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Search the School of Mathematical SciencesPeople matching "Mathematical biology" 
Professor Mathai Varghese Elder Professor of Mathematics, Australian Laureate Fellow, Fellow of the Australian Academy of Scie
More about Mathai Varghese... 
Courses matching "Mathematical biology" 
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, discretetime models, analysed using the mathematical tools of cobwebbing and linear stability analysis of fixed points; Linear stability analysis of systems of discretetime equations; The theory of dynamical systems for models comprised of linear and nonlinear scalar and coupled ordinary differential equations, including vector fields, phaseplane analysis and elementary bifurcation theory; Reactionadvectiondiffusion 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 policymakers on issues that
threaten human health or which have an adverse impact on the economy. It is this realworld 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
Discretetime and continuoustime discretestate 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 CramerRao lower bound, exponential families, sufficient statistics, the RaoBlackwell theorem, efficiency, consistency, maximum likelihood estimators, large sample properties; tests of hypotheses, most powerful tests, the NeymanPearson lemma, likelihood ratio, score and Wald tests, large sample properties.
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Events matching "Mathematical biology" 
tba 00:00 Wed 30 Nov, 0001 :: Lower Napier LG14 :: A/Prof Jessica Purcell :: Monash University


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


Stability of timeperiodic flows 15:10 Fri 10 Mar, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Andrew Bassom, School of Mathematics and
Statistics, University of Western Australia
Timeperiodic shear layers occur naturally in a wide
range of applications from engineering to physiology. Transition to
turbulence in such flows is of practical interest and there have been
several papers dealing with the stability of flows composed of a
steady component plus an oscillatory part with zero mean. In such
flows a possible instability mechanism is associated with the mean
component so that the stability of the flow can be examined using some
sort of perturbationtype analysis. This strategy fails when the mean
part of the flow is small compared with the oscillatory component
which, of course, includes the case when the mean part is precisely
zero.
This difficulty with analytical studies has meant that the stability
of purely oscillatory flows has relied on various numerical
methods. Until very recently such techniques have only ever predicted
that the flow is stable, even though experiments suggest that they do
become unstable at high enough speeds. In this talk I shall expand on
this discrepancy with emphasis on the particular case of the socalled
flat Stokes layer. This flow, which is generated in a deep layer of
incompressible fluid lying above a flat plate which is oscillated in
its own plane, represents one of the few exact solutions of the
NavierStokes equations. We show theoretically that the flow does
become unstable to waves which propagate relative to the basic motion
although the theory predicts that this occurs much later than has been
found in experiments. Reasons for this discrepancy are examined by
reference to calculations for oscillatory flows in pipes and
channels. Finally, we propose some new experiments that might reduce
this disagreement between the theoretical predictions of instability
and practical realisations of breakdown in oscillatory flows. 

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 onesemester course (2 lectures, 2 labs each
week), which includes handson problem solving and students eventually
creating their own problems. One or two exciting problems at
firstyear 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 settheoretic paradoxes including Russell's. But these sources
are rather too closely connected with Foundationalism: the view that
mathematics has a foundation such as logic or set theory or category
theory etc. It soon became apparent that inconsistent mathematical
structures are of interest in their own right and do not depend on the
existence of foundations. This paper will survey some of the results
in inconsistent mathematics and discuss the bearing on various
philosophical positions including Platonism, Logicism, Hilbert's
Formalism, and Brouwer's Intuitionism. 

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
noncommutative algebra. At the end of the talk I hope to be able to
say something about the part of homological algebra on which I have
worked, and its applications. That part is derived categories. 

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). References: Ho SYW et al. Time dependency of molecular rate estimates and
systematic overestimation of recent divergence
times. Mol. Biol. Evol. 22, 15611568 (2005);
Penny D, Nature 436, 183184 (2005).
 Bazin E., et al. Population size does not influence mitochondrial
genetic diversity in animals. Science 312, 570 (2006);
EyreWalker A. Size does not matter for mitochondrial DNA,
Science 312, 537 (2006).
 Shapiro B, et al. Rise and fall of the Beringian steppe
bison. Science 306: 15611565 (2004);
Chan et al. Bayesian estimation of the timing and severity of a
population bottleneck from ancient DNA. PLoS Genetics, 2 e59
(2006).
 Drummond et al. Measurably evolving populations, Trends in
Ecol. Evol. 18, 481488 (2003);
Drummond et al. Bayesian coalescent inference of past population
dynamics from molecular sequences. Molecular Biology Evolution
22, 118592 (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 continuummechanicsbased models for the
growth of biological tissue will be formulated and their properties
(particularly with regard to stability) described. 

A Bivariate Zeroinflated 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 (pretreatment, posttreatment) 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 zeroinflated bivariate Poisson regression (ZIBPR) model for the paired (pretreatment, 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 zeroinflated Poisson regression (ZIPR) model of the posttreatment count with the pretreatment 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 zeroinflated Poisson regression model in which the pretreatment 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
Media...Collapsing bridges and exploding rockets have been associated with vibrations in resonance with natural frequencies. As well, the stability of the solar system and the existence of solutions of SchrÃ¶dinger\'s equation and the wave equation are problematic in the presence of resonances. Such resonances can be avoided, or at least mitigated, by using ideas from Diophantine approximation, a branch of number theory. Applications of Diophantine approximation to these problems will be given and will include a connection with LISA (Laser Interferometer Space Antenna), a spacebased gravity wave detector under construction. 

Alberta Power Prices 15:10 Fri 9 Mar, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Robert Elliott
Media...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
Media...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
Media...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 cameraâs 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 cameraâs JPEG coder to demonstrate that such identification is possible, and that even when an image has subsequently been reprocessed, 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 inkjet printing, spinning of polymer and glass fibres, blowmoulding 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
Media...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 lowlying 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
Media...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 multirobot 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 genenetwork is employed by bacteria to provide a measure of their populationdensity 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 GÃ¡cs, will be given. A second approach is where the object is described as an incidence structure satisfying certain properties; here the geometry is not a priori embedded in a projective space. This will be illustrated by a characterization of the classical inversive plane in the odd case. Another quite recent beautiful result in Galois geometry is the discovery of an infinite class of hemisystems of the Hermitian variety in PG(3,q^2), leading to new interesting classes of incidence structures, graphs and codes; before this result, just one example for GF(9), due to Segre, was known. 

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 semisimple 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 1grading 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 socalled 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 wellknown differential operators are, of course, important in applied mathematics. This is just the tip of an iceberg. I shall indicate some of what lies beneath the surface. There are links with topology, physics, symmetry groups, finite element schemes, and more besides. This talk will touch on these different topics by means of examples. Little prior knowledge will be assumed beyond the equality of mixed partial derivatives. 

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 timelapse techniques have shown that there is a weblike network structure within the invasion wave. Furthermore, within this network, individual cell trajectories vary considerably.
We have developed a populationscale 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 cellbased model also produces an invasion wave with a welldefined 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 nontrivial zeros of the zeta function have real part onehalf) 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 secondyear undergraduate level; after all, the zeta function is much like the trigonometric sine function, and all (?) secondyear 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
Media...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
Media...Most students of high school mathematics will have encountered the technique of fitting a line to data by least squares. Those who have taken a university statistics course will also have heard this method referred to as regression. However, it is not obvious from common dictionary definitions why this should be the case. For example, "reversion to an earlier or less advanced state or form". In this talk, the mathematical phenomenon that gave regression its name will be explained and will be shown to have implications in some unexpected contexts.


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 abovementioned 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 websearch 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. Linkanalysis 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 linkanalysis 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 overdispersed 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 nonmonotone pressureradius relation which presages interesting nontrivial 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 inflationdeflation cycle, the pressureradius 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 pseudoelasticity. Stability in those complex cases is determined by a simple suggestive argument.
References:
[1] W.Kitsche, I.Muller, P.Strehlow. Simulation of pseudoelastic 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 surfacetension 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 inkjet 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. Surfacetension driven pinchoff and the subsequent recoil are examples of finitetime singularities in which the interfacial curvature becomes infinite at the point of disconnection. As a result, the flow near the point of disconnection becomes selfsimilar and independent of initial and farfield conditions. Similarity solutions will be presented for the cases of inviscid and very viscous flow, along with comparison to experiments. In each case, a boundaryintegral representation can be used both to examine the timedependent behaviour and as the basis of a modified Newton scheme for direct solution of the similarity equations. 

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

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

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 PantheonSorbonne
To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available.
Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.
Now nonstationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This nonstationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987).
Thus, using stationary unconditional moments suggest a global stationarity for the model, but using nonstationary unconditional moments or nonstationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior.
The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks.
1. What kinds of nonstationarity affect the major financial and economic data sets? How to detect them?
2. Local and global stationarities: How are they defined?
3. What is the impact of evidence of nonstationarity on the statistics computed from the global non stationary data sets?
4. How can we analyze data sets in the nonstationary global framework? Does the asymptotic theory work in nonstationary framework?
5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy?
These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.


The Mathematics of String Theory 15:10 Fri 2 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Peter Bouwknegt :: Department of Mathematics, ANU
String Theory has had, and continues to have, a profound impact on
many areas of mathematics and vice versa. In this talk I want to
address some relatively recent developments. In particular I will
argue, following Witten and others, that Dbrane charges take values
in the Ktheory of spacetime, rather than in integral cohomology as
one might have expected. I will also explore the mathematical
consequences of a particular symmetry, called Tduality, in this context.
I will give an intuitive introduction into Dbranes and Ktheory.
No prior knowledge about either String Theory, Dbranes or Ktheory
is required. 

The limits of proof 13:10 Wed 21 May, 2008 :: Napier 210 :: A/Prof Finnur Larusson
Media...The job of the mathematician is to discover new
truths about mathematical objects and their relationships.
Such truths are established by proving them. This raises a
fundamental question. Can every mathematical truth be
proved (by a sufficiently clever being) or are there truths
that will forever lie beyond the reach of proof?
Mathematics can be turned on itself to investigate this
question. In this talk, we will see that under certain
assumptions about proofs, there are truths that cannot be
proved. You must decide for yourself whether you think
these assumptions are valid!


Puzzlebased 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
Media...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 problemsolving skills by discussing a variety of puzzles. The talk makes an argument that this approach  called PuzzleBased Learning  is very beneficial for introducing mathematics, critical thinking, and problemsolving 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) fullsemester 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 (PuzzleBased 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 http://www.PuzzleBasedlearning.edu.au/ 

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

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


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

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 decisionmaking 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
endproducts are formed as a result of the surfacetensiondriven 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 wellknown 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 fullydeveloped 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 curvedpipe 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
Media...Most people will have heard of IVF (in vitro fertilisation), a
technology for helping infertile couples have a baby. Although there are
many IVF babies, many will also know that the success rate is still low
for the cost and inconvenience involved. The fact that some women
cannot make use of IVF because of lifethreatening 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.


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

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

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 timescales in the system under study to perform a singular perturbation analysis. Bursting also occurs in hormonesecreting pituitary cells, but is characterized by fast bursts with small electrical impulses. Although the separation of timescales 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 nonrealistic behaviour in cases of large dispersion and of flowfree filtration. In order to resolve the paradoxes, the porescale model is derived. The model can be transformed to Boltzmann equation with particle distribution over pores. Introduction of sinksource terms into Boltzmann equation results in much more simple calculations if compared with the traditional ChapmanEnskog 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 sinksource 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 abovementioned 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
Media...Histograms are convenient and easytouse 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 1020 dimensions to analyse and understand the shape of
these data.


