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Search the School of Mathematical SciencesPeople matching "Timereversal symmetric topology from physics" 
Professor Mathai Varghese Elder Professor of Mathematics, Australian Laureate Fellow, Fellow of the Australian Academy of Scie
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Courses matching "Timereversal symmetric topology from physics" 
Algebraic topology The aim of Algebraic Topology is to use algebraic structures and techniques to classify topological
spaces up to homeomorphism. Algebraic objects are associated to topological spaces in such a way
that ``natural" operations on the latter correspond to ``natural" operations on the formercontinuous
maps might correspond to group homomorphisms, homeomorphisms to isomorphisms, etc. In this
way, it is often possible to distinguish between different topological spaces by demonstrating that
certain associated algebraic objects are not isomorphic. It is rarely the case that the converse can be
shown; i.e., that two topological spaces with the same associated algebraic objects are actually
homeomorphic, but when this can be done, it is often regarded as a major triumph of the theory.
Within the realms of algebraic topology, there are several basic concepts that underly the theory and
serve as the building blocks and models for subsequent generalisation, the algebraic topology of
today being a very broad and highly generalised area that has pervaded much of contemporary
mathematics. Such concepts include homotopy, homology and cohomology, and the course will be
aimed at providing students with an introduction to these key ideas.
More about this course... 

Time Series III Time series consist of values of a variable recorded over a long period of time. Such data arise in just about every area of science and the humanities, including econometrics and finance, engineering, medicine, genetics, sociology, environmental science. What makes time series data special is the presence of dependence between observations in a series, and the fact that usually only one observation is made at any given point in time. This means that standard statistical methods are not appropriate, and special methods for statistical analysis are needed. This course provides an introduction to time series analysis using current methodology and software. Topics covered are: descriptive methods, plots, smoothing, differencing, the autocorrelation function, the correlogram and the variogram; the periodogram, estimation and elimination of trend and seasonal components; stationary processes, modelling and forecasting with autoregressive moving average (ARMA) models; spectral analysis, the fast Fourier transform, periodogram averages and other smooth estimates of the spectrum, timeinvariant linear filters; nonstationary and seasonal time series models. ARIMA processes, identification, estimation and diagnostic checking, forecasting, including extrapolation of polynomial trends, exponential smoothing, and the BoxJenkins approach.
More about this course... 

Topology and Analysis III Solving equations is a crucial aspect of working in mathematics, physics, engineering, and many other fields. These equations might be straightforward algebraic statements, or complicated systems of differential equations, but there are some fundamental questions common to all of these settings: does a solution exist? If so, is it unique? And if we know of the existence of some specific solution, how do we determine it explicitly or as accurately as possible? This course develops the foundations required to rigorously establish the existence of solutions to various equations, thereby laying the basis for the study of solutions. Through an understanding of the foundations of analysis, we obtain insight critical in numerous areas of application, such areas ranging across physics, engineering, economics and finance. Topics covered are: sets, functions, metric spaces and normed linear spaces, compactness, connectedness, and completeness. Banach fixed point theorem and applications, uniform continuity and convergence. General topological spaces, generating topologies, topological invariants, quotient spaces. Introduction to Hilbert spaces and bounded operators on Hilbert spaces.
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Events matching "Timereversal symmetric topology from physics" 
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. 

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).


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. 

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. 

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. 

Add one part chaos, one part topology, and stir well... 13:10 Fri 19 Oct, 2007 :: Engineering North 132 :: Dr Matt Finn :: School of Mathematical Sciences
Media...Stirring and mixing of fluids occurs everywhere, from adding milk to a cup of coffee, right through to industrialscale chemical blending. So why stir in the first place? Is it possible to do it badly? And how can you make sure you do it effectively? I will attempt to answer these questions using a few thought experiments, some dynamical systems theory and a little topology.


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. 

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

Global and Local stationary modelling in finance: Theory and empirical evidence 14:10 Thu 10 Apr, 2008 :: G04 Napier Building University of Adelaide :: Prof. Dominique Guégan :: Universite Paris 1 PantheonSorbonne
To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available.
Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.
Now nonstationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This nonstationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987).
Thus, using stationary unconditional moments suggest a global stationarity for the model, but using nonstationary unconditional moments or nonstationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior.
The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks.
1. What kinds of nonstationarity affect the major financial and economic data sets? How to detect them?
2. Local and global stationarities: How are they defined?
3. What is the impact of evidence of nonstationarity on the statistics computed from the global non stationary data sets?
4. How can we analyze data sets in the nonstationary global framework? Does the asymptotic theory work in nonstationary framework?
5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy?
These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.


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.


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. 

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. 

Impulsively generated drops 15:00 Fri 27 Feb, 2009 :: Napier LG29 :: Prof William Phillips :: Swinburne University of Technology
This talk is concerned with the evolution of an unbounded inviscid fluidfluid
interface subject to an axisymmetric impulse in pressure and how inertial,
interfacial and gravitational forces affect that evolution. The construct was
motivated by the occurrence of lung hemorrhage resulting from ultrasonic
imaging and pursues the notion that bursts of ultrasound act to expel droplets
that puncture the soft airfilled sacs in the lung plural surface allowing them
to fill with blood. The evolution of the free surface is described by a
boundary integral formulation which is integrated forward in time numerically.
As the interface evolves, it is seen, depending upon the levels of gravity and
surface tension, to form either axisymmetric surface jets, waves or droplets.
Moreover the droplets may be spherical, inverted tearshaped or pancake like.
Also of interest is the finite time singularity which occurs when the drop
pinches off; this is seen to be of the power law type with an exponent of 2/3.


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. 

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). 

Four classes of complex manifolds 13:10 Fri 8 May, 2009 :: School Board Room :: A/Prof Finnur Larusson :: University of Adelaide
We introduce the four classes of complex manifolds defined by having few or many holomorphic maps to or from the complex plane. Two of these classes have played an important role in complex geometry for a long time. A third turns out to be too large to be of much interest. The fourth class has only recently emerged from work of Abel Prize winner Mikhail Gromov. 

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.


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. 

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. 

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. 

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

Stable commutator length 13:40 Fri 25 Sep, 2009 :: Napier 102 :: Prof Danny Calegari :: California Institute of Technology
Stable commutator length answers the question: "what is the simplest
surface in a given space with prescribed boundary?" where "simplest"
is interpreted in topological terms. This topological definition is
complemented by several equivalent definitions  in group theory, as a
measure of noncommutativity of a group; and in linear programming, as
the solution of a certain linear optimization problem. On the
topological side, scl is concerned with questions such as computing
the genus of a knot, or finding the simplest 4manifold that bounds a
given 3manifold. On the linear programming side, scl is measured in
terms of certain functions called quasimorphisms, which arise from
hyperbolic geometry (negative curvature) and symplectic geometry
(causal structures). In these talks we will discuss how scl in free
and surface groups is connected to such diverse phenomena as the
existence of closed surface subgroups in graphs of groups, rigidity
and discreteness of symplectic representations, bounding immersed
curves on a surface by immersed subsurfaces, and the theory of multi
dimensional continued fractions and Klein polyhedra.
Danny Calegari is the Richard Merkin Professor of Mathematics at the California Institute of Technology, and is one of the recipients of the 2009 Clay Research Award for his work in geometric topology and geometric group theory. He received a B.A. in 1994 from the University of Melbourne, and a Ph.D. in 2000 from the University of California, Berkeley under the joint supervision of Andrew Casson and William Thurston. From 2000 to 2002 he was Benjamin Peirce Assistant Professor at Harvard University, after which he joined the Caltech faculty; he became Richard Merkin Professor in 2007.


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. 

The fluid mechanics of gels used in tissue engineering 15:10 Fri 9 Apr, 2010 :: Santos Lecture Theatre :: Dr Edward Green :: University of Western Australia
Tissue engineering could be called 'the science of spare parts'.
Although currently in its infancy, its longterm aim is to grow
functional tissues and organs in vitro to replace those which have
become defective through age, trauma or disease. Recent experiments
have shown that mechanical interactions between cells and the materials
in which they are grown have an important influence on tissue
architecture, but in order to understand these effects, we first need to
understand the mechanics of the gels themselves.
Many biological gels (e.g. collagen) used in tissue engineering have a
fibrous microstructure which affects the way forces are transmitted
through the material, and which in turn affects cell migration and other
behaviours. I will present a simple continuum model of gel mechanics,
based on treating the gel as a transversely isotropic viscous material.
Two canonical problems are considered involving thin twodimensional
films: extensional flow, and squeezing flow of the fluid between two
rigid plates. Neglecting inertia, gravity and surface tension, in each
regime we can exploit the thin geometry to obtain a leadingorder
problem which is sufficiently tractable to allow the use of analytical
methods. I discuss how these results could be exploited practically to
determine the mechanical properties of real gels. If time permits, I
will also talk about work currently in progress which explores the
interaction between gel mechanics and cell behaviour. 

"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. 

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". 

A variance constraining ensemble Kalman filter: how to improve forecast using climatic data of unobserved variables 15:10 Fri 28 May, 2010 :: Santos Lecture Theatre :: A/Prof Georg Gottwald :: The University of Sydney
Data assimilation aims to solve one of the fundamental problems ofnumerical weather prediction  estimating the optimal state of the
atmosphere given a numerical model of the dynamics, and sparse, noisy
observations of the system. A standard tool in attacking this
filtering problem is the Kalman filter.
We consider the problem when only partial observations are available.
In particular we consider the situation where the observational space
consists of variables which are directly observable with known
observational error, and of variables of which only their climatic
variance and mean are given. We derive the corresponding Kalman
filter in a variational setting.
We analyze the variance constraining Kalman filter (VCKF) filter for
a simple linear toy model and determine its range of optimal
performance. We explore the variance constraining Kalman filter in an
ensemble transform setting for the Lorenz96 system, and show that
incorporating the information on the variance on some unobservable
variables can improve the skill and also increase the stability of
the data assimilation procedure.
Using methods from dynamical systems theory we then systems where the
unobserved variables evolve deterministically but chaotically on a
fast time scale.
This is joint work with Lewis Mitchell and Sebastian Reich.


