Cambridge University Press Prize for 2013
Congratulations to Thomas Brown, jointly supervised by Ed Green and Ben Binder who won the AMSI/Cambridge University Press Prize for the best talk at the 2013 CSIRO Big Day In, recently held this month. After completion of their summer project, vacation scholars must submit a project report which summarises the project and addresses the nature of the topic, methods of investigation, results found, and benefits of the experience. The scholars then present a 15-minute presentation about their project at the CSIRO Big Day In (BDI). This experience enables students to meet and socialise with their peers, gain experience presenting to their colleagues and supervisors and learn about a range of careers in science by interacting with several CSIRO scientists (including mathematicians) in a discussion panel. This is a very pleasing result for Thomas, Ed and Ben as well as for the School of Mathematical Sciences. Well done Thomas. Posted Fri 15 Feb 13.
Outstanding results in the COMAP Mathematical Contest in Modeling
Congratulations to Parsa Kavkani, Alex Tam, Leon Chea, Helen Geng and Susan Pang, who participated in this year's Mathematical Contest in Modeling, run by the Consortium for Mathematics and Its Applications (COMAP). The team with Parsa Kavkani and Alex Tam was designated an "Outstanding Winner" for Problem A (on the spreading of Ebola) and was awarded an INFORMS award for their work. Only 5 outstanding winners were selected from over 5000 entries for this problem, which is an amazing achievement. The team with Leon Chea, Helen Geng and Susan Pang was designated a "Meritorious Winner" for Problem A. There were about 640 meritorious winners out of the 5000, which is also an excellent achievement. Posted Tue 28 Apr 15.

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Mr Hao Guo, 2016 B.H. Neumann Prize recipient
A fantastic way to end 2016 for Mr Hao Guo (supervisors: Varghese, Wang) on being awarded the prestigious 2016 B.H. Neumann Prize in December (Certificate). The School of Mathematical Sciences warmly congratulates Hao for this outstanding achievement! Posted Fri 23 Dec 16.

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A/Prof Joshua Ross, 2017 Moran Medal recipient
Congratulations to Associate Professor Joshua Ross who has won the 2017 Moran Medal, awarded by the Australian Academy of Science. The Moran Medal recognises outstanding research by scientists up to 10 years post-PhD in applied probability, biometrics, mathematical genetics, psychometrics and statistics. Associate Professor Ross has made influential contributions to public health and conservation biology using mathematical modelling and statistics to help in decision making. Posted Fri 23 Dec 16.

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ARC grant recipients
The School of Mathematical Sciences wishes to warmly congratulate the school recipients of the latest ARC grant round which was announced on Tuesday, 1 November. These grants include 1 Future Fellowship (Y. Stokes), 1 Discovery Early Career Research Award (Guo Chuan Thiang) and 1 Discovery Project grant (Varghese, Baraglia). Posted Fri 23 Dec 16.
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 Australia’s position at the forefront of international research in geometric analysis. Posted Thu 15 Jun 17.

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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.