Tummy troubles 12:10 Thu 9 Apr, 2009 :: Napier 210 :: Dr Ben Binder
Media...Hirschsprung's disease is relatively common, affecting roughly
1 in 5000 newly born babies each year in Australia. The disease
occurs when there is an incomplete formation of the nervous system in the gut. Mathematical models can help in determining the underlying
mechanisms that cause the disease. Comparisons between theoretical
predictions and experimental results will be made. 

TBA 15:10 Thu 16 Apr, 2009 :: TBA :: Prof Jonathan Borwein :: University of Newcastle


Multiscale 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 finitevolume 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 Continuoustime Financial Market Model 15:10 Fri 8 May, 2009 :: LG29 :: Associate Prof (Tony) Xuezhong He :: University of Technology Sydney
Within a continuoustime framework, this paper proposes a stochastic
heterogeneous agent model (HAM) of financial markets with time
delays to unify various moving average rules used in discretetime
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, pLaplacian growth, and bubbles contracting in HeleShaw cells with a powerlaw fluid. 15:10 Mon 15 Jun, 2009 :: Napier LG24 :: Dr Scott McCue :: Queensland University Technology
The classical HeleShaw flow problem is related to Laplacian growth and nullquadrature domains. A generalisation is constructed for powerlaw fluids, governed by the pLaplace 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 PredictorCorrector 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
predictorcorrector 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 predictorcorrector 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. 

TBA 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 largeE 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
Media...Turbulence is characterised by threedimensional 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 lowdimensional topology, in particular, from knot theory where the linear functions are replaced by braids or tangles. These geometric monoidal categories are often free in an appropriate sense, a fact that can be used to obtain algebraic invariants for manifolds. 

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

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

Understanding hypersurfaces through tropical geometry 12:10 Fri 25 Sep, 2009 :: Napier 102 :: Dr Mohammed Abouzaid :: Massachusetts Institute of Technology
Given a polynomial in two or more variables, one may study the
zero locus from the point of view of different mathematical subjects
(number theory, algebraic geometry, ...). I will explain how tropical
geometry allows to encode all topological aspects by elementary
combinatorial objects called "tropical varieties."
Mohammed Abouzaid received a B.S. in 2002 from the University of Richmond, and a Ph.D. in 2007 from the University of Chicago under the supervision of Paul Seidel. He is interested in symplectic topology and its interactions with algebraic geometry and differential topology, in particular the homological mirror symmetry conjecture. Since 2007 he has been a postdoctoral fellow at MIT, and a Clay Mathematics Institute Research Fellow. 

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

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. 

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

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 nanofluidic 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 :: HumboldtUniversity, Berlin


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

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 soilwater 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. Varyingcoefficient capital asset pricing model;
6. Semiparametric errorterm model;
7. Nonlinear and nonstationary model;
8. Partially linear ARCH model;
9. Continuoustime 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
Media...The mathematical research community is facing a great challenge to reevaluate 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 datamine 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 benchmarking examples of the opportunities and challenges we face. 

"The Emperor's New Mind": computers, minds, physics and biology 11:10 Wed 21 Apr, 2010 :: Napier 210 :: Prof Tony Roberts :: University of Adelaide
Media...In the mid1990s the computer 'Deep Blue' beat Kasparov, the world chess champion. Will computers soon overtake us humans in other endeavours of intelligence? Roger Penrose's thesis is that human intelligence is far more subtle than has previously been imagined, that the quest for humanlike artificial intelligence in computers, the holy grail of artificial intelligence, is hopeless. The argument ranges from icily clear mathematics of computation, through the amazing shadows of quantum physics, and thence to new conjectures in biology. 

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 policymakers 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 computationallyefficient methods for studying a mathematical model incorporating household structure. We will conclude by briefly discussing some "workinprogess" which utilises these methods to address the issues of inference, and mixing pattern and contact structure, for emerging infections. 

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 presentday 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
Media...High on a mathematician's todo list is classifying objects and structures that arise in mathematics. We see patterns in things and want to know what other sorts of things behave similarly. This poses several problems. How can you tell when two seemingly different mathematical objects are the same? Can you even tell when two seemingly similar mathematical objects are the same? In fact, what does "the same" even mean? How can you tell if two things are the same when you can't even see them! In this talk, we will take a walk through some areas of maths known as algebraic topology and category theory and I will show you some of the ways mathematicians have devised to tell when two things are "the same". 

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) genomewide, 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 recentlydescribed ancestral vs cladespecific 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. Statetrace analysis provides an approach to this problem which has gained increasing interest in recent years. In this talk, I explain statetrace 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 KhovanovLauda and Rouquier whose representation theory categorifies quantum groups of KacMoody Lie algebras). In fact, the glass bead game is tantalizingly simple, and may soon be marketed in your local toy store. I will explain how this game works, and some of the fascinating numerology that appears in the scoring of the plays. 

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 postevent 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 2007January 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 nonvariational (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, easeofuse, 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, pointandclick palettes, builtin 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 nontechnical 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 rolledup 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 workinprogress 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 oneonone 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: maryanne.noon@adelaide.edu.au
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.


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 volatileorganiccompound 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 PTRMS (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 longstanding 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 ENSbased 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 CaRe 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, highdimensional low sample size problems), nonGaussian data, and functional data (where the data are curves) are posing exciting challenges to statisticians, and have resulted in new research which extends the classical theory.
I begin with the classical PCA methodology and illustrate the challenges presented by the complex data that we are now able to collect. The main part of the talk focuses on extensions of PCA: the duality of PCA and the Principal Coordinates of Multidimensional Scaling, Sparse PCA, and consistency results relating to principal components, as the dimension grows. We will also look at newer developments such as Principal Component Regression and Supervised PCA, nonlinear PCA and Functional PCA.


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 noslip 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 noslip boundary condition by simple fluids flowing over nonwetting 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 LucasWashburn 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, selfcleaning 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 modelfreeexcept for a 'frictionless markets' assumption
necessary and sufficient conditions for absence of arbitrage given a set of
currenttime 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 pathdependent option, specifically a weighted variance swap, to
the
set of traded assets and ask what are the conditions on its time0 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 arbitragefree 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
Media...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 nanodevices. 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 nanooscillators, to produce frequencies in the gigahertz range, for applications such as ultrafast optical filters and nanoantennae. The sliding of an inner shell inside an outer shell of a multiwalled carbon nanotube can generate oscillatory frequencies up to several gigahertz, and the shorter the inner tube the higher the frequency. A C60nanotube oscillator generates high frequencies by oscillating a C60 fullerene inside a singlewalled carbon nanotube. Here we discuss the underlying mechanisms of nanooscillators and using the LennardJones potential together with the continuum approach, to mathematically model the C60nanotube nanooscillator. 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
Media...A lattice in a locally compact group G is a discrete subgroup of cofinite volume. Lattices in Lie groups are wellstudied, 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 KacMoody 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 nonclassical settings. 

To which extent the model of BlackScholes 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 suckup 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 metalorganic 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 metalorganic 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 metalorganic 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
Media...To every Gorenstein algebra of finite dimension greater than 1 over a field of characteristic zero, and a projection on its maximal ideal with range equal to the annihilator of the ideal, one can associate a certain algebraic hypersurface lying in the ideal. Such hypersurfaces possess remarkable properties. They can be used, for instance, to help decide whether two given Gorenstein algebras are isomorphic, which for the case of complex numbers leads to interesting consequences in singularity theory. Also, for the case of real numbers such hypersurfaces naturally arise in CRgeometry. In my talk I will discuss these hypersurfaces and some of their applications. 

How to value risk 12:10 Mon 11 Apr, 2011 :: 5.57 Ingkarni Wardli :: Leo Shen :: University of Adelaide
A key question in mathematical finance is: given a future random payoff X, what is its value today? If X represents a loss, one can ask how risky is X. To mitigate risk it must be modelled and quantified. The finance industry has used ValueatRisk and conditional ValueatRisk as measures. However, these measures are not time consistent and ValueatRisk can penalize diversification. A modern theory of risk measures is being developed which is related to solutions of backward stochastic differential equations in continuous time and stochastic difference equations in discrete time.
I first review risk measures used in mathematical finance, including static and dynamic risk measures. I recall results relating to backward stochastic difference equations (BSDEs) associated with a single jump process. Then I evaluate some numerical examples of the solutions of the backward stochastic difference equations and related risk measures. These concepts are new. I hope the examples will indicate how they might be used. 

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

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 realworld 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
timedependent 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)
timeinhomogeneous chains (the parameters may vary with time) and accounting
for observation error (a sample of the true state is observed). 

When statistics meets bioinformatics 12:10 Wed 11 May, 2011 :: Napier 210 :: Prof Patty Solomon :: School of Mathematical Sciences
Media...Bioinformatics is a new field of research which encompasses mathematics, computer science, biology, medicine and the physical sciences. It has arisen from the need to handle and analyse the vast amounts of data being generated by the new genomics technologies. The interface of these disciplines used to be informationpoor, but is now informationmegarich, and statistics plays a central role in processing this information and making it intelligible. In this talk, I will describe a published bioinformatics study which claimed to have developed a simple test for the early detection of ovarian cancer from a blood sample. The US Food and Drug Administration was on the verge of approving the test kits for market in 2004 when demonstrated flaws in the study design and analysis led to its withdrawal. We are still waiting for an effective early biomarker test for ovarian cancer. 

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

Statistical challenges in molecular phylogenetics 15:10 Fri 20 May, 2011 :: Mawson Lab G19 lecture theatre :: Dr Barbara Holland :: University of Tasmania
Media...This talk will give an introduction to the ways that mathematics and statistics gets used in the inference of evolutionary (phylogenetic) trees. Taking a modelbased 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. 

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

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

Stochastic models of reaction diffusion 15:10 Fri 17 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Jon Chapman :: Oxford University
Media...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
Media...Some path problems cannot be modelled
using semirings because the associated
algebraic structure is not distributive. Rather
than attempting to compute globally optimal
paths with such structures, it may be sufficient
in some cases to find locally optimal paths 
paths that represent a stable local equilibrium.
For example, this is the type of routing system that
has evolved to connect Internet Service Providers
(ISPs) where link weights implement
bilateral commercial relationships between them.
Previous work has shown that routing equilibria can
be computed for some nondistributive algebras
using algorithms in the BellmanFord family.
However, no polynomial time bound was known
for such algorithms. In this talk, we show that
routing equilibria can be computed using
Dijkstra's algorithm for one class of nondistributive
structures. This provides the first
polynomial time algorithm for computing locally
optimal solutions to path problems. 

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 nonEuclidean spaces, such as Lie Groups and Symmetric Spaces, or of strongly nonEuclidean spaces, such as spaces of treestructured 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 nonstandard mathematical statistics. 

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

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


Dealing with the GCcontent bias in secondgeneration DNA sequence data 15:10 Fri 12 Aug, 2011 :: Horace Lamb :: Prof Terry Speed :: Walter and Eliza Hall Institute
Media...The field of genomics is currently dealing with an explosion of data from socalled
secondgeneration 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: copynumber 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 postNewtonian expansions 15:10 Fri 19 Aug, 2011 :: 7.15 Ingkarni Wardli :: Dr Todd Oliynyk :: Monash University
Media...Einstein's general relativity is presently the most accurate theory of gravity. To completely determine the gravitational field, the Einstein field equations must be solved. These equations are extremely complex and outside of a small set of idealized situations, they are impossible to solve directly. However, to make physical predictions or understand physical phenomena, it is often enough to find approximate solutions that are governed by a simpler set of equations. For example, Newtonian gravity approximates general relativity very well in regimes where the typical velocity of the gravitating matter is small compared to the speed of light. Indeed, Newtonian gravity successfully explains much of the behaviour of our solar system and is a simpler theory of gravity. However, for many situations of interest ranging from binary star systems to GPS satellites, the Newtonian approximation is not accurate enough; general relativistic effects must be included. This desire to include relativistic corrections to Newtonian gravity lead to the development of the postNewtonian expansions. 