Vertex algebras and variational calculus II 13:10 Fri 11 Jun, 2010 :: School Board Room :: Dr Pedram Hekmati :: University of Adelaide
Last time I introduced the variational complex of an algebra of differential
functions and gave a sketchy definition of a vertex algebra. This week I will
make this notion more precise and explain how to apply it to the calculus of
variations. 

Some thoughts on wine production 15:05 Fri 18 Jun, 2010 :: School Board Room :: Prof Zbigniew Michalewicz :: School of Computer Science, University of Adelaide
In the modern information era, managers (e.g. winemakers) recognize the
competitive opportunities represented by decisionsupport tools which can
provide a significant cost savings & revenue increases for their businesses.
Wineries make daily decisions on the processing of grapes, from harvest time
(prediction of maturity of grapes, scheduling of equipment and labour, capacity
planning, scheduling of crushers) through tank farm activities (planning and
scheduling of wine and juice transfers on the tank farm) to packaging processes
(bottling and storage activities). As such operation is quite complex, the whole
area is loaded with interesting ORrelated issues. These include the issues of
global vs. local optimization, relationship between prediction and optimization,
operating in dynamic environments, strategic vs. tactical optimization, and
multiobjective optimization & tradeoff analysis. During the talk we address
the above issues; a few realworld applications will be shown and discussed to
emphasize some of the presented material. 

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.


The Hmm... Sessions 11:00 Wed 14 Jul, 2010 :: Maths DropIn Centre (Level 1 Schulz Building)
The aim of the Hmm... Sessions is for people to get together to solve
puzzles as a group. There will be lots of time to solve puzzles in groups
and to celebrate the clever solutions of others. The lunchbreak provides
time to socialise, play games or to continue solving puzzles (bring your own
lunch, or go out to nearby Rundle Mall to buy lunch on the day).
Hosted by Dr David Butler of the Maths Learning Service, University of
Adelaide. 

Higher nonunital Quillen K'theory 13:10 Fri 23 Jul, 2010 :: EngineeringMaths G06 :: Dr Snigdhayan Mahanta :: University of Adelaide
Quillen introduced a $K'_0$theory for possibly nonunital
rings and showed that it
agrees with the usual algebraic $K_0$theory if the ring is unital. We
shall introduce higher
$K'$groups for $k$algebras, where $k$ is a field, and discuss some
elementary properties
of this theory. We shall also show that for stable $C*$algebras the
higher $K'$theory agrees
with the topological $K$theory. If time permits we shall explain how
this provides a formalism
to treat topological $\mathbb{T}$dualities via Kasparov's bivariant $K$theory. 

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. 

A spatialtemporal point process model for fine resolution multisite rainfall data from Roma, Italy 14:10 Thu 19 Aug, 2010 :: Napier G04 :: A/Prof Paul Cowpertwait :: Auckland University of Technology
A point process rainfall model is further developed that has storm origins occurring in spacetime according to a Poisson process. Each storm origin has a random radius so that storms occur as circular regions in twodimensional
space, where the storm radii are taken to be independent exponential random
variables. Storm origins are of random type z, where z follows a continuous
probability distribution. Cell origins occur in a further spatial Poisson
process and have arrival times that follow a NeymanScott point process. Cell
origins have random radii so that cells form discs in twodimensional space.
Statistical properties up to third order are derived and used to fit the model
to 10 min series taken from 23 sites across the Roma region, Italy.
Distributional properties of the observed annual maxima are compared to
equivalent values sampled from series that are simulated using the fitted
model. The results indicate that the model will be of use in urban drainage
projects for the Roma region.


Index theory in 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.


Triangles, maps and curvature 13:10 Wed 8 Sep, 2010 :: Napier 210 :: Dr Thomas Leistner :: University of Adelaide
Euclidean space is flat but the real world is curved. This causes lots of problems for sailors, surveyors, mapmakers, and even geometers. In the talk I will explain how the notion of curvature evolved in mathematics starting off from practical applications such as geodesy and cartography and yielding less practical applications in modern physics. 

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. 

IGAAMSI Workshop: Dirac operators in geometry, topology, representation theory, and physics 10:00 Mon 18 Oct, 2010 :: 7.15 Ingkarni Wardli :: Prof Dan Freed :: University of Texas, Austin
Lecture Series by Dan Freed (University of Texas, Austin).
Dirac introduced his eponymous operator to describe electrons in quantum theory.
It was rediscovered by Atiyah and Singer in their study of the index problem on
manifolds. In these lectures we explore new theorems and applications. Several
of these also involve Ktheory in its recent twisted and differential
variations.
These lectures will be supplemented by additional talks by invited speakers. For more details, please see the conference webpage:
http://www.iga.adelaide.edu.au/workshops/WorkshopOct2010/ 

Statistical physics and behavioral adaptation to Creation's main stimuli: sex and food 15:10 Fri 29 Oct, 2010 :: E10 B17 Suite 1 :: Prof Laurent Seuront :: Flinders University and South Australian Research and Development Institute
Animals typically search for food and mates, while avoiding predators. This is particularly critical for keystone organisms such as intertidal gastropods and copepods (i.e. millimeterscale crustaceans) as they typically rely on nonvisual senses for detecting, identifying and locating mates in their two and threedimensional environments. Here, using stochastic methods derived from the field of nonlinear physics, we provide new insights into the nature (i.e. innate vs. acquired) of the motion behavior of gastropods and copepods, and demonstrate how changes in their behavioral properties can be used to identify the tradeoffs between foraging for food or sex. The gastropod Littorina littorea hence moves according to fractional Brownian motions while foraging for food (in accordance with the fractal nature of food distributions), and switch to Brownian motion while foraging for sex. In contrast, the swimming behavior of the copepod Temora longicornis belongs to the class of multifractal random walks (MRW; i.e. a form of anomalous diffusion), characterized by a nonlinear moment scaling function for distance versus time. This clearly differs from the traditional Brownian and fractional Brownian walks expected or previously detected in animal behaviors. The divergence between MRW and Levy flight and walk is also discussed, and it is shown how copepod anomalous diffusion is enhanced by the presence and concentration of conspecific waterborne signals, and is dramatically increasing malefemale encounter rates. 

Arbitrage bounds for weighted variance swap prices 15:05 Fri 3 Dec, 2010 :: Napier LG28 :: Prof Mark Davis :: Imperial College London
This paper builds on earlier work by Davis and Hobson (Mathematical Finance,
2007) giving 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. 

Surface quotients of hyperbolic buildings 13:10 Fri 18 Mar, 2011 :: Mawson 208 :: Dr Anne Thomas :: University of Sydney
Let I(p,v) be Bourdon's building, the unique simplyconnected 2complex such that all 2cells are regular rightangled hyperbolic pgons, and the link at each vertex is the complete bipartite graph K_{v,v}. We investigate and mostly determine the set of triples (p,v,g) for which there is a discrete group acting on I(p,v) so that the quotient is a compact orientable surface of genus g. Surprisingly, the existence of such a quotient depends upon the value of v. The remaining cases lead to open questions in tessellations of surfaces and in number theory. We use elementary group theory, combinatorics, algebraic topology and number theory. This is joint work with David Futer. 

Spherical tube hypersurfaces 13:10 Fri 8 Apr, 2011 :: Mawson 208 :: Prof Alexander Isaev :: Australian National University
We consider smooth real hypersurfaces in a complex vector space. Specifically, we are interested in tube hypersurfaces, i.e., hypersurfaces represented as the direct product of the imaginary part of the space and hypersurfaces lying in its real part. Tube hypersurfaces arise, for instance, as the boundaries of tube domains. The study of tube domains is a classical subject in several complex variables and complex geometry, which goes back to the beginning of the 20th century. Indeed, already Siegel found it convenient to realise certain symmetric domains as tubes.
One can endow a tube hypersurface with a socalled CRstructure, which is the remnant of the complex structure on the ambient vector space. We impose on the CRstructure the condition of sphericity. One way to state this condition is to require a certain curvature (called the CRcurvature of the hypersurface) to vanish identically. Spherical tube hypersurfaces possess remarkable properties and are of interest from both the complexgeometric and affinegeometric points of view. I my talk I will give an overview of the theory of such hypersurfaces. In particular, I will mention an algebraic construction arising from this theory that has applications in abstract commutative algebra and singularity theory. I will speak about these applications in detail in my colloquium talk later today. 

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. 

Centres of cyclotomic Hecke algebras 13:10 Fri 15 Apr, 2011 :: Mawson 208 :: A/Prof Andrew Francis :: University of Western Sydney
The cyclotomic Hecke algebras, or ArikiKoike algebras $H(R,q)$, are
deformations of the group algebras of certain complex reflection groups
$G(r,1,n)$, and also are quotients of the ubiquitous affine Hecke algebra.
The centre of the affine Hecke algebra has been understood since
Bernstein in terms of the symmetric group action on the weight lattice.
In this talk I will discuss the proof that over an arbitrary unital
commutative ring $R$, the centre of the affine Hecke algebra maps
\emph{onto} the centre of the cyclotomic Hecke algebra when $q1$ is
invertible in $R$. This is the analogue of the fact that the centre of
the Hecke algebra of type $A$ is the set of symmetric polynomials in
JucysMurphy elements (formerly known as he DipperJames conjecture). Key
components of the proof include the relationship between the trace
functions on the affine Hecke algebra and on the cyclotomic Hecke algebra,
and the link to the affine braid group. This is joint work with John
Graham and Lenny Jones. 