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Publications matching "Mathematical epidemiology with a focus on househol"

Inversion of analytically perturbed linear operators that are singular at the origin
Howlett, P; Avrachenkov, K; Pearce, Charles; Ejov, V, Journal of Mathematical Analysis and Applications 353 (68–84) 2009
Non-commutative correspondences, duality and D-branes in bivariant K-theory
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009
On Markov-modulated exponential-affine bond price formulae
Elliott, Robert; Siu, T, Applied Mathematical Finance 16 (1–15) 2009
T-duality as a duality of loop group bundles
Bouwknegt, Pier; Varghese, Mathai, Journal of Physics A: Mathematical and Theoretical (Print Edition) 42 (162001-1–162001-8) 2009
A discrete version of the Riemann Hilbert problem
Larusson, Finnur; Sadykov, T, Russian Mathematical Surveys 63 (973–975) 2008
D-branes, RR-fields and duality on noncommutative manifolds
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Communications in Mathematical Physics 277 (643–706) 2008
Dessins d'enfants and differential equations
Larusson, Finnur; Sadykov, T, St Petersburg Mathematical Journal 19 (1003–1014) 2008
Evolving gene frequencies in a population with three possible alleles at a locus
Hajek, Bronwyn; Broadbridge, P; Williams, G, Mathematical and Computer Modelling 47 (210–217) 2008
Mathematical modeling as an accurate predictive tool in capillary and microstructured fiber manufacture: The effects of preform rotation
Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Lightwave Technology 26 (791–798) 2008
Mathematical modeling of glucose supply toward successful in vitro maturation of mammalian oocytes
Stokes, Yvonne; Clark, Alys; Thompson, Jeremy, Tissue Engineering. Part A. Tissue Engineering 14 (1539–1547) 2008
The (Gamma)over-cap-genus and a regularization of an S1-equivariant Euler class
Lu, Rongmin, Journal of Physics A: Mathematical and Theoretical (Print Edition) 41 (425204-1–425204-13) 2008
The mathematical modelling of rotating capillary tubes for holey-fibre manufacture
Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Engineering Mathematics 60 (69–87) 2008
A combinatorial formula for homogeneous moments
Eastwood, Michael; Romao, Nuno, Mathematical Proceedings of the Cambridge Philosophical Society 142 (153–160) 2007
A note on N-k configurations and theorems in projective space
Glynn, David, Bulletin of the Australian Mathematical Society 76 (15–31) 2007
Entire cyclic homology of stable continuous trace algebras
Varghese, Mathai; Stevenson, Daniel, Bulletin of the London Mathematical Society 39 (71–75) 2007
Spectral curves and the mass of hyperbolic monopoles
Norbury, Paul; Romao, Nuno, Communications in Mathematical Physics 270 (295–333) 2007
Laguerre geometries and some connections to generalized quadrangles
Brown, Matthew, Journal of the Australian Mathematical Society 83 (335–355) 2007
Consumption of untreated tank rainwater and gastroenteritis among young children in South Australia
Heyworth, J; Glonek, Garique; Maynard, E; Baghurst, Peter; Finlay-Jones, J, International Journal of Epidemiology 35 (1051–1058) 2006
Does dog or cat ownership lead to increased gastroenteritis in young children in South Australia?
Heyworth, J; Cutt, H; Glonek, Garique, Epidemiology and Infection 134 (926–934) 2006
Flux compactifications on projective spaces and the S-duality puzzle
Bouwknegt, Pier; Evslin, J; Jurco, B; Varghese, Mathai; Sati, Hicham, Advances in Theoretical and Mathematical Physics 10 (345–394) 2006
Mathematical analysis of an extended mumford-shah model for image segmentation
Tao, Trevor; Crisp, David; Van Der Hoek, John, Journal of Mathematical Imaging and Vision 24 (327–340) 2006
Mathematical modelling of oxygen concentration in bovine and murine cumulus-oocyte complexes
Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006
Nonassociative Tori and Applications to T-Duality