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

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
Media...In the late 1990's, KumjianPaskRaeburnRenault introduced the class of graph C*algebras, building on previous work of CuntzKrieger and of EnomotoWatatani 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 SotoRojo :: University of Adelaide
In the last two decades heap bioleaching has become established as a successful commercial option for recovering copper from lowgrade secondary sulfide ores. Geneticsbased 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
Media...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 agespecific 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 schoolbased 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
Media...We consider the role that finite mixture distributions have played in the modelling of heterogeneous data, in particular for clustering continuous data via mixtures of normal distributions. A very brief history is given starting with the seminal papers by Day and Wolfe in the sixties before the appearance of the EM algorithm. It was the publication in 1977 of the latter algorithm by Dempster, Laird, and Rubin that greatly stimulated interest in the use of finite mixture distributions to model heterogeneous data. This is because the fitting of mixture models by maximum likelihood is a classic example of a problem that is simplified considerably by the EM's conceptual unification of maximum likelihood estimation from data that can be viewed as being incomplete. In recent times there has been a proliferation of applications in which the number of experimental units n is comparatively small but the underlying dimension p is extremely large as, for example, in microarraybased genomics and other highthroughput 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 highdimensional data using mixture distributions. 

Likelihoodfree 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
Media...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 ``likelihoodfree'' or approximate Bayesian computation (ABC), are now being applied extensively across many disciplines.
In this talk, I'll present a brief, nontechnical overview of the ideas behind likelihoodfree 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
Media...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. 

Mixing, dynamics, and probability 15:10 Fri 2 Mar, 2012 :: B.21 Ingkarni Wardli :: A/Prof Gary Froyland :: University of New South Wales
Media...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 timeseparation 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 gaugestring dualities 09:30 Mon 5 Mar, 2012 :: 7.15 Ingkarni Wardli :: Prof Rajesh Gopakumar :: HarishChandra Research Institute
Media...Lecture series by Rajesh Gopakumar (HarishChandra 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 :: HarishChandra Research Institute
Media...Space and time together constitute one of the most basic
elements of physical reality. Since Einstein spacetime has become an
active participant in the dynamics of the gravitational force.
However, our notion of a quantum spacetime is still rudimentary.
String theory, building upon hints provided from the physics of black
holes, seems to be suggesting a very novel, "holographic" picture of
what quantum spacetime might be. This relies on some very surprising
connections of gravity with quantum field theories (which provide the
framework for the description of the other fundamental interactions of
nature). In this talk, I will try and convey some of the flavour of
these connections as well as its significance. 

Forecasting electricity demand distributions using a semiparametric additive model 15:10 Fri 16 Mar, 2012 :: B.21 Ingkarni Wardli :: Prof Rob Hyndman :: Monash University
Media...Electricity demand forecasting plays an important role in shortterm load allocation and longterm 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 semiparametric 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
Media...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
Media...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
fibrereinforced 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 cellwall 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 selfsimilar group? 15:10 Fri 20 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Murray Elder :: University of Newcastle
Media...I will give a brief introduction to the theory of
selfsimilar groups, focusing on a couple of pertinent examples:
Grigorchuk's group of intermediate growth, and the basilica group.


Spatialpoint data sets and the Polya distribution 15:10 Fri 27 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Benjamin Binder :: The University of Adelaide
Media...Spatialpoint 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 spatialstate of the system. 

Mathematical modelling of the surface adsorption for methane on carbon nanostructures 12:10 Mon 30 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Olumide Adisa :: University of Adelaide
Media...In this talk, methane (CH4) adsorption is investigated on both graphite and in the region between two aligned singlewalled carbon nanotubes, which we refer to as the groove site. The LennardâJones 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 singlewalled 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 CH4âgroove site system is minimized when the CH4 carbon is 5.17 angstroms away from the common axis shared by the two aligned singlewalled 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 singlewalled 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
Media...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 individualbased and continuum models using a multiscale approach in which we analyse the collective motion of a population of interacting agents in a generalized latticebased 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 rodshaped 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
AtiyahPatodiSinger proved an index theorem for nonlocal boundary conditions
in the 1970's that has been widely used in mathematics and mathematical physics.
A key application of their theory gives the index theorem for signature operators on
oriented manifolds with boundary. As a consequence, they defined certain secondary
invariants that were metric independent. I will discuss some recent work with Benameur
where we extend the APS theory to signature operators twisted by an odd degree closed
differential form, and study the corresponding secondary invariants. 

Modelling protective antitumour immunity using a hybrid agentbased and delay differential equation approach 15:10 Fri 11 May, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Kim :: University of Sydney
Media...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 earlystage tumours and how this protection could be lost will provide insight into designing nextgeneration 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 agentbased 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
Media...What do practical topics such as linear programming and greedy
heuristics have to do with theoretical problems such as unknot
recognition and the Poincare conjecture? In this talk we explore new
approaches to old and difficult computational problems from geometry and
topology: how to tell whether a loop of string is knotted, or whether a
3dimensional space has no interesting topological features. Although
the best known algorithms for these problems run in exponential time,
there is increasing evidence that a polynomial time solution might be
possible. We outline several promising approaches in which
computational geometry, linear programming and greedy algorithms all
play starring roles. 

Enhancing the Jordan canonical form 15:10 Fri 1 Jun, 2012 :: B.21 Ingkarni Wardli :: A/Prof Anthony Henderson :: The University of Sydney
Media...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 blockdiagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal,
ones on the superdiagonal, 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.


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

IGA Workshop: Dendroidal sets 14:00 Tue 12 Jun, 2012 :: Ingkarni Wardli B17 :: Dr Ittay Weiss :: University of the South Pacific
Media...A series of four 2hour lectures by Dr. Ittay Weiss.
The theory of dendroidal sets was introduced by Moerdijk and Weiss in 2007 in the study of homotopy operads in algebraic topology. In the five years that have past since then several fundamental and highly nontrivial results were established. For instance, it was established that dendroidal sets provide models for homotopy operads in a way that extends the JoyalLurie approach to homotopy categories. It can be shown that dendroidal sets provide new models in the study of nfold loop spaces. And it is very recently shown that dendroidal sets model all connective spectra in a way that extends the modeling of certain spectra by Picard groupoids.
The aim of the lecture series will be to introduce the concepts mentioned above, present the elementary theory, and understand the scope of the results mentioned as well as discuss the potential for further applications. Sources for the course will include the article "From Operads to Dendroidal Sets" (in the AMS volume on mathematical foundations of quantum field theory (also on the arXiv)) and the lecture notes by Ieke Moerdijk "simplicial methods for operads and algebraic geometry" which resulted from an advanced course given in Barcelona 3 years ago.
No prior knowledge of operads will be assumed nor any knowledge of homotopy theory that is more advanced then what is required for the definition of the fundamental group. The basics of the language of presheaf categories will be recalled quickly and used freely. 

Notions of noncommutative metric spaces; why and how 15:10 Fri 15 Jun, 2012 :: B.21 Ingkarni Wardli :: Dr Ittay Weiss :: The University of the South Pacific
Media...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 nonsymmetry 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 1spaces, a new notion of generalized metric spaces. 

Three Minute Thesis 14:00 Mon 2 Jul, 2012 :: B.21 Ingkarni Wardli
Media...This session will feature the The School of Mathematical Sciences Three Minute Thesis competition. Each postgraduate participating will have three minutes to explain their thesis at a level appropriate for a nonspecialist audience. The competition is open to all postgraduates within the School. All staff are welcome to attend. 

Inquirybased learning: yesterday and today 15:30 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Prof Ron Douglas :: Texas A&M University
Media...The speaker will report on a project to develop and promote approaches to mathematics instruction closely related to the Moore method  methods which are called inquirybased 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 AMSISSAI Lecture: Approximate Bayesian computation (ABC): advances and limitations 11:00 Fri 13 Jul, 2012 :: Engineering South S112 :: Prof Christian Robert :: Universite ParisDauphine
Media...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 closedform 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
Media...Classical algebraic geometry is about studying solutions to systems of polynomial equations with complex coefficients. In arithmetic algebraic geometry, one digs deeper and studies the arithmetic properties of the solutions when the coefficients are rational, or even integral. From the usual point of view, it's impossible to go deeper than this for the simple reason that no smaller rings are available  the integers have no proper subrings. In this talk, I will explain how an emerging subject, lambdaalgebraic geometry, allows one to do just this and why one might care. 

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

Differential topology 101 13:10 Fri 17 Aug, 2012 :: Engineering North 218 :: Dr Nicholas Buchdahl :: University of Adelaide
Much of my recent research been directed at a problem in the
theory of compact complex surfacestrying to fill in a gap
in the EnriquesKodaira classification.
Attempting to classify some collection of mathematical
objects is a very common activity for pure mathematicians,
and there are many wellknown examples of successful
classification schemes; for example, the classification of
finite simple groups, and the classification of simply
connected topological 4manifolds.
The aim of this talk will be to illustrate how techniques
from differential geometry can be used to classify compact
surfaces. The level of the talk will be very elementary, and
the material is all very well known, but it is sometimes
instructive to look back over simple cases of a general
problem with the benefit of experience to gain greater
insight into the more general and difficult cases. 

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
Media...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 wellposed 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
Media...The mathematical study of humantohuman transmissible pathogens has
established itself as a complementary methodology to the traditional
epidemiological approach. The classic susceptibleinfectiousrecovered
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 withinhost dynamics of viral (or bacterial or parasite)
infections, with implications for our understanding of infection,
emergence of drug resistance and optimal druginterventions.
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
Media...What network topologies should we use in order to achieve efficient information transmission? Of course answer to this question depends on how we measure efficiency of information dissemination. If we measure it by the minimum gossiping time under the storeandforward, allport and fullduplex model, we show that certain Cayley graphs associated with Frobenius groups are `perfect' in a sense. (A Frobenius group is a permutation group which is transitive but not regular such that only the identity element can fix two points.) Such graphs are also optimal for alltoall routing in the sense that the maximum load on edges achieves the minimum. In this talk we will discuss this theory of optimal network design. 

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 welldefined formal difference of finitedimensional 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
Media...The "Quantisation commutes with reduction" principle is an idea from physics, which has powerful applications in mathematics. It basically states that the ways in which symmetry can be used to simplify a physical system in classical and quantum mechanics, are compatible. This provides a strong link between the areas in mathematics used to describe symmetry in classical and quantum mechanics: symplectic geometry and representation theory, respectively. It has been proved in the 1990s that quantisation indeed commutes with reduction, under the important assumption that all spaces and symmetry groups involved are compact. This talk is an introduction to this principle and, if time permits, its mathematical relevance. 

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
Media...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 selforganization 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
Media...It is a wellknown 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 socalled
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 lowReynoldsnumber microorganisms and microrobots,
the friction properties of superhydrophobic surfaces in microfluidics and
problems of viscous sintering and the manufacture of microstructured optic fibres (MOFs). 