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). 

Change detection in rainfall time series for Perth, Western Australia 12:10 Mon 16 May, 2011 :: 5.57 Ingkarni Wardli :: Farah Mohd Isa :: University of Adelaide
There have been numerous reports that the rainfall in south Western Australia,
particularly around Perth has observed a step change decrease, which is
typically attributed to climate change. Four statistical tests are used to
assess the empirical evidence for this claim on time series from five
meteorological stations, all of which exceed 50 years. The tests used in this
study are: the CUSUM; Bayesian Change Point analysis; consecutive ttest and the
Hotellingâs TÂ²statistic. Results from multivariate Hotellingâs TÂ² analysis are
compared with those from the three univariate analyses. The issue of multiple
comparisons is discussed. A summary of the empirical evidence for the claimed
step change in Perth area is given. 

Where is the best place in Australia to build an enhanced geothermal system? 12:10 Mon 30 May, 2011 :: 5.57 Ingkarni Wardli :: Ms Josephine Varney :: University of Adelaide
This week, my parents will join around 185,000 other Australians, in a significant move towards renewable energy, and install solar panels on the roof of their house. While solar energy is an important and useful form of renewable energy it is not able to provide power all the time.
Opponents of renewable energy maintain that until renewable energy can provide energy all the time, traditional fossilfuel generated power will be required to produce our baseload power.
Geothermal energy is a renewable energy that can provide energy all the time. However, due to its special geological requirements, it can only be produced in a very small number of places in the world.
An Enhanced Geothermal System (EGS) is a new technology which allows geothermal energy to be produced in a much wider range of places than traditional geothermal energy. Currently, there are ten different companies investigating possible EGS sties within Australia. This seminar investigates the question, that all these companies hope they have answered well, 'Where is the best place in Australia for an EGS facility?' 

Optimal experimental design for stochastic population models 15:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Dan Pagendam :: CSIRO, Brisbane
Markov population processes are popular models for studying a wide range of
phenomena including the spread of disease, the evolution of chemical reactions
and the movements of organisms in population networks (metapopulations). Our
ability to use these models effectively can be limited by our knowledge about
parameters, such as disease transmission and recovery rates in an epidemic.
Recently, there has been interest in devising optimal experimental designs for
stochastic models, so that practitioners can collect data in a manner that
maximises the precision of maximum likelihood estimates of the parameters for
these models. I will discuss some recent work on optimal design for a variety
of population models, beginning with some simple oneparameter models where the
optimal design can be obtained analytically and moving on to more complicated
multiparameter models in epidemiology that involve latent states and
nonexponentially distributed infectious periods. For these more complex
models, the optimal design must be arrived at using computational methods and we
rely on a Gaussian diffusion approximation to obtain analytical expressions for
Fisher's information matrix, which is at the heart of most optimality criteria
in experimental design. I will outline a simple crossentropy algorithm that
can be used for obtaining optimal designs for these models. We will also
explore the improvements in experimental efficiency when using the optimal
design over some simpler designs, such as the design where observations are
spaced equidistantly in time. 

Priority queueing systems with random switchover times and generalisations of the KendallTakacs equation 16:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge
In this talk I will review existing analytical results for priority queueing
systems with Poisson incoming flows, general service times and a single server
which needs some (random) time to switch between requests of different priority.
Specifically, I will discuss analytical results for the busy period and workload
of such systems with a special structure of switchover times.
The results related to the busy period can be seen as generalisations of the
famous KendallTak\'{a}cs functional equation for $MG1$:
being formulated in terms of LaplaceStieltjes transform, they represent systems
of functional recurrent equations.
I will present a methodology and algorithms of their numerical solution;
the efficiency of these algorithms is achieved by acceleration of the numerical
procedure of solving the classical KendallTak\'{a}cs equation.
At the end I will identify open problems with regard to such systems; these open
problems are mainly related to the modelling of switchover times.


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. 

Modelling computer network topologies through optimisation 12:10 Mon 1 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Rhys Bowden :: University of Adelaide
The core of the Internet is made up of many different computers (called routers) in many different interconnected networks, owned and operated by many different organisations. A popular and important field of study in the past has been "network topology": for instance, understanding which routers are connected to which other routers, or which networks are connected to which other networks; that is, studying and modelling the connection structure of the Internet. Previous study in this area has been plagued by unreliable or flawed experimental data and debate over appropriate models to use. The Internet Topology Zoo is a new source of network data created from the information that network operators make public. In order to better understand this body of network information we would like the ability to randomly generate network topologies resembling those in the zoo. Leveraging previous wisdom on networks produced as a result of optimisation processes, we propose a simple objective function based on possible economic constraints. By changing the relative costs in the objective function we can change the form of the resulting networks, and we compare these optimised networks to a variety of networks found in the Internet Topology Zoo. 

The 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. 

Spectra alignment/matching for the classification of cancer and control patients 12:10 Mon 8 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide
Proteomic timeofflight mass spectrometry produces a spectrum based on the peptides (chains of amino acids) in each patientâs serum sample. The spectra contain data points for an xaxis (peptide weight) and a yaxis (peptide frequency/count/intensity). It is our end goal to differentiate cancer (and subtypes) and control patients using these spectra. Before we can do this, peaks in these data must be found and common peptides to different spectra must be found. The data are noisy because of biotechnological variation and calibration error; data points for different peptide weights may in fact be same peptide. An algorithm needs to be employed to find common peptides between spectra, as performing alignment âby handâ is almost infeasible. We borrow methods suggested in the literature by metabolomic gas chromatographymass spectrometry and extend the methods for our purposes. In this talk I will go over the basic tenets of what we hope to achieve and the process towards this.


Boundaries of unsteady Lagrangian Coherent Structures 15:10 Wed 10 Aug, 2011 :: 5.57 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: Connecticut College, USA and the University of Adelaide
For steady flows, the boundaries of Lagrangian Coherent Structures
are segments of manifolds connected to fixed points. In the general
unsteady situation, these boundaries are timevarying manifolds of
hyperbolic trajectories. Locating these boundaries, and attempting
to meaningfully quantify fluid flux across them, is difficult since they
are moving with time. This talk uses a newly developed tangential movement
theory to locate these boundaries in nearlysteady compressible flows.


There are no magnetically charged particlelike solutions of the EinsteinYangMills equations for models with Abelian residual groups 13:10 Fri 19 Aug, 2011 :: B.19 Ingkarni Wardli :: Dr Todd Oliynyk :: Monash University
According to a conjecture from the 90's, globally regular, static, spherically symmetric (i.e. particlelike) solutions with nonzero total magnetic charge are not expected to exist in EinsteinYangMills theory. In this talk, I will describe recent work done in collaboration with M. Fisher where we establish the validity of this conjecture under certain restrictions on the residual gauge group. Of particular interest is that our nonexistence results apply to the most widely studied models with Abelian residual groups. 

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

Alignment of time course gene expression data sets using Hidden Markov Models 12:10 Mon 5 Sep, 2011 :: 5.57 Ingkarni Wardli :: Mr Sean Robinson :: University of Adelaide
Time course microarray experiments allow for insight into biological processes by measuring gene expression over a time period of interest. This project is concerned with time course data from a microarray experiment conducted on a particular variety of grapevine over the development of the grape berries at a number of different vineyards in South Australia. The aim of the project is to construct a methodology for combining the data from the different vineyards in order to obtain more precise estimates of the underlying behaviour of the genes over the development process. A major issue in doing so is that the rate of development of the grape berries is different at different vineyards.
Hidden Markov models (HMMs) are a well established methodology for modelling time series data in a number of domains and have been previously used for gene expression analysis. Modelling the grapevine data presents a unique modelling issue, namely the alignment of the expression profiles needed to combine the data from different vineyards. In this seminar, I will describe our problem, review HMMs, present an extension to HMMs and show some preliminary results modelling the grapevine data. 

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. 

Tduality via bundle gerbes I 13:10 Fri 23 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide
In physics Tduality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the Hflux). In this talk we will use bundle gerbes to give a geometric realisation of the Hflux and explain how to construct the Tdual of a line bundle together with its Tdual bundle gerbe. 

Understanding the dynamics of event networks 15:00 Wed 28 Sep, 2011 :: B.18 Ingkarni Wardli :: Dr Amber Tomas :: The University of Oxford
Within many populations there are frequent communications between
pairs of individuals. Such communications might be emails sent within a
company, radio communications in a disaster zone or diplomatic
communications
between states. Often it is of interest to understand the factors that
drive the observed patterns of such communications, or to study how these
factors are changing over over time. Communications can be thought of as
events
occuring on the edges of a network which connects individuals in the
population.
In this talk I'll present a model for such communications which uses ideas
from
social network theory to account for the complex correlation structure
between
events. Applications to the Enron email corpus and the dynamics of hospital
ward transfer patterns will be discussed. 