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Communications in Mathematical Physics 264 (41–69) 2006
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 2006
Yang-Mills theory for bundle gerbes
Varghese, Mathai; Roberts, David, Journal of Physics A: Mathematical and Theoretical (Print Edition) 39 (6039–6044) 2006
Resolving the multitude of microscale interactions accurately models stochastic partial differential equations
Roberts, Anthony John, London Mathematical Society. Journal of Computation and Mathematics 9 (193–221) 2006
Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis
Clarke, Richard; Jensen, O; Billingham, J; Williams, P, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 462 (913–933) 2006
Rumours, partitions mathematical genealogy
Pearce, Charles, chapter in Proceedings of the fourth brazilian symposium on mathematical and computational biology / First international symposium on mathematical and computational biology (E-papers Servicos Editorials Ltda) 357–375, 2005
Arithmetic properties of eigenvalues of generalized harper operators on graphs
Dodziuk, Josef; Varghese, Mathai; Yates, Stuart, Communications in Mathematical Physics 262 (269–297) 2005
Best causal mathematical models for a nonlinear system
Torokhti, Anatoli; Howlett, P; Pearce, Charles, IEEE Transactions on Circuits and Systems I - regular papers 52 (1013–1020) 2005
Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
Carey, Alan; Johnson, Stuart; Murray, Michael; Stevenson, Daniel; Wang, Bai-Ling, Communications in Mathematical Physics 259 (577–613) 2005
Characterizations of continuous distributions and associated goodness of fit tests
Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 131 (5630–5645) 2005
Effect of social networks on 10 year survival in very old Australians: the Australian longitudinal study of aging
Giles, Lynne Catherine; Glonek, Garique; Luszcz, M; Andrews, G, Journal of Epidemiology and Community Health 59 (574–579) 2005
Gauged vortices in a background
Romao, Nuno, Journal of Physics A: Mathematical and Theoretical (Print Edition) 38 (9127–9144) 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
Riemann-Siegel sums via stationary phase
Tuck, Ernest, Bulletin of the Australian Mathematical Society 72 (325–328) 2005
Sufficient conditions for convexity in a class of functions arising in telecommunications
Peake, M; Pearce, Charles, Mathematical Inequalities & Applications 8 (365–372) 2005
T-duality for principal torus bundles and dimensionally reduced Gysin sequences
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Advances in Theoretical and Mathematical Physics 9 (1–25) 2005
T-duality for torus bundles with H-fluxes via noncommutative topology
Varghese, Mathai; Rosenberg, J, Communications in Mathematical Physics 253 (705–721) 2005
Tests resulting from characterizations using record values
Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 131 (5646–5656) 2005
Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: "quorum" sensing by a single bacterium
Koerber, Adrian; King, J; Williams, P, Journal of Mathematical Biology 50 (440–488) 2005
The Cartan Product
Eastwood, Michael, Bulletin of the Belgian Mathematical Society-Simon Stevin 11 (641–651) 2005
Bundle 2-gerbes
Stevenson, Daniel, Proceedings of the London Mathematical Society 88 (405–435) 2004
Characters of the discrete Heisenberg group and of its completion
Tandra, Haryono; Moran, W, Mathematical Proceedings of the Cambridge Philosophical Society 136 (525–539) 2004
Eggs in PG(4n - 1, q), q even, containing a pseudo-conic
Brown, Matthew; Lavrauw, M, Bulletin of the London Mathematical Society 36 (633–639) 2004
Goodness-of-fit tests using dual versions of characterizations via moments of order statistics
Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 122 (3365–3383) 2004
Goodness-of-fit tests using dual versions of characterizations via moments of record values
Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 122 (3384–3403) 2004