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

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


Interaction of doublestranded DNA inside singlewalled carbon nanotubes 12:10 Mon 5 Nov, 2012 :: B.21 Ingkarni Wardli :: Mr Mansoor Alshehri :: University of Adelaide
Media...Here we investigate the interaction of deoxyribonucleic acid (DNA) inside
single walled carbon nanotubes (SWCNTs). Using classical applied mathematical
modeling, we derive explicit analytical expressions for the encapsulation of
DNA inside singlewalled carbon nanotubes. We adopt the 612 LennardJones
potential function together with the continuous approach to determine the
preferred minimum energy position of the dsDNA molecule inside a singlewalled
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
Media...Dynamo action is the process by which magnetic fields in astrophysical bodies (and recently, laboratory fluids) are maintained against resistive losses by Faraday induction. For many years a favoured model of this process, known as meanfield electrodynamics, has been widely used to produce tractable models. I shall present a critique of this theory and contrast it it with another dynamo process (small scale dynamo action) that does not, unlike meanfield electrodynamics, rely on broken reflection symmetry or scale separation. Finally, I shall talk about very recent rigorous results concerning the Archontis dynamo, in which the magnetic and velocity fields are closely aligned.


Asymptotic independence of (simple) twodimensional Markov processes 15:10 Fri 1 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Guy Latouche :: Universite Libre de Bruxelles
Media...The onedimensional birthand 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 productform. We investigate the conditions under which this property holds, and we show how to use the knowledge to find productform 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
Media...Harmonic functions are realanalytic and so automatically extend as functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated conformal geometry. Nothing will be supposed about such matters: I shall base the constructions on an elementary yet mysterious formula of Bateman from 1904. This is joint work with Feng Xu. 

A multiscale approach to reactiondiffusion processes in domains with microstructure 15:10 Fri 15 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Malte Peter :: University of Augsburg
Media...Reactiondiffusion 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 multiscale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.
The talk will give an introduction to multiscale 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
Media...We derive extended Lorentz transformations between inertial frames for relative velocities greater than the speed of light, and which are complementary to the Lorentz transformation giving rise to the Einstein special theory of relativity. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide welldefined expressions. 

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

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

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

The boundary conditions for macroscale modelling of a discrete diffusion system with periodic diffusivity 12:10 Mon 29 Apr, 2013 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide
Media...Many mathematical and engineering problems have a multiscale nature. There are a vast of theories supporting multiscale modelling on infinite domain, such as homogenization theory and centre manifold theory. To date, there are little consideration of the correct boundary conditions to be used at the edge of macroscale model. In this seminar, I will present how to derive macroscale boundary conditions for the diffusion system. 

Models of cellextracellular matrix interactions in tissue engineering 15:10 Fri 3 May, 2013 :: B.18 Ingkarni Wardli :: Dr Ed Green :: University of Adelaide
Media...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 cellECM 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
Media...In mathematical finance, as in many other fields where applied mathematics is a powerful tool, we assume that a model is good enough when it captures different sources of randomness affecting the quantity of interests, which in this case is the electricity prices. The power market is very different from other markets in terms of the randomness sources that can be observed in the prices feature and evolution. We start from suggesting a new model that simulates the electricity prices, this new model is constructed by adding a periodicity term, a jumps terms and a positives mean reverting term. The later term is driven by a nonobservable Markov process. So in order to prices some financial product, we have to use some of the filtering theory to deal with the nonobservable process, these techniques are gaining very much of interest from practitioners and researchers in the field of financial mathematics. 

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

Progress in the prediction of buoyancyaffected turbulence 15:10 Fri 17 May, 2013 :: B.18 Ingkarni Wardli :: Dr Daniel Chung :: University of Melbourne
Media...Buoyancyaffected 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 buoyancyaffected
turbulence using direct and largeeddy simulations, along with implications
for the characterisation of mixing in the ocean and the lowcloud 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 subgridscale model that captures the anisotropic character of stratified
mixing will be developed for largeeddy simulation of buoyancyaffected
turbulence. Finally, the subgridscale model is utilised to perform a
systematic largeeddy simulation investigation of the archetypal lowcloud
regimes, from which the link between the lowertropospheric stability
criterion and the cloud fraction interpreted. 

Heat kernel estimates on noncompact Riemannian manifolds: why and how? 15:10 Fri 7 Jun, 2013 :: B.18 Ingkarni Wardli :: Prof Thierry Coulhon :: Australian National University
Media...We will describe what is known and remains to be known about the connection between the large scale geometry of noncompact 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
Media...A central theme in 19th century mathematics was invariant theory, which was viewed as a bridge between geometry and algebra. David Hilbert revolutionized the field with two seminal papers in 1890 and 1893 with techniques such as Hilbert's basis theorem, Hilbert's Nullstellensatz and Hilbert's syzygy theorem that spawned the modern field of commutative algebra. After Hilbert's groundbreaking work, the field of invariant theory remained largely inactive until the 1960's when David Mumford revitalized the field by reinterpreting Hilbert's ideas in the context of algebraic geometry which ultimately led to the influential construction of the moduli space of smooth curves. Today invariant theory remains a vital research area with connections to various mathematical disciplines: representation theory, algebraic geometry, commutative algebra, combinatorics and nonlinear differential operators.
The goal of this talk is to provide an introduction to invariant theory with an emphasis on Hilbert's and Mumford's contributions. Time permitting, I will explain recent research with Maksym Fedorchuk and David Smyth which exploits the ideas of Hilbert, Mumford as well as Kempf to answer a classical question concerning the stability of algebraic curves. 

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

The Hamiltonian Cycle Problem and Markov Decision Processes 15:10 Fri 2 Aug, 2013 :: B.18 Ingkarni Wardli :: Prof Jerzy Filar :: Flinders University
Media...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 01 probability transition matrix whose nonzero 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 socalled "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
Media...After normalization, an evolving real nonnegative 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 fourthorder diffusion equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a selfconsistent 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
Media...I'll begin with the Jones polynomial, a knot invariant discovered 30 years ago that radically changed our view of topology. From there, we'll visit the complexity of evaluating the Jones polynomial, the topological field theories related to the Jones polynomial, and how all these ideas come together to offer an unorthodox model for quantum computation. 

Thinfilm flow in helical channels 12:10 Mon 9 Sep, 2013 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide
Media...Spiral particle separators are used in the mineral processing industry to refine ores. A slurry, formed by mixing crushed ore with a fluid, is run down a helical channel and at the end of the channel, the particles end up sorted in different sections of the channel. Design of such devices is largely experimentally based, and mathematical modelling of flow in helical channels is relatively limited. In this talk, I will outline some of the work that I have been doing on thinfilm 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
Media...Klein's Erlangen program classified geometries based on their (transitive) groups of symmetries, e.g. Euclidean geometry is the quotient of the rigid motion group by the subgroup of rotations. While this perspective is homogeneous, Riemann's generalization of Euclidean geometry is in general very "lumpy"  i.e. there exist Riemannian manifolds that have no symmetries at all. A common generalization where a group still plays a dominant role is Cartan geometry, which first arose in Cartan's solution to the equivalence problem for geometric structures, and which articulates what a "curved version" of a flat (homogeneous) model means. Parabolic geometries are Cartan geometries modelled on (generalized) flag varieties (e.g. projective space, isotropic Grassmannians) which are wellknown objects from the representation theory of semisimple Lie groups. These curved versions encompass a zoo of interesting geometries, including conformal, projective, CR, systems of 2nd order ODE, etc. This interaction between differential geometry and representation theory has proved extremely fruitful in recent years. My talk will be an examplebased tour of various types of parabolic geometries, which I'll use to outline some of the main aspects of the theory (suppressing technical details). The main thread throughout the talk will be the symmetry gap problem: For a given type of Cartan geometry, the maximal symmetry dimension is realized by the flat model, but what is the next possible ("submaximal") symmetry dimension? I'll sketch a recent solution (in joint work with Boris Kruglikov) for a wide class of parabolic geometries which gives a combinatorial recipe for reading the submaximal symmetry dimension from a Dynkin diagram. 

The irrational line on the torus 12:35 Mon 23 Sep, 2013 :: B.19 Ingkarni Wardli :: Kelli FrancisStaite :: University of Adelaide
The torus is very common example of a surface in R^3, but it's a lot more interesting than just a donut! I will introduce some standard mathematical descriptions of the torus, a bit of number theory, and finally what the irrational line on the torus is.
Why is this interesting? Well despite donuts being yummy to eat, the irrational line on the torus gives a range of pathological counterexamples. In Differential Geometry, it is an example of a manifold that is a subset of another manifold, but not a submanifold. In Lie theory, it is an example of a subgroup of a Lie group which is not a Lie subgroup.
If that wasn't enough of a mouthful, I may also provide some sweet incentives to come along! Does anyone know the location of a good donut store? 

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
Media...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 24dimensional 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
Media...It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in R^n. (A lattice is simply a grid of points.) This technique is called the "geometry of numbers." We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects. 

Gravitational slingshot and space mission design 15:10 Fri 11 Oct, 2013 :: B.18 Ingkarni Wardli :: Prof Pawel Nurowski :: Polish Academy of Sciences
Media...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 3body 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
Media...Patterns are everywhere in nature, whether they be the spots and stripes on animals' coats, or the intricate arrangement of different cell types in a tissue. But how do these patterns arise? Whilst every cell contains a plan of the organism in its genes, the cells need to organise themselves so that each knows what it should do to achieve this plan. Mathematics can help biologists explore how different types of signals might be used to control the patterning process. In this talk, I will introduce two simple mathematical theories of biological pattern formation: Turing patterns where, surprisingly, the essential ingredient for producing the pattern is diffusion, which usually tends to make things more uniform; and the KellerSegel 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
Media...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 doublestranded DNA inside singlewalled carbon nanotubes 12:35 Mon 28 Oct, 2013 :: B.19 Ingkarni Wardli :: Mansoor Alshehri :: University of Adelaide
Media...Here we investigate the interaction of deoxyribonucleic acid (DNA) inside single walled carbon nanotubes (SWCNTs). Using classical applied mathematical modeling, we derive explicit analytical expressions for the encapsulation of DNA inside singlewalled carbon nanotubes. We adopt the 612 LennardJones potential function together with the continuous approach to determine the preferred minimum energy position of the dsDNA molecule inside a singlewalled 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 nonholonomic mechanics 15:10 Fri 1 Nov, 2013 :: B.18 Ingkarni Wardli :: Prof Robert Bryant :: Duke University
Media...In mechanics, the system of a sphere rolling over a plane without slipping or twisting is a fundamental example of what is called a nonholonomic mechanical system, the study of which belongs to the subject of control theory. The more general case of one surface rolling over another without slipping or twisting is, similarly, of great interest for both practical and theoretical reasons. In this talk, which is intended for a general mathematical audience (i.e., no familiarity with control theory or differential geometry will be assumed), I will describe some of the basic features of this problem, a bit of its history, and some of the surprising developments that its study reveals, such as the unexpected appearance of the exceptional group G_2. 