Statistical modelling for some problems in bioinformatics 11:10 Fri 14 Oct, 2011 :: B.17 Ingkarni Wardli :: Professor Geoff McLachlan :: The University of Queensland
Media...In this talk we consider some statistical analyses of data arising in
bioinformatics. The problems include the detection of differential
expression in microarray geneexpression data, the clustering of
timecourse geneexpression data and, lastly, the analysis of
modernday cytometric data. Extensions are considered to the procedures
proposed for these three problems in McLachlan et al. (Bioinformatics, 2006),
Ng et al. (Bioinformatics, 2006), and Pyne et al. (PNAS, 2009), respectively.
The latter references are available at http://www.maths.uq.edu.au/~gjm/. 

Tduality via bundle gerbes II 13:10 Fri 21 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide
In physics Tduality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the Hflux). In this talk we will use bundle gerbes to give a geometric realisation of the Hflux and explain how to construct the Tdual of a line bundle together with its Tdual bundle gerbe. 

Applications of tropical geometry to groups and manifolds 13:10 Mon 21 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Stephan Tillmann :: University of Queensland
Tropical geometry is a young field with multiple origins. These include the work of Bergman on logarithmic limit sets of algebraic varieties; the work of the Brazilian computer scientist Simon on discrete mathematics; the work of Bieri, Neumann and Strebel on geometric invariants of groups; and, of course, the work of Newton on polynomials. Even though there is still need for a unified foundation of the field, there is an abundance of applications of tropical geometry in group theory, combinatorics, computational algebra and algebraic geometry. In this talk I will give an overview of (what I understand to be) tropical geometry with a bias towards applications to group theory and lowdimensional topology. 

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. 

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 de Rham Complex 12:10 Mon 19 Mar, 2012 :: 5.57 Ingkarni Wardli :: Mr Michael Albanese :: University of Adelaide
Media...The de Rham complex is of fundamental importance in differential geometry. After first introducing differential forms (in the familiar setting of Euclidean space), I will demonstrate how the de Rham complex elegantly encodes one half (in a sense which will become apparent) of the results from vector calculus. If there is time, I will indicate how results from the remaining half of the theory can be concisely expressed by a single, far more general theorem. 

Financial risk measures  the theory and applications of backward stochastic difference/differential equations with respect to the single jump process 12:10 Mon 26 Mar, 2012 :: 5.57 Ingkarni Wardli :: Mr Bin Shen :: University of Adelaide
Media...This is my PhD thesis submitted one month ago. Chapter 1 introduces the backgrounds of the research fields. Then each chapter is a published or an accepted paper.
Chapter 2, to appear in Methodology and Computing in Applied Probability, establishes the theory of Backward Stochastic Difference Equations with respect to the single jump process in discrete time.
Chapter 3, published in Stochastic Analysis and Applications, establishes the theory of Backward Stochastic Differential Equations with respect to the single jump process in continuous time.
Chapter 2 and 3 consist of Part I Theory.
Chapter 4, published in Expert Systems With Applications, gives some examples about how to measure financial risks by the theory established in Chapter 2.
Chapter 5, accepted by Journal of Applied Probability, considers the question of an optimal transaction between two investors to minimize their risks. It's the applications of the theory established in Chapter 3.
Chapter 4 and 5 consist of Part II Applications. 

Correcting Errors in RSA Private Keys 12:10 Mon 23 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Wilko Henecka :: University of Adelaide
Media...Let pk=(N,e) be an RSA public key with corresponding secret key sk=(d,p,q,...). Assume that we obtain partial errorfree information of sk, e.g., assume that we obtain half of the most significant bits of p. Then there are wellknown algorithms to recover the full secret key. As opposed to these algorithms that allow for correcting erasures of the key sk, we present for the first time a heuristic probabilistic algorithm that is capable of correcting errors in sk provided that e is small. That is, on input of a full but errorprone secret key sk' we reconstruct the original sk by correcting the faults.
More precisely, consider an error rate of d in [0,1), where we flip each bit in sk with probability d resulting in an erroneous key sk'. Our LasVegas type algorithm allows to recover sk from sk' in expected time polynomial in logN with success probability close to 1, provided that d is strictly less than 0.237. We also obtain a polynomial time LasVegas factorization algorithm for recovering the factorization (p,q) from an erroneous version with error rate d strictly less than 0.084. 

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. 

Change detection in rainfall times series for Perth, Western Australia 12:10 Mon 14 May, 2012 :: 5.57 Ingkarni Wardli :: Ms Farah Mohd Isa :: University of Adelaide
Media...There have been numerous reports that the rainfall in south Western Australia,
particularly around Perth has observed a step change decrease, which is
typically attributed to climate change. Four statistical tests are used to
assess the empirical evidence for this claim on time series from five
meteorological stations, all of which exceed 50 years. The tests used in this
study are: the CUSUM; Bayesian Change Point analysis; consecutive ttest and the
Hotelling's T^2statistic. Results from multivariate Hotelling's T^2 analysis are
compared with those from the three univariate analyses. The issue of multiple
comparisons is discussed. A summary of the empirical evidence for the claimed
step change in Perth area is given. 

Computational complexity, taut structures and triangulations 13:10 Fri 18 May, 2012 :: Napier LG28 :: Dr Benjamin Burton :: University of Queensland
There are many interesting and difficult algorithmic problems in
lowdimensional topology. Here we study the problem of finding a taut
structure on a 3manifold triangulation, whose existence has implications
for both the geometry and combinatorics of the triangulation. We prove
that detecting taut structures is "hard", in the sense that it is NPcomplete.
We also prove that detecting taut structures is "not too hard", by showing
it to be fixedparameter tractable. This is joint work with Jonathan Spreer.


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

Geometric modular representation theory 13:10 Fri 1 Jun, 2012 :: Napier LG28 :: Dr Anthony Henderson :: University of Sydney
Representation theory is one of the oldest areas of algebra, but many basic questions in it are still unanswered. This is especially true in the modular case, where one considers vector spaces over a field F of positive characteristic; typically, complications arise for particular small values of the characteristic. For example, from a vector space V one can construct the symmetric square S^2(V), which is one easy example of a representation of the group GL(V). One would like to say that this representation is irreducible, but that statement is not always true: if F has characteristic 2, there is a nontrivial invariant subspace. Even for GL(V), we do not know the dimensions of all irreducible representations in all characteristics.
In this talk, I will introduce some of the main ideas of geometric modular representation theory, a more recent approach which is making progress on some of these old problems. Essentially, the strategy is to reformulate everything in terms of homology of various topological spaces, where F appears only as the field of coefficients and the spaces themselves are independent of F; thus, the modular anomalies in representation theory arise because homology with modular coefficients is detecting something about the topology that rational coefficients do not. In practice, the spaces are usually varieties over the complex numbers, and homology is replaced by intersection cohomology to take into account the singularities of these varieties. 

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

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

Introduction to quantales via axiomatic analysis 13:10 Fri 15 Jun, 2012 :: Napier LG28 :: Dr Ittay Weiss :: University of the South Pacific
Quantales were introduced by Mulvey in 1986 in the context of noncommutative topology with the aim of providing a concrete noncommutative framework for the foundations of quantum mechanics. Since then quantales found applications in other areas as well, among others in the work of Flagg. Flagg considers certain special quantales, called value quantales, that are desigend to capture the essential properties of ([0,\infty],\le,+) that are relevant for analysis. The result is a well behaved theory of value quantale enriched metric spaces. I will introduce the notion of quantales as if they were desigend for just this purpose, review most of the known results (since there are not too many), and address a some new results, conjectures, and questions. 

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. 

Comparison of spectral and wavelet estimators of transfer function for linear systems 12:10 Mon 18 Jun, 2012 :: B.21 Ingkarni Wardli :: Mr Mohd Aftar Abu Bakar :: University of Adelaide
Media...We compare spectral and wavelet estimators of the response amplitude operator (RAO) of a linear system, with various input signals and added noise scenarios. The comparison is based on a model of a heaving buoy wave energy device (HBWED), which oscillates vertically as a single mode of vibration linear system.
HBWEDs and other single degree of freedom wave energy devices such as the oscillating wave surge convertors (OWSC) are currently deployed in the ocean, making single degree of freedom wave energy devices important systems to both model and analyse in some detail. However, the results of the comparison relate to any linear system.
It was found that the wavelet estimator of the RAO offers no advantage over the spectral estimators if both input and response time series data are noise free and long time series are available. If there is noise on only the response time series, only the wavelet estimator or the spectral estimator that uses the crossspectrum of the input and response signals in the numerator should be used. For the case of noise on only the input time series, only the spectral estimator that uses the crossspectrum in the denominator gives a sensible estimate of the RAO. If both the input and response signals are corrupted with noise, a modification to both the input and response spectrum estimates can provide a good estimator of the RAO. However, a combination of wavelet and spectral methods is introduced as an alternative RAO estimator.
The conclusions apply for autoregressive emulators of sea surface elevation, impulse, and pseudorandom binary sequences (PRBS) inputs. However, a wavelet estimator is needed in the special case of a chirp input where the signal has a continuously varying frequency. 

Ktheory and unbounded Fredholm operators 13:10 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Dr Jerry Kaminker :: University of California, Davis
There are several ways of viewing elements of K^1(X). One
of these is via families of unbounded selfadjoint Fredholm operators on X. Each operator will have discrete spectrum, with infinitely many positive and negative eigenvalues of finite multiplicity. One can associate to such a family a geometric object, its graph, and the Chern character and other invariants of the family can be studied from this perspective. By restricting the dimension of the eigenspaces one may sometimes use algebraic topology to completely determine the family up to equivalence. This talk will describe the general framework and some applications to families on lowdimensional manifolds
where the methods work well. Various notions related to spectral flow, the index gerbe and Berry phase play roles which will be discussed. This is joint work with Ron Douglas.


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. 