M-theory, type IIA superstrings, and elliptic cohomology
Kriz, I; Sati, Hicham, Advances in Theoretical and Mathematical Physics 8 (345–394) 2004
On dual characterizations of continuous distributions in terms of expected values of two functions of order statistics and record values
Alinowska, I; Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 121 (2664–2673) 2004
On the boundary-layer equations for power-law fluids
Denier, James; Dabrowski, Paul, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 460 (3143–3158) 2004
T-duality: Topology change from H-flux
Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Communications in Mathematical Physics 249 (383–415) 2004
Cell-signalling repression in bacterial quorum sensing
Ward, J; King, J; Koerber, Adrian; Croft, J; Sockett, R; Williams, P, Mathematical Medicine and Biology (Print Edition) 21 (169–204) 2004
Connes-Dixmier traces, singular symmetric functionals, and measurable elements in the sense of Connes
Lord, Steven; Sedaev, A; Sukochev, F, Mathematical Notes 76 (884–889) 2004
A Probabilistic algorithm for determining the fundamental matrix of a block M/G/1 Markov chain
Hunt, Emma, Mathematical and Computer Modelling 38 (1203–1209) 2003
A general fractional white noise theory and applications to finance
Elliott, Robert; Van Der Hoek, John, Mathematical Finance 13 (301–330) 2003
A note on monopole moduli spaces
Murray, Michael; Singer, Michael, Journal of Mathematical Physics 44 (3517–3531) 2003
A philosophy for the modelling of realistic nonlinear systems
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Proceedings of the American Mathematical Society 132 (353–363) 2003
An approximate formula for the stress intensity factor for the pressurized star crack
Clements, David; Widana, Inyoman, Mathematical and Computer Modelling 37 (689–694) 2003
Chern character in twisted K-theory: Equivariant and holomorphic cases
Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003
Complex analysis and the Funk transform
Bailey, T; Eastwood, Michael; Gover, A; Mason, L, Journal of the Korean Mathematical Society 40 (577–593) 2003
Dynamics of the cell and its extracellular matrix - A simple mathematical approach
Saha, Asit; Mazumdar, Jagan, IEEE Transactions on NanoBioscience 2 (89–93) 2003
Exponential stability and partial averaging
Grammel, G; Maizurna, Isna, Journal of Mathematical Analysis and Applications 283 (276–286) 2003
Higgs fields, bundle gerbes and string structures
Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 243 (541–555) 2003
Optimal mathematical models for nonlinear dynamical systems
Torokhti, Anatoli; Howlett, P; Pearce, Charles, Mathematical and Computer Modelling of Dynamical Systems 9 (327–343) 2003
Rumours, epidemics, and processes of mass action: Synthesis and analysis
Dickinson, Rowland; Pearce, Charles, Mathematical and Computer Modelling 38 (1157–1167) 2003
The generalised Hadamard inequality, g-convexity and functional Stolarsky means
Neuman, E; Pearce, Charles; Pecaric, Josip; Simic, V, Bulletin of the Australian Mathematical Society 68 (303–316) 2003
Approximating Spectral invariants of Harper operators on graphs II
Varghese, Mathai; Schick, T; Yates, S, Proceedings of the American Mathematical Society 131 (1917–1923) 2003
Early development and quorum sensing in bacterial biofilms
Ward, J; King, J; Koerber, Adrian; Croft, J; Sockett, R; Williams, P, Journal of Mathematical Biology 47 (23–55) 2003
Modelling host tissue degradation by extracellular bacterial pathogens
King, J; Koerber, Adrian; Croft, J; Ward, J; Williams, P; Sockett, R, Mathematical Medicine and Biology (Print Edition) 20 (227–260) 2003
A mathematical study of peristaltic transport of a Casson fluid
Mernone, Anacleto; Mazumdar, Jagan; Lucas, S, Mathematical and Computer Modelling 35 (895–912) 2002
An entire function defined by a nonlinear recurrence relation
Hone, Andrew; Joshi, Nalini; Kitaev, Alexandre, Journal of the London Mathematical Society 66 (377–387) 2002