A gentle introduction to bubble evolution in HeleShaw flows 15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT
A HeleShaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a HeleShaw 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 HeleShaw cell or SaffmanTaylor instability on YouTube). From a mathematical perspective, modelling these HeleShaw 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) twodimensional moving boundary problems are so tractable. More generally, HeleShaw 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
Media...In this talk we will outline a general view of optimal control of a continuoustime Markov chain, and how this naturally leads to the theory of Backward Stochastic Differential Equations. We will see how this class of equations gives a natural setting to study these problems, and how we can calculate numerical solutions in many settings. These will include problems with payoffs with memory, with random terminal times, with ergodic and infinitehorizon value functions, and with finite and infinitely many states. Examples will be drawn from finance, networks and electronic engineering. 

Weak Stochastic Maximum Principle (SMP) and Applications 15:10 Thu 12 Dec, 2013 :: B.21 Ingkarni Wardli :: Dr Harry Zheng :: Imperial College, London
Media...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 preexisting immunity 15:10 Fri 7 Mar, 2014 :: B.18 Ingkarni Wardli :: Associate Professor Jane Heffernan :: York University, Canada
Media...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 (inhost) 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 multiscale 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 illposed 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
Media...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 recentlyproposed 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
Media...The job of the mathematician is to discover new truths about mathematical objects and their relationships. Such truths are established by proving them. This raises a fundamental question. Can every mathematical truth be proved (by a sufficiently clever being) or are there truths that will forever lie beyond the reach of proof?
Mathematics can be turned on itself to investigate this question. In this talk, we will see that under certain assumptions about proofs, there are truths that cannot be proved. You must decide for yourself whether you think these assumptions are valid! 

Flow barriers and flux in unsteady flows 15:10 Fri 4 Apr, 2014 :: B.21 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: The University of Adelaide
Media...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. 

Networkbased 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
Media...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 largescale 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 networkbased prediction methods, which we will then compare to the common singlegene and geneset 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
Media...The Mandelbrot set is an icon of modern mathematics, an image which fires the popular imagination when accompanied by the words 'chaos' and 'fractal'. However, few could give even a vague definition of this mysterious set and fewer still know the mathematical meaning behind it. In this talk we will be looking at the role that the Mandelbrot set plays in complex dynamics, the study of iterated complex valued functions. We shall discuss attracting and repelling cycles and how they are related to the different components of the Mandelbrot set. 

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
Media...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 welldefined average, i.e. is it ergodic?
How does this longterm 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 selflimiting 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
Media...In an era of climate change, it is becoming increasingly important to model the dynamics of seaice 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
Media...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 twostate continuoustime 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
Media...Groups are algebraic structures which show up in many branches of
mathematics and other areas of science; Computational Group Theory is
on the cutting edge of pure research in group theory and its interplay
with computational methods.
In this talk, we consider a practical aspect
of Computational Group Theory: how to represent a group in a computer,
and how to work with such a description efficiently. We will first
recall some wellestablished methods for permutation group; we will
then discuss some recent progress for matrix groups. 

Optimal transportation and MongeAmpere type equation 15:10 Fri 13 Jun, 2014 :: B.21 Ingkarni Wardli :: Professor XuJia Wang :: Centre for Mathematics and its Applications, Australian National University
Media...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)=xy, 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 MongeAmpere 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, ChengYau, 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 MongeAmpere equation, sharp conditions on the cost function have been found by the speaker and his collaborators. For Monge's cost function xy, 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
Media...I will describe a new method for numerically computing eigenfunctions and eigenvalues on certain plane domains, derived from the socalled "scaling method" of Vergini and Saraceno. It is based on properties of the DirichlettoNeumann map on the domain, which relates a function f on the boundary of the domain to the normal derivative (at the boundary) of the eigenfunction with boundary data f. This is a topic of independent interest in pure mathematics. In my talk I will try to emphasize the inteplay between theory and applications, which is very rich in this situation. This is joint work with numerical analyst Alex Barnett (Dartmouth). 

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

Neural Development of the Visual System: a laminar approach 15:10 Fri 29 Aug, 2014 :: N132 Engineering North :: Dr Andrew Oster :: Eastern Washington University
Media...In this talk, we will introduce the architecture of the visual
system in higher order primates and cats. Through activitydependent
plasticity mechanisms, the left and right eye streams segregate in the
cortex in a stripelike 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 leadingorder 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 activitydependent plasticity mechanisms, the left and right eye streams segregate in the cortex in a stripelike 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 leadingorder dynamics of the system. 

Problems in pandemic preparedness 15:10 Fri 12 Sep, 2014 :: N132 Engineering North :: Dr Joshua Ross :: The University of Adelaide
Media...The emergence of novel strains of viruses pose an everpresent
threat to our health and wellbeing. 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 postexposure 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 SmithMiles :: Monash University
Media...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 NamTrung Nguyen :: Griffith University
Media...Microfluidics is rich in multiphysics 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 lowcost, 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 magnetisminduced phenomena in a microfluidic device has the advantage of welldefined experimental condition such as temperature and magnetic field because of the system size. This talk presents recent interesting phenomena in both continuousflow and digital micro magnetofluidics. 

What happens when you eat pizza?: the science and mathematics behind digestion 14:10 Mon 27 Oct, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. Sarthok Sircar :: School of Mathematical Sciences
Media...Our stomach is an inferno with acidic juices that are strong enough to bore a hole through our hands. Ever wondered why the stomach does not digest itself ? The answer lies in an interesting defence mechanism along the stomach lining which also aids in digestion of food.
In this talk I will present this mechanism and briefly present the physics, chemistry, biology and (off course !) the mathematics to describe this system. The talk may also answer your queries regarding heartburn especially when you eat a lot of freefood !! 

Predicting pressure drops in pipelines due to pump trip events 12:10 Mon 2 Mar, 2015 :: Napier LG29 :: David Arnold :: University of Adelaide
Media...Sunwater is a Queensland company that designs, builds and manages largescale 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 (macroscale); the cell level (mesoscale); and the subcellular level (microscale), 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 offlattice based models (cell centre and vertex based representations). The subcellular 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, (http://www.cs.ox.ac.uk/chaste/)
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 pseudorandomly 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 Ktheory 11:10 Thu 2 Apr, 2015 :: Ingkarni Wardli B18 :: Guo Chuan Thiang :: University of Adelaide
The notion of fundamental particles, as well as phases of condensed matter, evolves as new mathematical tools become available to the physicist. I will explain how Ktheory provides a powerful language for describing quantum mechanical symmetries, homotopies of their realisations, and topological insulators. Real Ktheory is crucial in this framework, and its rich structure is still being explored both physically and mathematically. 

IGA Workshop on Symmetries and Spinors: Interactions Between Geometry and Physics 09:30 Mon 13 Apr, 2015 :: Conference Room 7.15 on Level 7 of the Ingkarni Wardli building :: J. FigueroaO'Farrill (University of Edinburgh), M. Zabzine (Uppsala University), et al
Media...The interplay between physics and geometry has lead to stunning advances and enriched the internal structure of each field. This is vividly exemplified in the theory of supergravity, which is a supersymmetric extension of Einstein's relativity theory to the small scales governed by the laws of quantum physics. Sophisticated mathematics is being employed for finding solutions to the generalised Einstein equations and in return, they provide a rich source for new exotic geometries. This workshop brings together worldleading scientists from both, geometry and mathematical physics, as well as young researchers and students, to meet and learn about each others work. 

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 signaltonoise 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 heavytailed 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
Media...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" (SusceptibleInfectedRecovered) 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. 

Can mathematics help save energy in computing? 15:10 Fri 22 May, 2015 :: Engineering North N132 :: Prof Markus Hegland :: ANU
Media...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 KeatingHughes :: University of Adelaide
Media...The pyramids of Giza, the depths of the Mariana trench, the massive Einstein Cross Quasar; all of these things are big and weird. Big weird things aren't just apparent in the physical world though, they appear in mathematics too! In this talk I will try to motivate a mathematical big thing and then show that it is weird.
In particular, we will introduce the necessary topology and homotopy theory in order to show that although all finite dimensional spheres are (almost canonically) noncontractible spaces  an infinite dimensional sphere IS contractible! This result's significance will then be explained in the context of Kuiper's Theorem if time permits. 

Complex Systems, Chaotic Dynamics and Infectious Diseases 15:10 Fri 5 Jun, 2015 :: Engineering North N132 :: Prof Michael Small :: UWA
Media...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 :: HeriotWatt University
We give an overview of the various approaches to studying
supersymmetric quiver gauge theories on ALE spaces, and their conjectural
connections to twodimensional conformal field theory via AGTtype
dualities. From a mathematical perspective, this is formulated as a
relationship between the equivariant cohomology of certain moduli spaces
of sheaves on stacks and the representation theory of infinitedimensional
Lie algebras. We introduce an orbifold compactification of the minimal
resolution of the Atype toric singularity in four dimensions, and then
construct a moduli space of framed sheaves which is conjecturally
isomorphic to a Nakajima quiver variety. We apply this construction to
derive relations between the equivariant cohomology of these moduli spaces
and the representation theory of the affine Lie algebra of type A.


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

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 'bioactive' microstructure, like
suspensions of swimming bacteria or assemblies of immersed biopolymers
and motorproteins, are important examples of socalled active matter.
These internally driven fluids can have strange mechanical properties,
and show persistent activitydriven flows and selforganization. I will
show how firstprinciples 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.


Noncrossing quantiles 15:10 Fri 14 Aug, 2015 :: Ingkarni Wardli B21 :: Dr Yanan Fan :: UNSW
Media...Quantile regression has received increased attention in the statistics community in recent years. However, since the quantile regression curves are estimated separately, the curves can cross, leading to invalid response distribution. Many authors have proposed remedies for this in the context of frequentist estimation. In this talk, I will explain some of the existing approaches, and then describe a new Bayesian semiparametric approach for fitting noncrossing 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 SylvesterUhlmann.
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. 

Analytic complexity of bivariate holomorphic functions and cluster trees 12:10 Fri 2 Oct, 2015 :: Ingkarni Wardli B17 :: Timur Sadykov :: Plekhanov University, Moscow
The KolmogorovArnold 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 multivalued analytic function. According to Beloshapka's local definition, the order of complexity of any univariate function is equal to zero while the nth 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 (n1)th complexity class. Such a represenation is meant to be valid for suitable germs of multivalued 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
Media...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 âpredictive policingâ computer program that zerosin 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 "predictivepolicing" 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
Media...Epidemic models have proved useful in a number of applications in epidemiology. In this work, I will present two areas that we have used modelling to make informed decisions. Firstly, we have used an age structured mathematical model to describe the transmission of Respiratory Syncytial Virus in a developed country setting and to explore different vaccination strategies. We found that delayed infant vaccination has significant potential in reducing the number of hospitalisations in the most vulnerable group and that most of the reduction is due to indirect protection. It also suggests that marked public health benefit could be achieved through RSV vaccine delivered to age groups not seen as most at risk of severe disease. The second application is in the optimal design of studies aimed at collection of householdstratified infection data. A design decision involves making a tradeoff between the number of households to enrol and the sampling frequency. Two commonly used study designs are considered: crosssectional and cohort. The search for an optimal design uses Bayesian methods to explore the joint parameterdesign space combined with Shannon entropy of the posteriors to estimate the amount of information for each design. We found that for the crosssectional designs, the amount of information increases with the sampling intensity while the cohort design often exhibits a tradeoff between the number of households sampled and the intensity of followup. 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
Media...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 discretetime systems in dimension three.
This is joint work with C. Bonatti, A. Gogolev, and R. Potrie. 