Star Wars Vs The Lord of the Rings: A Survival Analysis 12:10 Mon 27 Aug, 2012 :: B.21 Ingkarni Wardli :: Mr Christopher Davies :: University of Adelaide
Media...Ever wondered whether you are more likely to die in the Galactic Empire or Middle Earth? Well this is the postgraduate seminar for you!
I'll be attempting to answer this question using survival analysis, the statistical method of choice for investigating time to event data.
Spoiler Warning: This talk will contain references to the deaths of characters in the above movie sagas. 

Classification of a family of symmetric graphs with complete quotients 13:10 Fri 7 Sep, 2012 :: Engineering North 218 :: A/Prof Sanming Zhou :: University of Melbourne
A finite graph is called symmetric if its automorphism group is
transitive on the set of arcs (ordered pairs of adjacent vertices) of the
graph. This is to say that all arcs have the same status in the graph. I
will talk about recent results on the classification of a family of
symmetric graphs with complete quotients. The most interesting graphs
arising from this classification are defined in terms of Hermitian unitals
(which are specific block designs), and they admit unitary groups as
groups of automorphisms. I will also talk about applications of our
results in constructing large symmetric graphs of given degree and
diameter.
This talk contains joint work with M. Giulietti, S. Marcugini and F.
Pambianco.


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. 

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

Krylov Subspace Methods or: How I Learned to Stop Worrying and Love GMRes 12:10 Mon 17 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr David Wilke :: University of Adelaide
Media...Many problems within applied mathematics require the solution of a linear system of equations. For instance, models of arterial umbilical blood flow are obtained through a finite element approximation, resulting in a linear, n x n system. For small systems the solution is (almost) trivial, but what happens when n is large? Say, n ~ 10^6? In this case matrix inversion is expensive (read: completely impractical) and we seek approximate solutions in a reasonable time.
In this talk I will discuss the basic theory underlying Krylov subspace methods; a class of nonstationary iterative methods which are currently the methodsofchoice for large, sparse, linear systems. In particular I will focus on the method of Generalised Minimum RESiduals (GMRes), which is of the most popular for nonsymmetric systems. It is hoped that through this presentation I will convince you that a) solving linear systems is not necessarily trivial, and that b) my lack of any tangible results is not (entirely) a result of my own incompetence. 

Rescaling the coalescent 12:30 Mon 8 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr Adam Rohrlach :: University of Adelaide
Media...Recently I gave a short talk about how researchers use mathematics to estimate the time since a species' most recent common ancestor. I also pointed out why this generally doesn't work when a population hasn't had a constant population size. Then I quickly changed the subject. In this talk I aim to reintroduce the Coalescent Model, show how it works in general, and finally how researcher's deal with varying a population size. 

Supermanifolds and the moduli space of instantons 13:10 Fri 19 Oct, 2012 :: Engineering North 218 :: Prof Ugo Bruzzo :: International School for Advanced Studies (SISSA), Trieste
I will give an example of an application of supermanifold theory to physics, i.e., how to "superize" the moduli space of instantons on a 4fold and use it to give a description of the BRST transformations, to compute the "supermeasure" of the moduli space, and the Nekrasov partition function. 

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

AD Model Builder and the estimation of lobster abundance 12:10 Mon 22 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr John Feenstra :: University of Adelaide
Media...Determining how many millions of lobsters reside in our waters and how it changes over time is a central aim of lobster stock assessment. ADMB is powerful optimisation software to model and solve complex nonlinear problems using automatic differentiation and plays a major role in SA and worldwide in fisheries stock assessment analyses. In this talk I will provide a brief description of an example modelling problem, key features and use of ADMB. 

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

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

The space of cubic rational maps 13:10 Fri 26 Oct, 2012 :: Engineering North 218 :: Mr Alexander Hanysz :: University of Adelaide
For each natural number d, the space of rational maps of degree d on the Riemann sphere has the structure of a complex manifold. The topology of these manifolds has been extensively studied. The recent development of Oka theory raises some new and interesting questions about their complex structure. We apply geometric invariant theory to the degree 3 case, studying a double action of the Mobius group on the space of cubic rational maps. We show that the categorical quotient is C, and that the space of cubic rational maps enjoys the holomorphic flexibility properties of strong dominability and Cconnectedness. 

Spatiotemporally Autoregressive Partially Linear Models with Application to the Housing Price Indexes of the United States 12:10 Mon 12 Nov, 2012 :: B.21 Ingkarni Wardli :: Ms Dawlah Alsulami :: University of Adelaide
Media...We propose a Spatiotemporal Autoregressive Partially Linear Regression ( STARPLR) model for data observed irregularly over space and regularly in time. The model is capable of catching possible non linearity and nonstationarity in space by coefficients to depend on locations. We suggest twostep procedure to estimate both the coefficients and the unknown function, which is readily implemented and can be computed even for large spatiotemoral data sets. As an illustration, we apply our model to analyze the 51 States' House Price Indexes (HPIs) in USA. 

Modular forms: a rough guide 12:10 Mon 18 Mar, 2013 :: B.19 Ingkarni Wardli :: Damien Warman :: University of Adelaide
Media...I recently found the need to learn a little about what I had naively believed to be an abstruse branch of number theory, but which turns out to be a ubiquitous and intriguing theory.
I'll introduce some of the geometry underlying the elementary theory of modular functions and modular forms. We'll look at some pictures and play with sage, time permitting. 

Einstein's special relativity beyond the speed of light 14:10 Mon 18 Mar, 2013 :: 7.15 Ingkarni Wardli :: Prof. Jim Hill :: School of Mathematical Sciences
Media...We derive extended Lorentz transformations between inertial frames for relative velocities greater than the speed of light, and which are complementary to the Lorentz transformation giving rise to the Einstein special theory of relativity. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide welldefined expressions. 

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

Coincidences 14:10 Mon 20 May, 2013 :: 7.15 Ingkarni Wardli :: A/Prof. Robb Muirhead :: School of Mathematical Sciences
Media...This is a lighthearted (some would say contentfree) talk about coincidences, those surprising concurrences of events that are often perceived as meaningfully related, with no apparent causal connection. Time permitting, it will touch on topics like:
Patterns in data and the dangers of looking for patterns, unspecified ahead of time, and trying to "explain" them; e.g. post hoc subgroup analyses, cancer clusters, conspiracy theories ...
Matching problems; e.g. the birthday problem and extensions
People who win a lottery more than once  how surprised should we really be? What's the question we should be asking?
When you become familiar with a new word, and see it again soon afterwards, how surprised should you be?
Caution: This is a shortened version of a talk that was originally prepared for a group of nonmathematicians and nonstatisticians, so it's mostly nontechnical. It probably does not contain anything you don't already know  it will be an amazing coincidence if it does! 

Multiscale modelling couples patches of wavelike simulations 12:10 Mon 27 May, 2013 :: B.19 Ingkarni Wardli :: Meng Cao :: University of Adelaide
Media...A multiscale model is proposed to significantly reduce the expensive numerical simulations of complicated waves over large spatial domains. The multiscale model is built from given microscale simulations of complicated physical processes such as sea ice or turbulent shallow water. Our long term aim is to enable macroscale simulations obtained by coupling small patches of simulations together over large physical distances. This initial work explores the coupling of patch simulations of wavelike pdes. With the line of development being to water waves we discuss the dynamics of two complementary fields called the 'depth' h and 'velocity' u. A staggered grid is used for the microscale simulation of the depth h and velocity u. We introduce a macroscale staggered grid to couple the microscale patches. Linear or quadratic interpolation provides boundary conditions on the field in each patch. Linear analysis of the whole coupled multiscale system establishes that the resultant macroscale dynamics is appropriate. Numerical simulations support the linear analysis. This multiscale method should empower the feasible computation of large scale simulations of wavelike dynamics with complicated underlying physics. 

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. 

Birational geometry of M_g 12:10 Fri 21 Jun, 2013 :: Ingkarni Wardli B19 :: Dr Jarod Alper :: Australian National University
In 1969, Deligne and Mumford introduced a beautiful compactification of the moduli space of smooth curves which has proved extremely influential in geometry, topology and physics. Using recent advances in higher dimensional geometry and the minimal model program, we study the birational geometry of M_g. In particular, in an effort to understand the canonical model of M_g, we study the log canonical models as well as the associated divisorial contractions and flips by interpreting these models as moduli spaces of particular singular curves. 

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

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. 

Four hats, three prisoners, two colours and a jailer 12:35 Mon 5 Aug, 2013 :: B.19 Ingkarni Wardli :: Kale Davies :: University of Adelaide
Media...It was a dark and stormy night. Theodore Jailer sat alone in his office scrawling notes on a piece of paper, muttering to himself in frustration. Suddenly he stops, his eyes widen in excitement and a smile spreads across his face. No, not a smile, but a grimace, for you see, evil was afoot! For Jailer, who was the jailer at a local prison had devised a nefarious scheme in order to execute all of the prisoners once and for all. Can his evil plans be thwarted in time? Stay tuned to find out! 

Geometry of moduli spaces 12:10 Fri 30 Aug, 2013 :: Ingkarni Wardli B19 :: Prof Georg Schumacher :: University of Marburg
We discuss the concept of moduli spaces in complex geometry. The main examples are moduli of compact Riemann surfaces, moduli of compact projective varieties and moduli of holomorphic vector bundles, whose points correspond to isomorphism classes of the given objects. Moduli spaces carry a natural topology, whereas a complex structure that reflects the variation of the structure in a family exists in general only under extra conditions. In a similar way, a natural hermitian metric (WeilPetersson metric) on moduli spaces that induces a symplectic structure can be constructed from the variation of distinguished metrics on the fibers. In this way, various questions concerning the underlying symplectic structure, the curvature of the WeilPetersson metric, hyperbolicity of moduli spaces, and construction of positive/ample line bundles on compactified moduli spaces can be answered. 