Mathematical methods for spatially cohesive reserve design
McDonnell, Mark; Possingham, Hugh; Ball, Ian; Cousins, Elizabeth, Environmental Modeling & Assessment 7 (107–114) 2002
Means, g-convex dominated functions & Hadamard-type inequalities
Dragomir, S; Pearce, Charles; Pecaric, Josip, Tamsui Oxford University Journal of Mathematical Sciences 18 (161–173) 2002
On some inequalities for the moments of guessing mapping
Dragomir, S; Pecaric, Josip; Van Der Hoek, John, Mathematical Journal of Ibaraki University 34 (1–16) 2002
Quasilinearity & Hadamard's inequality
Dragomir, S; Pearce, Charles, Mathematical Inequalities & Applications 5 (463–471) 2002
The Orevkov invariant of an affine plane curve
Neumann, W; Norbury, Paul, Transactions of the American Mathematical Society 355 (519–538) 2002
The universal gerbe, Dixmier-Douady class, and gauge theory
Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 59 (47–60) 2002
Twisted K-theory and K-theory of bundle gerbes
Bouwknegt, Pier; Carey, Alan; Varghese, Mathai; Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 228 (17–45) 2002
The value of mathematical models
Metcalfe, Andrew, chapter in Research methods for postgraduates (Oxford University Press) 269–278, 2002
A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: Quorum sensing and the build-up to invasion
Koerber, Adrian; King, J; Ward, J; Williams, P; Croft, J; Sockett, R, Bulletin of Mathematical Biology 64 (239–259) 2002
A goodness-of-fit test for the uniform distribution based on a characterization
Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 106 (2719–2724) 2001
Commutative geometries are spin manifolds
Rennie, Adam, Reviews in Mathematical Physics 13 (409–464) 2001
Coupled Painlev systems and quartic potentials
Hone, Andrew, Journal of Physics A: Mathematical and Theoretical (Print Edition) 34 (2235–2245) 2001
Hilbert C*-systems for actions of the circle group
Baumgaertel, H; Carey, Alan, Reports on Mathematical Physics 47 (349–361) 2001
Integrated solutions of stochastic evolution equations with additive noise
Filinkov, Alexei; Maizurna, Isna, Bulletin of the Australian Mathematical Society 64 (281–290) 2001
Linearised cavity theory with smooth detachment
Haese, Peter, Australian Mathematical Society Gazette 28 (187–193) 2001
Non-Schlesinger deformations of ordinary differential equations with rational coefficients
Kitaev, Alexandre, Journal of Physics A: Mathematical and Theoretical (Print Edition) 34 (2259–2272) 2001
On a generalized 2 + 1 dispersive water wave hierarchy
Gordoa, P; Joshi, Nalini; Pickering, A, Publications of the Research Institute for Mathematical Sciences 37 (327–347) 2001
On the continuum limit of fermionic topological charge in lattice gauge theory
Adams, David, Journal of Mathematical Physics 42 (5522–5533) 2001
Poisson manifolds in generalised Hamiltonian biomechanics
Ivancevic, V; Pearce, Charles, Bulletin of the Australian Mathematical Society 64 (515–526) 2001
Regularizing the KdV equation near a blow-up surface
Joshi, Nalini, Theoretical and Mathematical Physics 127 (744–750) 2001
Statistical modelling and prediction associated with the HIV/AIDS epidemic
Solomon, Patricia; Wilson, Susan, The Mathematical Scientist 26 (87–102) 2001
Truncation-type methods and Bcklund transformations for ordinary differential equations: The third and fifth Painlev equations
Gordoa, P; Joshi, Nalini; Pickering, A, Glasgow Mathematical Journal 43A (23–32) 2001
Twisted index theory on good orbifolds, II: Fractional quantum numbers
Marcolli, M; Varghese, Mathai, Communications in Mathematical Physics 217 (55–87) 2001
Hadamard and Dragomir-Agarwal inequalities, higher-order convexity and the Euler formula
Dedio, L; Pearce, Charles; Peoario, J, Journal of the Korean Mathematical Society (–) 2001
Mathematical modelling of quorum sensing in bacteria
Ward, J; King, J; Koerber, Adrian; Williams, P; Croft, J; Sockett, R, Mathematical Medicine and Biology (Print Edition) 18 (263–292) 2001
More on the relative position of means I