Connecting withinhost and betweenhost dynamics to understand how pathogens evolve 15:10 Fri 1 Apr, 2016 :: Engineering South S112 :: A/Prof Mark Tanaka :: University of New South Wales
Media...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 withinhost or the betweenhost level. Here I describe steps towards bridging the two scales. First, I present a model of influenza virus evolution that incorporates withinhost dynamics to obtain the betweenhost rate of molecular substitution as a function of the mutation rate, the withinhost reproduction number and other factors. Second, I discuss a model of viral evolution in which some hosts are immunocompromised, thereby extending opportunities for withinhost virus evolution which then affects populationlevel evolution. Finally, I describe a model of Mycobacterium tuberculosis in which multidrug resistance evolves within hosts and spreads by transmission between hosts. 

Extreme eigenvalues 15:10 Fri 29 Apr, 2016 :: Engineering South S112 :: Dr Julie Clutterbuck :: Monash University
Media...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
Media...The immune response plays an important role in the resolution of primary influenza infection and prevention of subsequent infection in an individual. However, the relative roles of each component of the immune response in clearing infection, and the effects of interaction between components, are not well quantified.
We have constructed a model of the immune response to influenza based on data from viral interference experiments, where ferrets were exposed to two influenza strains within a short time period. The changes in viral kinetics of the second virus due to the first virus depend on the strains used as well as the interval between exposures, enabling inference of the timing of innate and adaptive immune response components and the role of crossreactivity in resolving infection. Our model provides a mechanistic explanation for the observed variation in viruses' abilities to protect against subsequent infection at short interexposure 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 crossreactive cellular adaptive immune responses. To account for intersubject as well as intervirus 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
Media...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. 

Time series analysis of paleoclimate proxies (a mathematical perspective) 15:10 Fri 27 May, 2016 :: Engineering South S112 :: Dr Thomas Stemler :: University of Western Australia
Media...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 AustralianSouth East Asian monsoon system
during the last couple of thousand years.
From a time series perspective paleoclimate 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 nonstationary, nonuniform 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 nonuniform 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 paleoclimate 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
Media...MAST10006 Calculus 2 is the largest subject in the School of Mathematics and Statistics at the University of Melbourne, accounting for about 2200 out of 7400 first year enrolments. Despite excellent and consistent feedback from students on lectures, tutorials and teaching materials, scaled failure rates in Calculus 2 averaged an unacceptably high 29.4% (with raw failure rates reaching 40%) by the end of 2014. To understand the issues behind the poor student performance, we studied the exam papers of students with grades of 4049% over a threeyear 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 studentsâ secondary school mathematical skills that inhibit their ability to successfully complete Calculus 2. Since 2015, we have employed a number of approaches to support studentsâ 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. 

Multiscale modeling in biofluids and particle aggregation 15:10 Fri 17 Jun, 2016 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide
In today's seminar I will give 2 examples in mathematical biology which describes the multiscale organization at 2 levels: the meso/micro level and the continuum/macro level. I will then detail suitable tools in statistical mechanics to link these different scales.
The first problem arises in mathematical physiology: swellingdeswelling mechanism of mucus, an ionic gel. Mucus is packaged inside cells at high concentration (volume fraction) and when released into the extracellular environment, it expands in volume by two orders of magnitude in a matter of seconds. This rapid expansion is due to the rapid exchange of calcium and sodium that changes the crosslinked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a twophase, polymer/solvent mixture theory (in the continuum level description), together with the chemistry of the polymer, its nearest neighbor interaction and its binding with the dissolved ionic species (in the microscale description). The problem is posed as a freeboundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibriumstates of the ionic gels are analyzed.
In the second example, we numerically study the adhesion fragmentation dynamics of rigid, round particles clusters subject to a homogeneous shear flow. In the macro level we describe the dynamics of the number density of these cluster. The description in the microscale includes (a) binding/unbinding of the bonds attached on the particle surface, (b) bond torsion, (c) surface potential due to ionic medium, and (d) flow hydrodynamics due to shear flow. 

Probabilistic Meshless Methods for Bayesian Inverse Problems 15:10 Fri 5 Aug, 2016 :: Engineering South S112 :: Dr Chris Oates :: University of Technology Sydney
Media...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, modelbased approach to discretisation error encourages statistical inferences to be more conservative in the presence of significant solver error. In addition, (i) a principled learningtheoretic approach to minimise the impact of solver error is developed, and (ii) the challenge of nonlinear PDEs is considered. The method is applied to parameter inference problems in which nonnegligible 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
Media...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 agentbased models realized on empirical social networks, and ending up with populationlevel 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 populationlevel 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 centurylong 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
Media...Turbulence is characterised by threedimensional 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 NavierStokes 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 NavierStokes 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 NavierStokes equations. 

Singular vector bundles and topological semimetals 12:10 Fri 2 Sep, 2016 :: Ingkarni Wardli B18 :: Guo Chuan Thiang :: University of Adelaide
Media...The elusive Weyl fermion was recently realised as quasiparticle excitations of a topological semimetal. I will explain what a semimetal is, and the precise mathematical sense in which they can be "topological", in the sense of the general theory of topological insulators. This involves understanding vector bundles with singularities, with the aid of MayerVietoris principles, gerbes, and generalised degree theory. 

Modelling evolution of postmenopausal human longevity: The Grandmother Hypothesis 15:10 Fri 2 Sep, 2016 :: Napier G03 :: Dr Peter Kim :: University of Sydney
Media...Human postmenopausal 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 agentbased model that incorporates two sexes and mating, fertilitylongevity 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 lifehistories, one humanlike 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
Media...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 wellbeing 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
Media...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 divideandconquer strategies, by determining efficient subsamples. 

Symmetric functions and quantum integrability 15:10 Fri 30 Sep, 2016 :: Napier G03 :: Dr Paul ZinnJustin :: University of Melbourne/Universite Pierre et Marie Curie
Media...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 twodimensional 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. fivevertex model). We'll then discuss recent work (in collaboration with M. Wheeler) that extends this approach to HallLittlewood 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
Media...The Willmore energy of a surface captures its bending. Originally discovered 200 years ago by Sophie Germain in the context of elasticity theory, it has since then been rediscovered numerous times in several areas of science: general relativity, optics, string theory, conformal geometry, and cell biology. For example, our red blood cells assume a peculiar shape that minimises the Willmore energy.
In this talk, I will present the thrilling history of the Willmore energy, its applications, and its main properties. The presentation will be accessible to all mathematicians as well as to advanced undergraduate students. 

Measuring and mapping carbon dioxide from remote sensing satellite data 15:10 Fri 21 Oct, 2016 :: Napier G03 :: Prof Noel Cressie :: University of Wollongong
Media...This talk is about environmental statistics for global remote sensing of atmospheric carbon dioxide, a leading greenhouse gas. An important compartment of the carbon cycle is atmospheric carbon dioxide (CO2), where it (and other gases) contribute to climate change through a greenhouse effect. There are a number of CO2 observational programs where measurements are made around the globe at a small number of groundbased locations at somewhat regular time intervals. In contrast, satellitebased 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 Observatory2 (OCO2), whose principal objective is to retrieve a geographical distribution of CO2 sources and sinks. OCO2's measurement of columnaveraged mole fraction, XCO2, is designed to achieve this, through a dataassimilation 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 spatialstatistical modelling. 

Introduction to Lorentz Geometry: Riemann vs Lorentz 12:10 Fri 18 Nov, 2016 :: Engineering North N132 :: Abdelghani Zeghib :: Ecole Normale Superieure de Lyon
Media...The goal is to compare Riemannian and Lorentzian geometries and see what one loses and wins when going from the Riemann to Lorentz. Essentially, one loses compactness and ellipticity, but wins causality structure and mathematical and physical situations
when natural Lorentzian metrics emerge.


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. 

Onelayer liquid films loaded with selfpropelled particles and twolayer 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 selfpropelled particles (swimmers) in a thin liquid film resting on a solid plate with deformable liquidgas interface. The local surface tension of the liquidgas interface is altered by the local density of swimmers due to the solutoMarangoni 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 twolayer liquid films. For gravitationally stable twolayer 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 RayleighTaylor 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 wellunderstood. Conjectured connections have applications to quantum topology and physics, 3manifold geometry and topology, and knot theory. In this talk, we will describe several results relating the hyperbolic geometry of a knot or link to other invariants, and their implications. 

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 nonoptimal or irrational human behaviour. This talk presents preliminary evidence suggesting, however, that in both cases this pattern of behaviour is sensible given certain assumptions about the structure of the world and the nature of beliefs. In the case of vaccination, we model people's choices using expected utility theory. This reveals that their ignorance about the nature of diseases like whooping cough makes them underweight the negative utility attached to contracting such a disease. When that ignorance is addressed, their values and utilities shift. In the case of extreme positions, we use simulations of chains of Bayesian learners to demonstrate that whenever information is propagated in groups, the views of the most extreme learners naturally gain more traction. This effect emerges as the result of basic mathematical assumptions rather than human irrationality. 

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 NavierStokes 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 longstanding mystery how the extraordinarily complex communication networks inside living cells, comprising thousands of different interacting molecules, are able to function robustly since complexity is generally associated with fragility. Mathematics has now suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from a just small number of welldefined universal modules (or "motifs"), connected together. The existence of these newlydiscovered modules has important implications for evolutionary biology, embryology and development, cancer research, and drug development. 

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

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

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

Measuring the World's Biggest Bubble 13:10 Tue 19 Sep, 2017 :: Napier LG23 :: Prof Matt Roughan :: School of Mathematical Sciences
Media...Recently I had a bit of fun helping Graeme Denton measure his Guinness World Record (GWR) Largest (Indoor) Soap Bubble. It was a lot harder than I initially thought it would be.
Soap films are interesting mathematically  in principle they form minimal surfaces, and have constant curvature. So it should have been fairly easy. But really big bubbles aren't ideal, so measuring the GWR bubble required a mix of maths and pragmatism. It's a good example of mathematical modeling in general, so I thought it was worth a few words. I'll tell you what we did, and how we estimated how big the bubble actually was.
Some links:
http://www.9news.com.au/goodnews/2017/08/02/13/44/adelaidemanwinsworldrecordforlargestbubble
http://www.abc.net.au/news/20170803/scienceperformercreatesworldslargestindoorsoapbubble/8770260


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 morphogenreceptor 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 multiprotein 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 continuoustime branching processes, which makes them wellsuited for realworld 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 CahnLarche 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 phaseseparation processes observed in lipid monolayers in filmbalance experiments, the starting point of the model is the CahnHilliard equation coupled with the equations of linear elasticity, the socalled CahnLarche 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 periodichomogenisation techniques.
For the full nonlinear problem the socalled homogenised problem is then obtained by letting epsilon tend to zero using the method of asymptotic expansion.
Furthermore, we present a linearised CahnLarche system and use the method of twoscale 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 constraintbased 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 3Manifolds 15:10 Fri 23 Mar, 2018 :: Horace Lamb 1022 :: A/Prof Stephan Tillmann :: University of Sydney
In this talk, I will give a general introduction to complexity of
3manifolds and explain the connections between combinatorics, algebra,
geometry, and topology that arise in its study.
The complexity of a 3manifold is the minimum number of tetrahedra in a
triangulation of the manifold. It was defined and first studied by Matveev
in 1990. The complexity is generally difficult to compute, and various
upper and lower bounds have been derived during the last decades using
fundamental group, homology or hyperbolic volume.
Effective bounds have only been found in joint work with Jaco, Rubinstein
and, more recently, Spreer. Our bounds not only allowed us to determine the
first infinite classes of minimal triangulations of closed 3manifolds, but
they also lead to a structure theory of minimal triangulations of
3manifolds. 