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

Ktheory and solid state physics 12:10 Fri 13 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Keith Hannabuss :: Balliol College, Oxford
More than 50 years ago Dyson showed that there is a ninefold classification of random matrix models, the classes of which are each associated with Riemannian symmetric spaces. More recently it was realised that a related argument enables one to classify the insulating properties of fermionic systems (with the addition of an extra class to give 10 in all), and can be described using Ktheory. In this talk I shall give a survey of the ideas, and a brief outline of work with Guo Chuan Thiang. 

Controlling disease, one household at a time. 12:10 Mon 23 Sep, 2013 :: B.19 Ingkarni Wardli :: Michael Lydeamore :: University of Adelaide
Pandemics and Epidemics have always caused significant disruption to society. Attempting to model each individual in any reasonable sized population is unfeasible at best, but we can get surprisingly good results just by looking at a single household in a population. In this talk, I'll try to guide you through the logic I've discovered this year, and present some of the key results we've obtained so far, as well as provide a brief indication of what's to come. 

Recent developments in special holonomy manifolds 12:10 Fri 1 Nov, 2013 :: Ingkarni Wardli 7.15 :: Prof Robert Bryant :: Duke University
One of the big classification results in differential geometry from the past century has been the classification of the possible holonomies of affine manifolds, with the major first step having been taken by Marcel Berger in his 1954 thesis. However, Berger's classification was only partial, and, in the past 20 years, an extensive research effort has been expended to complete this classification and extend it in a number of ways. In this talk, after recounting the major parts of the history of the subject, I will discuss some of the recent results and surprising new examples discovered as a byproduct of research into Finsler geometry. If time permits, I will also discuss some of the open problems in the subject. 

Developing Multiscale Methodologies for Computational Fluid Mechanics 12:10 Mon 11 Nov, 2013 :: B.19 Ingkarni Wardli :: Hammad Alotaibi :: University of Adelaide
Media...Recently the development of multiscale methods is one of the most fertile research areas in mathematics, physics, engineering and computer science. The need for multiscale modeling comes usually from the fact that the available macroscale models are not accurate enough, and the microscale models are not efficient enough. By combining both viewpoints, one hopes to arrive at a reasonable compromise between accuracy and efficiency.
In this seminar I will give an overview of the recent efforts on developing multiscale methods such as patch dynamics scheme which is used to address an important class of time dependent multiscale problems. 

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. 

The density property for complex manifolds: a strong form of holomorphic flexibility 12:10 Fri 24 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Frank Kutzschebauch :: University of Bern
Compared with the real differentiable case, complex manifolds in general are more rigid, their groups of holomorphic diffeomorphisms are rather small (in general trivial). A long known exception to this behavior is affine nspace C^n for n at least 2. Its group of holomorphic diffeomorphisms is infinite dimensional. In the late 1980s Andersen and Lempert proved a remarkable
theorem which stated in its generalized version due to Forstneric and Rosay that any local holomorphic phase flow given on a Runge subset of C^n can be locally uniformly approximated by a global holomorphic diffeomorphism. The main ingredient in the proof was formalized by Varolin and called the density property: The Lie algebra generated by complete holomorphic vector fields is dense in the Lie algebra of all holomorphic vector fields. In these manifolds a similar local to global approximation of AndersenLempert type holds. It is a precise way of saying that the group of holomorphic diffeomorphisms is large.
In the talk we will explain how this notion is related to other more recent flexibility notions in complex geometry, in particular to the notion of a OkaForstneric manifold. We will give examples of manifolds with the density property and sketch applications of the density property. If time permits we will explain criteria for the density property developed by Kaliman and the speaker.


Geometric quantisation in the noncompact setting 12:10 Fri 7 Mar, 2014 :: Ingkarni Wardli B20 :: Peter Hochs :: University of Adelaide
Geometric quantisation is a way to construct quantum mechanical phase spaces (Hilbert spaces) from classical mechanical phase spaces (symplectic manifolds). In the presence of a group action, the quantisation commutes with reduction principle states that geometric quantisation should be compatible with the ways the group action can be used to simplify (reduce) the classical and quantum phase spaces. This has deep consequences for the link between symplectic geometry and representation theory.
The quantisation commutes with reduction principle has been given explicit meaning, and been proved, in cases where the symplectic manifold and the group acting on it are compact. There have also been results where just the group, or the orbit space of the action, is assumed to be compact. These are important and difficult, but it is somewhat frustrating that they do not even apply to the simplest example from the physics point of view: a free particle in Rn. This talk is about a joint result with Mathai Varghese where the group, manifold and orbit space may all be noncompact. 

The phase of the scattering operator from the geometry of certain infinite dimensional Lie groups 12:10 Fri 14 Mar, 2014 :: Ingkarni Wardli B20 :: Jouko Mickelsson :: University of Helsinki
This talk is about some work on the phase of the time evolution operator in QED and QCD, related to the geometry of certain infinitedimensional
groups (essentially modelled by PSDO's). 

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. 

The Dynamics of Falling 12:10 Mon 7 Apr, 2014 :: B.19 Ingkarni Wardli :: Lyron Winderbaum :: University of Adelaide
Media...As most of you know I am addicted to climbing. So I thought I might talk abit about some math related to climbing, ropes, tension, and to be entirely honest, mostly statics  not dynamics, but the title was catchy. I'll explain a little about climbing, and the different ways in which you can go about protecting yourself from a fall by using ropes. This involves some interesting formulae for friction that most of you probably haven't seen before, and even some trig for the geometry enthusiast, but be warned  it delves into the realms of physics. I even uncovered a few unexpected and somewhat antiintuitive results that might interest you. 

CARRYING CAPACITY FOR FINFISH AQUACULTURE IN SPENCER GULF: RAPID ASSESSMENT USING HYDRODYNAMIC AND NEARFIELD, SEMI  ANALYTIC SOLUTIONS 15:10 Fri 11 Apr, 2014 :: 5.58 Ingkarni Wardli :: Associate Professor John Middleton :: SARDI Aquatic Sciences and University of Adelaide
Aquaculture farming involves daily feeding of finfish and a subsequent excretion of nutrients into Spencer Gulf. Typically, finfish farming is done in six or so 50m diameter cages and over 600m X 600m lease sites. To help regulate the industry, it is desired that the finfish feed rates and the associated nutrient flux into the ocean are determined such that the maximum nutrient concentration c does not exceed a prescribed value (say cP) for ecosystem health. The prescribed value cP is determined by guidelines from the E.P.A. The concept is known as carrying capacity since limiting the feed rates limits the biomass of the farmed finfish.
Here, we model the concentrations that arise from a constant input flux (F) of nutrients in a source region (the cage or lease) using the (depthaveraged) two dimensional, advection diffusion equation for constant and sinusoidal (tides) currents. Application of the divergence theorem to this equation results in a new scale estimate of the maximum flux F (and thus feed rate) that is given by
F= cP /T* (1)
where cP is the maximum allowed concentration and T* is a new time scale of âflushingâ that involves both advection and diffusion. The scale estimate (1) is then shown to compare favourably with mathematically exact solutions of the advection diffusion equation that are obtained using Greenâs functions and Fourier transforms. The maximum nutrient flux and associated feed rates are then estimated everywhere in Spencer Gulf through the development and validation of a hydrodynamic model. The model provides seasonal averages of the mean currents U and horizontal diffusivities KS that are needed to estimate T*. The diffusivities are estimated from a shear dispersal model of the tides which are very large in the gulf. The estimates have been provided to PIRSA Fisheries and Aquaculture to assist in the sustainable expansion of finfish aquaculture.


A generalised KacPeterson cocycle 11:10 Thu 17 Apr, 2014 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide
The KacPeterson cocycle appears in the study of highest weight modules of infinite dimensional Lie algebras and determines a central extension. The vanishing of its cohomology class is tied to the existence of a cubic Dirac operator whose square is a quadratic Casimir element. I will introduce a closely related Lie algebra cocycle that comes about when constructing spin representations and gives rise to a Banach Lie group with a highly nontrivial topology. I will also explain how to make sense of the cubic Dirac operator in this setting and discuss its relation to twisted Ktheory. This is joint work with Jouko Mickelsson. 

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. 

Group meeting 15:10 Fri 6 Jun, 2014 :: 5.58 Ingkarni Wardli :: Meng Cao and Trent Mattner :: University of Adelaide
Meng Cao:: Multiscale modelling couples patches of nonlinear wavelike simulations ::
Abstract:
The multiscale gaptooth scheme is built from given microscale simulations of complicated physical processes to empower macroscale simulations. By coupling small patches of simulations over unsimulated physical gaps, large savings in computational time are possible. So far the gaptooth scheme has been developed for dissipative systems, but wave systems are also of great interest. This article develops the gaptooth scheme to the case of nonlinear microscale simulations of wavelike systems. Classic macroscale interpolation provides a generic coupling between patches that achieves arbitrarily high order consistency between the multiscale scheme and the underlying microscale dynamics. Eigenanalysis indicates that the resultant gaptooth scheme empowers feasible computation of large scale simulations of wavelike dynamics with complicated underlying physics. As an pilot study, we implement numerical simulations of dambreaking waves by the gaptooth scheme. Comparison between a gaptooth simulation, a microscale simulation over the whole domain, and some published experimental data on dam breaking, demonstrates that the gaptooth scheme feasibly computes large scale wavelike dynamics with computational savings.
Trent Mattner :: Coupled atmospherefire simulations of the Canberra 2003 bushfires using WRFSfire :: Abstract:
The Canberra fires of January 18, 2003 are notorious for the extreme fire behaviour and fireatmospheretopography interactions that occurred, including leeslope fire channelling, pyrocumulonimbus development and tornado formation. In this talk, I will discuss coupled fireweather simulations of the Canberra fires using WRFSFire. In these simulations, a firebehaviour model is used to dynamically predict the evolution of the fire front according to local atmospheric and topographic conditions, as well as the associated heat and moisture fluxes to the atmosphere. It is found that the predicted fire front and heat flux is not too bad, bearing in mind the complexity of the problem and the severe modelling assumptions made. However, the predicted moisture flux is too low, which has some impact on atmospheric dynamics. 