Pearce, Charles; Pecaric, Josip, Mathematical Gazette (112–114) 2001
Some new inequalities for the logarithmic map, with applications entropy and mutual information
Dragomir, S; Pearce, Charles; Pecaric, Josip, Kyungpook Mathematical Journal 41 (115–125) 2001
A brief survey and synthesis of the roles of time in petri nets
Bowden, Fred David John, Mathematical and Computer Modelling 31 (55–68) 2000
A family of 2-dimensional laguerre planes of generalised shear type
Polster, Burkhard; Steinke, G, Bulletin of the Australian Mathematical Society 61 (69–83) 2000
A gerbe obstruction to quantization of fermions on odd-dimensional manifolds with boundary
Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 51 (145–160) 2000
A new perspective on the normalization of invariant measures for loss networks and other product form systems
Bean, Nigel; Stewart, Mark, Mathematical and Computer Modelling 31 (47–54) 2000
A remark of Schwarz's topological field theory
Adams, David; Prodanov, E, Letters in Mathematical Physics 51 (249–255) 2000
Algorithms for second moments in batch-movement queueing systems
Hunt, Emma, Mathematical and Computer Modelling 31 (299–305) 2000
Bundle gerbes applied to quantum field theory
Carey, Alan; Mickelsson, J; Murray, Michael, Reviews in Mathematical Physics 12 (65–90) 2000
Bundle gerbes: stable isomorphism and local theory
Murray, Michael; Stevenson, Daniel, Journal of the London Mathematical Society 62 (925–937) 2000
Cauchy-Schwarz functionals
Cho, Y; Dragomir, S; Kim, S-S; Pearce, Charles, Bulletin of the Australian Mathematical Society 62 (479–491) 2000
Drawing with complex numbers
Eastwood, Michael; Penrose, R, Mathematical Intelligencer 22 (8–13) 2000
Flowing windowpanes: a comparison of Newtonian and Maxwell fluid models
Stokes, Yvonne, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 456 (1861–1864) 2000
Gauss-Plya type results and the Hlder Inequality
Dragomir, S; Pearce, Charles; Sunde, J, Tamsui Oxford University Journal of Mathematical Sciences 16 (17–23) 2000
Generalizations of some inequalities of Ostrowski-gruss type
Pearce, Charles; Pecaric, Josip; Ujevic, N; Varosanec, S, Mathematical Inequalities & Applications 3 (25–34) 2000
Maximal profit dimensioning and tariffing of loss networks with cross-connects
Bean, Nigel; Brown, Deborah; Taylor, Peter, Mathematical and Computer Modelling 31 (21–30) 2000
On the complete integrability of the discrete Nahm equations
Murray, Michael; Singer, Michael, Communications in Mathematical Physics 210 (497–519) 2000
Ovoids of PG(3, q), q even, with a conic section
Brown, Matthew, Journal of the London Mathematical Society 62 (569–582) 2000
Positive random variables and the A-G-H inequality
Pearce, Charles, Australian Mathematical Society Gazette 27 (91–95) 2000
Quasi-reversibility and networks of queues with nonstandard batch movements
Taylor, Peter, Mathematical and Computer Modelling 31 (335–341) 2000
The Andre/Bruck and Bose representation in PG(2h, q): unitals and Baer subplanes
Barwick, Susan; Casse, Rey; Quinn, Catherine, Bulletin of the Belgian Mathematical Society-Simon Stevin 7 (173–197) 2000
The Euler formulae and convex functions
Dedic, L; Pearce, Charles; Pecaric, Josip, Mathematical Inequalities & Applications 3 (211–221) 2000
The exact solution of the general stochastic rumour
Pearce, Charles, Mathematical and Computer Modelling 31 (289–298) 2000
The paradox of Parrondo's games
Harmer, Gregory; Abbott, Derek; Taylor, Peter, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 456 (247–259) 2000
When is a MAP poisson?
Bean, Nigel; Green, David, Mathematical and Computer Modelling 31 (31–46) 2000
m-systems of polar spaces and maximal arcs in projective planes
Hamilton, N; Quinn, Catherine, Bulletin of the Belgian Mathematical Society-Simon Stevin 7 (237–248) 2000
More on the pizza theorem
Pearce, Charles, Australian Mathematical Society Gazette 27 (4–5) 2000

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