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

Stability Through a Geometric Lens 15:10 Fri 18 May, 2018 :: Horace Lamb 1022 :: Dr Robby Marangell :: University of Sydney
Focussing on the example of the Fisher/KPP equation, I will show how geometric information can be used to establish (in)stability results in some partial differential equations (PDEs). Viewing standing and travelling waves as fixed points of a flow in an infinite dimensional system, leads to a reduction of the linearised stability problem to a boundary value problem in a linear nonautonomous ordinary differential equation (ODE). Next, by exploiting the linearity of the system, one can use geometric ideas to reveal additional structure underlying the determination of stability. I will show how the Riccati equation can be used to produce a reasonably computable detector of eigenvalues and how such a detector is related to another, wellknown eigenvalue detector, the Evans function. If there is time, I will try to expand on how to generalise these ideas to systems of PDEs. 

Modelling phagocytosis 15:10 Fri 25 May, 2018 :: Horace Lamb 1022 :: Prof Ngamta (Natalie) Thamwattana :: University of Wollongong
Phagocytosis refers to a process in which one cell type fully encloses and consumes unwanted cells,
debris or particulate matter. It plays an important role in immune systems through the destruction of
pathogens and the inhibiting of cancerous cells. In this study, we combine models on cellcell adhesion
and on predatorprey modelling to generate a new model for phagocytosis that is capable of relating
the interaction between cells in both space and time. Numerical results are presented, demonstrating
the behaviours of cells during the process of phagocytosis. 

Quantifying language change 15:10 Fri 1 Jun, 2018 :: Horace Lamb 1022 :: A/Prof Eduardo Altmann :: University of Sydney
Mathematical methods to study natural language are increasingly important because of the ubiquity of textual data in the Internet. In this talk I will discuss mathematical models and statistical methods to quantify the variability of language, with focus on two problems: (i) How the vocabulary of languages changed over the last centuries? (ii) How the language of scientific disciplines relate to each other and evolved in the last decades? One of the main challenges of these analyses stem from universal properties of word frequencies, which show high temporal variability and are fattailed distributed. The later feature dramatically affects the statistical properties of entropybased estimators, which motivates us to compare vocabularies using a generalized JensonShannon divergence (obtained from entropies of order alpha). 

Quantifying language change 15:10 Fri 1 Jun, 2018 :: Napier 208 :: A/Prof Eduardo Altmann :: University of Sydney
Mathematical methods to study natural language are increasingly important because of the ubiquity of textual data in the Internet. In this talk I will discuss mathematical models and statistical methods to quantify the variability of language, with focus on two problems: (i) How the vocabulary of languages changed over the last centuries? (ii) How the language of scientific disciplines relate to each other and evolved in the last decades? One of the main challenges of these analyses stem from universal properties of word frequencies, which show high temporal variability and are fattailed distributed. The later feature dramatically affects the statistical properties of entropybased estimators, which motivates us to compare vocabularies using a generalized JensonShannon divergence (obtained from entropies of order alpha). 

Tales of Multiple Regression: Informative Missingness, Recommender Systems, and R2D2 15:10 Fri 17 Aug, 2018 :: Napier 208 :: Prof Howard Bondell :: University of Melbourne
In this talk, we briefly discuss two projects tangentially related under the umbrella of highdimensional regression.
The first part of the talk investigates informative missingness in the framework of recommender systems. In this setting, we envision a potential rating for every objectuser pair. The goal of a recommender system is to predict the unobserved ratings in order to recommend an object that the user is likely to rate highly. A typically overlooked piece is that the combinations are not missing at random. For example, in movie ratings, a relationship between the user ratings and their viewing history is expected, as human nature dictates the user would seek out movies that they anticipate enjoying. We model this informative missingness, and place the recommender system in a sharedvariable regression framework which can aid in prediction quality.
The second part of the talk deals with a new class of prior distributions for shrinkage regularization in sparse linear regression, particularly the high dimensional case. Instead of placing a prior on the coefficients themselves, we place a prior on the regression Rsquared. This is then distributed to the coefficients by decomposing it via a Dirichlet Distribution. We call the new prior R2D2 in light of its RSquared Dirichlet Decomposition. Compared to existing shrinkage priors, we show that the R2D2 prior can simultaneously achieve both high prior concentration at zero, as well as heavier tails. These two properties combine to provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals. 

Discrete fluxes and duality in gauge theory 11:10 Fri 24 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Siye Wu :: National Tsinghua University
We explore the notions of discrete electric and magnetic fluxes introduced by 't Hooft in the late 1970s. After explaining
their physics origin, we consider the description in mathematical terminology. We finally study their role in duality. 

Geometry and Topology of Crystals 11:10 Fri 31 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Vanessa Robins :: Australian National University
This talk will cover some highlights of the mathematical description of crystal structure from the platonic polyhedra of ancient Greece to the current picture of crystallographic groups as orbifolds. Modern materials synthesis raises fascinating questions about the enumeration and classification of periodic interwoven or entangled frameworks, that might be addressed by techniques from 3manifold topology and knot theory. 

Topological Data Analysis 15:10 Fri 31 Aug, 2018 :: Napier 208 :: Dr Vanessa Robins :: Australian National University
Topological Data Analysis has grown out of work focussed on deriving qualitative and yet quantifiable information about the shape of data. The underlying assumption is that knowledge of shape  the way the data are distributed  permits highlevel reasoning and modelling of the processes that created this data. The 0th order aspect of shape is the number pieces: "connected components" to a topologist; "clustering" to a statistician. Higherorder topological aspects of shape are holes, quantified as "nonbounding cycles" in homology theory. These signal the existence of some type of constraint on the datagenerating process.
Homology lends itself naturally to computer implementation, but its naive application is not robust to noise. This inspired the development of persistent homology: an algebraic topological tool that measures changes in the topology of a growing sequence of spaces (a filtration). Persistent homology provides invariants called the barcodes or persistence diagrams that are sets of intervals recording the birth and death parameter values of each homology class in the filtration. It captures information about the shape of data over a range of length scales, and enables the identification of "noisy" topological structure.
Statistical analysis of persistent homology has been challenging because the raw information (the persistence diagrams) are provided as sets of intervals rather than functions. Various approaches to converting persistence diagrams to functional forms have been developed recently, and have found application to data ranging from the distribution of galaxies, to porous materials, and cancer detection. 

Mathematical modelling of the emergence and spread of antimalarial drug resistance 15:10 Fri 14 Sep, 2018 :: Napier 208 :: Dr Jennifer Flegg :: University of Melbourne
Malaria parasites have repeatedly evolved resistance to antimalarial drugs, thwarting efforts to eliminate the disease and contributing to an increase in mortality. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. For example, results will be presented from Bayesian geostatistical models that have quantified the spacetime trends in drug resistance in Africa and Southeast Asia. I will discuss how the results of these models have been used to update public health policy. 

Exceptional quantum symmetries 11:10 Fri 5 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Scott Morrison :: Australian National University
I will survey our current understanding of "quantum symmetries", the mathematical models of topological order, in particular through the formalism of fusion categories. Our very limited classification results to date point to nearly all examples being built out of data coming from finite groups, quantum groups at roots of unity, and cohomological data. However, there are a small number of "exceptional" quantum symmetries that so far appear to be disconnected from the world of classical symmetries as studied in representation theory and group theory. I'll give an update on recent progress understanding these examples. 

Interactive theorem proving for mathematicians 15:10 Fri 5 Oct, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University
Mathematicians use computers to write their proofs (LaTeX), and to do their calculations (Sage, Mathematica, Maple, Matlab, etc, as well as custom code for simulations or searches). However today we rarely use computers to help us to construct and understand proofs.
There is a long tradition in computer science of interactive and automatic theorem proving; particularly today these are important tools in engineering correct software, as well as in optimisation and compilation. There have been some notable examples of formalisation of modern mathematics (e.g. the odd order theorem, the Kepler conjecture, and the fourcolour theorem). Even in these cases, huge engineering efforts were required to translate the mathematics to a form a computer could understand. Moreover, in most areas of research there is a huge gap between the interests of human mathematicians and the abilities of computer provers.
Nevertheless, I think it's time for mathematicians to start getting interested in interactive theorem provers! It's now possible to write proofs, and write tools that help write proofs, in languages which are expressive enough to encompass most of modern mathematics, and ergonomic enough to use for general purpose programming.
I'll give an informal introduction to dependent type theory (the logical foundation of many modern theorem provers), some examples of doing mathematics in such a system, and my experiences working with mathematics students in these systems. 

Twisted Ktheory of compact Lie groups and extended Verlinde algebras 11:10 Fri 12 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: ChiKwong Fok :: University of Adelaide
In a series of recent papers, Freed, Hopkins and Teleman put forth a deep result which identifies the twisted K theory of a compact Lie group G with the representation theory of its loop group LG. Under suitable conditions, both objects can be enhanced to the Verlinde algebra, which appears in mathematical physics as the Frobenius algebra of a certain topological quantum field theory, and in algebraic geometry as the algebra encoding information of moduli spaces of Gbundles over Riemann surfaces. The Verlinde algebra for G with nice connectedness properties have been wellknown. However, explicit descriptions of such for disconnected G are lacking. In this talk, I will discuss the various aspects of the FreedHopkinsTeleman Theorem and partial results on an extension of the Verlinde algebra arising from a disconnected G. The talk is based on work in progress joint with David Baraglia and Varghese Mathai. 

Random walks 15:10 Fri 12 Oct, 2018 :: Napier 208 :: A/Prof Kais Hamza :: Monash University
A random walk is arguably the most basic stochastic process one can define. It is also among the most intuitive objects in the theory of probability and stochastic processes. For these and other reasons, it is one of the most studied processes or rather family of processes, finding applications in all areas of science, technology and engineering.
In this talk, I will start by recalling some of the classical results for random walks and then discuss some of my own recent explorations in this area of research that has maintained relevance for decades. 

Bayesian Synthetic Likelihood 15:10 Fri 26 Oct, 2018 :: Napier 208 :: A/Prof Chris Drovandi :: Queensland University of Technology
Complex stochastic processes are of interest in many applied disciplines. However, the likelihood function associated with such models is often computationally intractable, prohibiting standard statistical inference frameworks for estimating model parameters based on data. Currently, the most popular simulationbased parameter estimation method is approximate Bayesian computation (ABC). Despite the widespread applicability and success of ABC, it has some limitations. This talk will describe an alternative approach, called Bayesian synthetic likelihood (BSL), which overcomes some limitations of ABC and can be much more effective in certain classes of applications. The talk will also describe various extensions to the standard BSL approach. This project has been a joint effort with several academic collaborators, postdocs and PhD students. 