Hydrodynamics and rheology of selfpropelled colloids 15:10 Fri 8 Aug, 2014 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide
The subcellular world has many components in common with soft condensed matter systems (polymers, colloids and liquid crystals). But it has novel properties, not present in traditional complex fluids, arising from a rich spectrum of nonequilibrium behavior: flocking, chemotaxis and bioconvection.
The talk is divided into two parts. In the first half, we will (get an idea on how to) derive a hydrodynamic model for selfpropelled particles of an arbitrary shape from first principles, in a sufficiently dilute suspension limit, moving in a 3dimensional space inside a viscous solvent. The model is then restricted to particles with ellipsoidal geometry to quantify the interplay of the longrange excluded volume and the shortrange selfpropulsion effects. The expression for the constitutive stresses, relating the kinetic theory with the momentum transport equations, are derived using a combination of the virtual work principle (for extra elastic stresses) and symmetry arguments (for active stresses).
The second half of the talk will highlight on my current numerical expertise. In particular we will exploit a specific class of spectral basis functions together with RK4 timestepping to determine the dynamical phases/structures as well as phasetransitions of these ellipsoidal clusters. We will also discuss on how to define the order (or orientation) of these clusters and understand the other rheological quantities.


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

A Random Walk Through Discrete State Markov Chain Theory 12:10 Mon 22 Sep, 2014 :: B.19 Ingkarni Wardli :: James Walker :: University of Adelaide
Media...This talk will go through the basics of Markov chain theory; including how to construct a continuoustime Markov chain (CTMC), how to adapt a Markov chain to include nonmemoryless distributions, how to simulate CTMC's and some key results. 

Inferring absolute population and recruitment of southern rock lobster using only catch and effort data 12:35 Mon 22 Sep, 2014 :: B.19 Ingkarni Wardli :: John Feenstra :: University of Adelaide
Media...Abundance estimates from a datalimited version of catch survey analysis are compared to those from a novel oneparameter deterministic method. Bias of both methods is explored using simulation testing based on a more complex datarich stock assessment population dynamics fishery operating model, exploring the impact of both varying levels of observation error in data as well as model process error. Recruitment was consistently better estimated than legal size population, the latter most sensitive to increasing observation errors. A hybrid of the datalimited methods is proposed as the most robust approach. A more statistically conventional errorinvariables approach may also be touched upon if enough time. 

A Hybrid Markov Model for Disease Dynamics 12:35 Mon 29 Sep, 2014 :: B.19 Ingkarni Wardli :: Nicolas Rebuli :: University of Adelaide
Media...Modelling the spread of infectious diseases is fundamental to protecting ourselves from potentially devastating epidemics. Among other factors, two key indicators for the severity of an epidemic are the size of the epidemic and the time until the last infectious individual is removed. To estimate the distribution of the size and duration of an epidemic (within a realistic population) an epidemiologist will typically use Monte Carlo simulations of an appropriate Markov process. However, the number of states in the simplest Markov epidemic model, the SIR model, is quadratic in the population size and so Monte Carlo simulations are computationally expensive. In this talk I will discuss two methods for approximating the SIR Markov process and I will demonstrate the approximation error by comparing probability distributions and estimates of the distributions of the final size and duration of an SIR epidemic. 

Topology, geometry, and moduli spaces 12:10 Fri 10 Oct, 2014 :: Ingkarni Wardli B20 :: Nick Buchdahl :: University of Adelaide
In recent years, moduli spaces of one kind or
another have been shown to be of great utility, this
quite apart from their inherent interest. Many of their
applications involve their topology, but as we all know,
understanding of topological structures is often
facilitated through the use of geometric methods, and
some of these moduli spaces carry geometric structures that are
considerable interest in their own right.
In this talk, I will describe some of the background and
the ideas in this general context, focusing on questions
that I have been considering lately together with my
colleague Georg Schumacher from Marburg in Germany, who
was visiting us recently. 

Optimally Chosen Quadratic Forms for Partitioning Multivariate Data 13:10 Tue 14 Oct, 2014 :: Ingkarni Wardli 715 Conference Room :: Assoc. Prof. Inge Koch :: School of Mathematical Sciences
Media...Quadratic forms are commonly used in linear algebra. For ddimensional vectors they have a matrix representation, Q(x) = x'Ax, for some symmetric matrix A. In statistics quadratic forms are defined for ddimensional random vectors, and one of the bestknown quadratic forms is the Mahalanobis distance of two random vectors.
In this talk we want to partition a quadratic form Q(X) = X'MX, where X is a random vector, and M a symmetric matrix, that is, we want to find a ddimensional random vector W such that Q(X) = W'W. This problem has many solutions. We are interested in a solution or partition W of X such that pairs of corresponding variables (X_j, W_j) are highly correlated and such that W is simpler than the given X.
We will consider some natural candidates for W which turn out to be suboptimal in the sense of the above constraints, and we will then exhibit the optimal solution. Solutions of this type are useful in the wellknown Tsquare statistic. We will see in examples what these solutions look like. 

Compact pseudoRiemannian solvmanifolds 12:10 Fri 17 Oct, 2014 :: Ingkarni Wardli B20 :: Wolfgang Globke :: University of Adelaide
A compact solvmanifold M is a quotient of a solvable Lie group G by a cocompact closed subgroup H. A pseudoRiemannian metric on M is induced by an Hinvariant symmetric 2tensor on G. In this talk I will describe some foundations and results of my ongoing work with Oliver Baues on the nature of this 2tensor and what it can imply for the subgroup H. 

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 !! 

Topology Tomography with Spatial Dependencies 15:00 Tue 25 Nov, 2014 :: Engineering North N132 :: Darryl Veitch :: The University of Melbourne
Media...There has been quite a lot of tomography inference work on measurement networks with a tree topology. Here observations are made, at the leaves of the tree, of `probes' sent down from the root and copied at each branch point. Inference can be performed based on loss or delay information carried by probes, and used in order to recover loss parameters, delay parameters, or the topology, of the tree. In all of these a strong assumption of spatial independence between links in the tree has been made in prior work. I will describe recent work on topology inference, based on loss measurement, which breaks that assumption. In particular I will introduce a new model class for loss with non trivial spatial dependence, the `Jump Independent Models', which are well motivated, and prove that within this class the topology is identifiable. 

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. 

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. 

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. 

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

A Collision Algorithm for Sea Ice 12:10 Mon 4 May, 2015 :: Napier LG29 :: Lucas Yiew :: University of Adelaide
Media...The waveinduced collisions between sea ice are highly complex and nonlinear, and involves a multitude of subprocesses. Several collision models do exist, however, to date, none of these models have been successfully integrated into seaice forecasting models.
A key component of a collision model is the development of an appropriate collision algorithm. In this seminar I will present a timestepping, eventdriven algorithm to detect, analyse and implement the pre and postcollision processes. 

Indefinite spectral triples and foliations of spacetime 12:10 Fri 8 May, 2015 :: Napier 144 :: Koen van den Dungen :: Australian National University
Motivated by Dirac operators on Lorentzian manifolds, we propose a new framework to deal with nonsymmetric and nonelliptic operators in noncommutative geometry. We provide a definition for indefinite spectral triples, which correspond bijectively with certain pairs of spectral triples.
Next, we will show how a special case of indefinite spectral triples can be constructed from a family of spectral triples. In particular, this construction provides a convenient setting to study the Dirac operator on a spacetime with a foliation by spacelike hypersurfaces.
This talk is based on joint work with Adam Rennie (arXiv:1503.06916). 

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. 

Medical Decision Making 12:10 Mon 11 May, 2015 :: Napier LG29 :: Eka Baker :: University of Adelaide
Media...Practicing physicians make treatment decisions based on clinical trial data every day. This data is based on trials primarily conducted on healthy volunteers, or on those with only the disease in question. In reality, patients do have existing conditions that can affect the benefits and risks associated with receiving these treatments.
In this talk, I will explain how we modified an already existing Markov model to show the progression of treatment of a single condition over time. I will then explain how we adapted this to a different condition, and then created a combined model, which demonstrated how both diseases and treatments progressed on the same patient over their lifetime. 

Big things are weird 12:10 Mon 25 May, 2015 :: Napier LG29 :: Luke KeatingHughes :: University of Adelaide
Media...The pyramids of Giza, the depths of the Mariana trench, the massive Einstein Cross Quasar; all of these things are big and weird. Big weird things aren't just apparent in the physical world though, they appear in mathematics too! In this talk I will try to motivate a mathematical big thing and then show that it is weird.
In particular, we will introduce the necessary topology and homotopy theory in order to show that although all finite dimensional spheres are (almost canonically) noncontractible spaces  an infinite dimensional sphere IS contractible! This result's significance will then be explained in the context of Kuiper's Theorem if time permits. 