The role of microenvironment in regulation of cell infiltration and bortezomibOV therapy in glioblastoma 15:10 Fri 11 Jan, 2019 :: IW 5.57 :: Professor Yangjin Kim :: Konkuk University, South Korea
Tumor microenvironment (TME) plays a critical role in regulation of tumor cell invasion in glioblastoma. Many microenvironmental factors such as extracllular matrix, microglia and astrocytes can either block or enhance this critical infiltration step in brain [4]. Oncolytic viruses such as herpes simplex virus1 (oHSV) are genetically modified to target and kill cancer cells while not harming healthy normal cells and are currently under multiple clinical trials for safety and efficacy [1]. Bortezomib is a peptidebased proteasome inhibitor and is an FDAapproved drug for myeloma and mantle cell lymphoma. Yoo et al (2) have previously demonstrated that bortezomibinduced unfolded protein response (UPR) in many tumor cell lines (glioma, ovarian, and head and neck) upregulated expression of heat shock protein 90 (HSP90), which then enhanced viral replication through promotion of nuclear localization of the viral polymerase in vitro. This led to synergistic tumor cell killing in vitro, and a combination treatment of mice with oHSV and bortezomib showed improved antitumor efficacy in vivo [2]. This combination therapy also increased the surface expression levels of NK cell activating markers and enhanced proinflammatory cytokine secretion. These findings demonstrated that the synergistic interaction between oHSV and bortezomib, a clinically relevant proteasome inhibitor, augments the cancer cell killing and promotes overall therapeutic efficacy. We investigated the role of NK cells in combination therapy with oncolytic virus (OV) and bortezomib. NK cells display rapid and potent immunity to metastasis and hematological cancers, and they overcome immunosuppressive effects of tumor microenvironment. We developed a mathematical model, a system of PDEs, in order to address the question of how the density of NK cells affects the growth of the tumor [3]. We found that the antitumor efficacy increases when the endogenous NKs are depleted, and also when exogenous NK cells are injected into the tumor. We also show that the TME plays a significant role in antitumor efficacy in OV combination therapy, and illustrate the effect of different spatial patterns of OV injection [5]. The results illustrate a possible phenotypic switch within tumor populations in a given microenvironment, and suggest new antiinvasion therapies. These predictions were validated by our in vivo and in vitro experiments.
References
1] Â Kanai R, â¦ Rabkin SD, âOncolytic herpes simplex virus vectors and chemotherapy: are combinatorial strategies more effective for cancer?â, Future Oncology, 6(4), 619â634, 2010. â¨
[2] Â Yoo J, et al., âBortezomibinduced unfolded protein response increases oncolytic hsv1 replication resulting in synergistic antitumor effectâ, Clin Cancer Res , Vol. 20(14), 2014, pp. 37873798. â¨
[3] Â Yangjin Kim,..Balveen Kaur and Avner Friedman, âComplex role of NK cells in regulation of oncolytic virusbortezomib therapyâ, PNAS, 115 (19), pp. 49274932, 2018. â¨
[4] Yangjin Kim, ..Sean Lawler, and Mark Chaplain, âRole of extracellular matrix and microenvironment in regulation of tumor growth and LARmediated invasion in glioblastomaâ, PLoS One, 13(10):e0204865, 2018. â¨
[5] Yangjin Kim, â¦, Hans G. Othmer, âSynergistic effects of bortezomibOV therapy and antiinvasiveâ¨strategies in glioblastoma: A mathematical modelâ, Special issue, submitted, 2018. 
News matching "Mathematical biology" 
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.
http://vrs.amsi.org.au/
University of Adelaide Summer Research Scholarships: Closing date Friday 7th October.
http://www.ecms.adelaide.edu.au/scholarships/summer/
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.
20082010: $645,000
Prof RJ Elliott:
Dynamic risk measures.
(Australian Professorial Fellowship)
20082012: $897,000
Dr MD Finn:
Topological Optimisation of Fluid Mixing.
20082010: $249,000
Prof PG Bouwknegt; Prof M Varghese; A/Prof S Wu:
Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program.
20082010: $240,000
The latter grant is held through the ANU Posted Wed 26 Sep 07. 

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 8storey, 6star 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 website 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 firstyear
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. Fixedterm 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 2022 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.More information... 

Three postdoc positions advertised The School of Mathematical Sciences is seeking to appoint three postdoctoral 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.More information... 

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.More information... 

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.More information... 

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 1822, 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 trafficmatrix synthesis, $290,000 over three years;
Prof Patricia Solomon, A/Prof John Moran, Statistical methods for the analysis of critical care data, with application to the Australian and New Zealand Intensive Care Database, $310,000 over 3 years;
Prof Mathai Varghese, Prof Peter Bouwknegt, Supersymmetric quantum field theory, topology and duality, $375,000 over 3 years;
Prof Peter Taylor, Prof Nigel Bean, Dr Sophie Hautphenne, Dr Mark Fackrell, Dr Malgorzata O'Reilly, Prof Guy Latouche, Advanced matrixanalytic methods with applications, $600,000 over 3 years.
Congratulations to the following staff for their success in the Linkage Project scheme:
Prof Simon Beecham, Prof Lee White, A/Prof John Boland, Prof Phil Howlett, Dr Yvonne Stokes, Mr John Wells, Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements, $370,000 over 3 years;
Dr Amie Albrecht, Prof Phil Howlett, Dr Andrew Metcalfe, Dr Peter Pudney, Prof Roderick Smith, Saving energy on trains  demonstration, evaluation, integration, $540,000 over 3 years
Posted Fri 29 Oct 10. 

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

ARC 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 AustralianNew Zealand Rotating Flows Workshop The first AustralianNew 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 gaugestring 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 HarishChandra Research Institute. These lectures will be supplemented by talks by other invited speakers. Posted Tue 6 Dec 11.More information... 

Topup 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 15minute 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.More information... 

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.More information... 

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 postPhD in applied probability, biometrics, mathematical genetics, psychometrics and statistics.
Associate Professor Ross has made influential contributions to public health and conservation biology using mathematical modelling and statistics to help in decision making.
Posted Fri 23 Dec 16.More information... 

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 Australiaâs position at the forefront of international research in geometric analysis. Posted Thu 15 Jun 17.More information... 

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

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  Medical imaging and processing methods for cardiac flow reconstruction Wong, Kelvin; Kelso, Richard; Worthley, Stephen; Sanders, Prashanthan; Mazumdar, Jagan; Abbott, Derek, Journal of Mechanics in Medicine and Biology 9 (1–20) 2009  Noncommutative correspondences, duality and Dbranes in bivariant Ktheory Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009  On Markovmodulated exponentialaffine bond price formulae Elliott, Robert; Siu, T, Applied Mathematical Finance 16 (1–15) 2009  Tduality as a duality of loop group bundles Bouwknegt, Pier; Varghese, Mathai, Journal of Physics A: Mathematical and Theoretical (Print Edition) 42 (1620011–1620018) 2009  A discrete version of the Riemann Hilbert problem Larusson, Finnur; Sadykov, T, Russian Mathematical Surveys 63 (973–975) 2008  Dbranes, RRfields 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)overcapgenus and a regularization of an S1equivariant Euler class Lu, Rongmin, Journal of Physics A: Mathematical and Theoretical (Print Edition) 41 (4252041–42520413) 2008  The mathematical modelling of rotating capillary tubes for holeyfibre manufacture Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Engineering Mathematics 60 (69–87) 2008  The mir200 family and mir205 regulate epithelial to mesenchymal transition by targeting ZEB1 and SIP1 Gregory, P; Bert, A; Paterson, Emily; Barry, Simon; Tsykin, Anna; Farshid, Gelareh; Vadas, Matthew Alexander; KhewGoodall, Yeesim; Goodall, Gregory, Nature Cell Biology 10 (593–601) 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 Nk 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  Fractal landscape method an alternative approach to measuring arearestricted searching behavior Tremblay, Y; Roberts, Anthony John; Costa, D, Journal of Experimental Biology 210 (935–945) 2007  Laguerre geometries and some connections to generalized quadrangles Brown, Matthew, Journal of the Australian Mathematical Society 83 (335–355) 2007  Flux compactifications on projective spaces and the Sduality puzzle Bouwknegt, Pier; Evslin, J; Jurco, B; Varghese, Mathai; Sati, Hicham, Advances in Theoretical and Mathematical Physics 10 (345–394) 2006  Genetic regulators of myelopoiesis and leukemic signaling identified by gene profiling and linear modeling Brown, Anna; Wilkinson, Christopher; Waterman, S; Kok, Chung; Salerno, Diana; Diakiw, Sonya; Reynolds, Brenton; Scott, Hamish; Tsykin, Anna; Glonek, Garique; Goodall, Gregory; Solomon, Patricia; Gonda, Thomas; D'Andrea, Richard, Journal of Leukocyte Biology 80 (433–447) 2006  Mathematical analysis of an extended mumfordshah 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 cumulusoocyte complexes Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006  Nonassociative Tori and Applications to TDuality Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Communications in Mathematical Physics 264 (41–69) 2006  Tduality for torus bundles with Hfluxes via noncommutative topology, II: the highdimensional case and the Tduality group Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 2006  YangMills 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  Threedimensional flow due to a microcantilever oscillating near a wall: an unsteady slenderbody analysis Clarke, Richard; Jensen, O; Billingham, J; Williams, P, Proceedings of the Royal Society of London Series AMathematical 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 (Epapers 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 ChernSimons and WessZuminoWitten theories Carey, Alan; Johnson, Stuart; Murray, Michael; Stevenson, Daniel; Wang, BaiLing, 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  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  RiemannSiegel 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  Tduality 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  Tduality for torus bundles with Hfluxes 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 SocietySimon Stevin 11 (641–651) 2005  Bundle 2gerbes 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 pseudoconic Brown, Matthew; Lavrauw, M, Bulletin of the London Mathematical Society 36 (633–639) 2004  Goodnessoffit tests using dual versions of characterizations via moments of order statistics Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 122 (3365–3383) 2004  Goodnessoffit tests using dual versions of characterizations via moments of record values Morris, Kerwin; Szynal, D, Journal of Mathematical Sciences 122 (3384–3403) 2004  Mtheory, 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 boundarylayer equations for powerlaw fluids Denier, James; Dabrowski, Paul, Proceedings of the Royal Society of London Series AMathematical Physical and Engineering Sciences 460 (3143–3158) 2004  Tduality: Topology change from Hflux Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Communications in Mathematical Physics 249 (383–415) 2004  Cellsignalling 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  ConnesDixmier 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 Ktheory: 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, gconvexity 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, gconvex dominated functions & Hadamardtype inequalities Dragomir, S; Pearce, Charles; Pecaric, Josip, Tamsui Oxford University Journal of Mathematical Sciences 18 (161–173) 2002  Misclassification, correlation, and cause of death studies Tallis, George, Human Biology 74 (75–81) 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, DixmierDouady class, and gauge theory Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 59 (47–60) 2002  Twisted Ktheory and Ktheory 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 partialthickness burnwound infection by Pseudomonas aeruginosa: Quorum sensing and the buildup to invasion Koerber, Adrian; King, J; Ward, J; Williams, P; Croft, J; Sockett, R, Bulletin of Mathematical Biology 64 (239–259) 2002  A goodnessoffit 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  NonSchlesinger 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 blowup 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  Truncationtype 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 DragomirAgarwal inequalities, higherorder 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 2dimensional 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 odddimensional 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 batchmovement 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  CauchySchwarz functionals Cho, Y; Dragomir, S; Kim, SS; 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 AMathematical Physical and Engineering Sciences 456 (1861–1864) 2000  GaussPlya 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 Ostrowskigruss 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 crossconnects 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 AGH inequality Pearce, Charles, Australian Mathematical Society Gazette 27 (91–95) 2000  Quasireversibility 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 SocietySimon 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 AMathematical 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  msystems of polar spaces and maximal arcs in projective planes Hamilton, N; Quinn, Catherine, Bulletin of the Belgian Mathematical SocietySimon Stevin 7 (237–248) 2000  More on the pizza theorem Pearce, Charles, Australian Mathematical Society Gazette 27 (4–5) 2000 
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