Monodromy of the Hitchin system and components of representation varieties 12:10 Fri 29 May, 2015 :: Napier 144 :: David Baraglia :: University of Adelaide
Representations of the fundamental group of a compact Riemann surface into a reductive Lie group form a moduli space, called a representation variety. An outstanding problem in topology is to determine the number of components of these varieties. Through a deep result known as nonabelian Hodge theory, representation varieties are homeomorphic to moduli spaces of certain holomorphic objects called Higgs bundles. In this talk I will describe recent joint work with L. Schaposnik computing the monodromy of the Hitchin fibration for Higgs bundle moduli spaces. Our results give a new unified proof of the number of components of several representation varieties. 

Group Meeting 15:10 Fri 29 May, 2015 :: EM 213 :: Dr Judy Bunder :: University of Adelaide
Talk : Patch dynamics for efficient exascale simulations
Abstract
Massive parallelisation has lead to a dramatic increase in available computational power.
However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must be developed which minimise the transfer of data. Patch dynamics is a computational macroscale modelling scheme which provides a coarse macroscale solution of a problem defined on a fine microscale by dividing the domain into many nonoverlapping, coupled patches. Patch dynamics is readily adaptable to massive parallelisation as each processor core can evaluate the dynamics on one, or a few, patches. However, patch coupling conditions interpolate across the unevaluated parts of the domain between patches and require almost continuous data transfer. We propose a modified patch dynamics scheme which minimises data transfer by only reevaluating the patch coupling conditions at `mesoscale' time scales which are significantly larger than the microscale time of the microscale problem. We analyse and quantify the error arising from patch dynamics with mesoscale temporal coupling. 

Dirac operators and Hamiltonian loop group action 12:10 Fri 24 Jul, 2015 :: Engineering and Maths EM212 :: Yanli Song :: University of Toronto
A definition to the geometric quantization for compact Hamiltonian Gspaces is given by Bott, defined as the index of the SpincDirac operator on the manifold. In this talk, I will explain how to generalize this idea to the Hamiltonian LGspaces. Instead of quantizing infinitedimensional manifolds directly, we use its equivalent finitedimensional model, the quasiHamiltonian Gspaces. By constructing twisted spinor bundle and twisted prequantum bundle on the quasiHamiltonian Gspace, we define a Dirac operator whose index are given by positive energy representation of loop groups. A key role in the construction will be played by the algebraic cubic Dirac operator for loop algebra. If time permitted, I will also explain how to prove the quantization commutes with reduction theorem for Hamiltonian LGspaces under this framework. 

Workshop on Geometric Quantisation 10:10 Mon 27 Jul, 2015 :: Level 7 conference room Ingkarni Wardli :: Michele Vergne, Weiping Zhang, Eckhard Meinrenken, Nigel Higson and many others
Media...Geometric quantisation has been an increasingly active area since before the 1980s, with links to physics, symplectic geometry, representation theory, index theory, and differential geometry and geometric analysis in general. In addition to its relevance as a field on its own, it acts as a focal point for the interaction between all of these areas, which has yielded farreaching and powerful results. This workshop features a large number of international speakers, who are all wellknown for their work in (differential) geometry, representation theory and/or geometric analysis. This is a great opportunity for anyone interested in these areas to meet and learn from some of the top mathematicians in the world. Students are especially welcome. Registration is free. 

In vitro models of colorectal cancer: why and how? 15:10 Fri 7 Aug, 2015 :: B19 Ingkarni Wardli :: Dr Tamsin Lannagan :: Gastrointestinal Cancer Biology Group, University of Adelaide / SAHMRI
1 in 20 Australians will develop colorectal cancer (CRC) and it is the second most common cause of cancer death. Similar to many other cancer types, it is the metastases rather than the primary tumour that are lethal, and prognosis is defined by Ã¢ÂÂhow farÃ¢ÂÂ the tumour has spread at time of diagnosis. Modelling in vivo behavior through rapid and relatively inexpensive in vitro assays would help better target therapies as well as help develop new treatments. One such new in vitro tool is the culture of 3D organoids. Organoids are a biologically stable means of growing, storing and testing treatments against bowel cancer. To this end, we have just set up a human colorectal organoid bank across Australia. This consortium will help us to relate in vitro growth patterns to in vivo behaviour and ultimately in the selection of patients for personalized therapies. Organoid growth, however, is complex. There appears to be variable growth rates and growth patterns. Together with members of the ECMS we recently gained funding to better quantify and model spatial structures in these colorectal organoids. This partnership will aim to directly apply the expertise within the ECMS to patient care. 

A relaxed introduction to resamplingbased multiple testing 12:10 Mon 10 Aug, 2015 :: Benham Labs G10 :: Ngoc Vo :: University of Adelaide
Media...Pvalues and false positives are two phrases that you commonly see thrown around in scientific literature. More often than not, experimenters and analysts are required to quote pvalues as a measure of statistical significance â how strongly does your evidence support your hypothesis? But what happens when this "strong evidence" is just a coincidence? What happens if you have lots of theses hypotheses â up to tens of thousands â to test all at the same time and most of your significant findings end up being just "coincidences"? 

Modelling terrorism risk  can we predict future trends? 12:10 Mon 10 Aug, 2015 :: Benham Labs G10 :: Stephen Crotty :: University of Adelaide
Media...As we are all aware, the incidence of terrorism is increasing in the world today. This is confirmed when viewing terrorism events since 1970 as a time series. Can we model this increasing trend and use it to predict terrorism events in the future? Probably not, but we'll give it a go anyway. 

Vanishing lattices and moduli spaces 12:10 Fri 28 Aug, 2015 :: Ingkarni Wardli B17 :: David Baraglia :: The University of Adelaide
Media...Vanishing lattices are symplectic analogues of root systems. As with roots systems, they admit a classification in terms of certain Dynkin diagrams (not the usual ones from Lie theory). In this talk I will discuss this classification and if there is time I will outline my work (in progress) showing that the monodromy of the SL(n,C) Hitchin fibration is essentially a vanishing lattice. 

Bezout's Theorem 12:10 Mon 7 Sep, 2015 :: Benham Labs G10 :: David Bowman :: University of Adelaide
Media...Generically, a line intersects a parabola at two distinct points. BezoutÃ¢ÂÂs theorem generalises this idea to the intersection of two arbitrary polynomial plane curves. We discuss exceptional cases and how they are corrected by introducing the notion of multiplicity and by extending the plane to projective space. We shall also discuss applications, time permitting.


Tduality and bulkboundary correspondence 12:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B17 :: Guo Chuan Thiang :: The University of Adelaide
Media...Bulkboundary correspondences in physics can be modelled as topological boundary homomorphisms in Ktheory, associated to an extension of a "bulk algebra" by a "boundary algebra". In joint work with V. Mathai, such bulkboundary maps are shown to Tdualize into simple restriction maps in a large number of cases, generalizing what the Fourier transform does for ordinary functions. I will give examples, involving both complex and real Ktheory, and explain how these results may be used to study topological phases of matter and Dbrane charges in string theory. 

Queues and cooperative games 15:00 Fri 18 Sep, 2015 :: Ingkarni Wardli B21 :: Moshe Haviv :: Department of Statistics and the Federmann Center for the Study of Rationality, The Hebrew Universit
Media...The area of cooperative game theory deals with models in which a number of individuals, called players, can form coalitions so as to improve the utility of its members. In many cases, the formation of the grand coalition is a natural result of some negotiation or a bargaining procedure.
The main question then is how the players should split the gains due to their cooperation among themselves. Various solutions have been suggested among them the Shapley value, the nucleolus and the core.
Servers in a queueing system can also join forces. For example, they can exchange service capacity among themselves or serve customers who originally seek service at their peers. The overall performance improves and the question is how they should split the gains, or,
equivalently, how much each one of them needs to pay or be paid in order to cooperate with the others. Our major focus is in the core of the resulting cooperative game and in showing that in many queueing games the core is not empty.
Finally, customers who are served by the same server can also be looked at as players who form a grand coalition, now inflicting damage on each other in the form of additional waiting time. We show how cooperative game theory, specifically the AumannShapley prices, leads to a way in which this damage can be attributed to individual customers or groups of customers. 

Predicting the Winning Time of a Stage of the Tour de France 12:10 Mon 21 Sep, 2015 :: Benham Labs G10 :: Nic Rebuli :: University of Adelaide
Media...Sports can be lucrative, especially popular ones. But for all of us mere mortals, the only money we will ever glean from sporting events is through gambling (responsibly). When it comes to cycling, people generally choose their favourites based on individual and team performance, throughout the world cycling calendar. But what can be said for the duration of a given stage or the winning time of the highly sort after General Classification? In this talk I discuss a basic model for predicting the winning time of the Tour de France. I then apply this model to predicting the outcome of the 2012 and 2013 Tour de France and discuss the results in context. 

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.


Real Lie Groups and Complex Flag Manifolds 12:10 Fri 9 Oct, 2015 :: Ingkarni Wardli B17 :: Joseph A. Wolf :: University of California, Berkeley
Media...Let G be a complex simple direct limit group. Let G_R be a real form of G that corresponds to an hermitian symmetric space. I'll describe the corresponding bounded symmetric domain in the context of the Borel embedding, Cayley transforms, and the BergmanShilov boundary. Let Q be a parabolic subgroup of G. In finite dimensions this means that G/Q is a complex projective variety, or equivalently has a Kaehler metric invariant under a maximal compact subgroup of G. Then I'll show just how the bounded symmetric domains describe cycle spaces for open G_R orbits on G/Q. These cycle spaces include the complex bounded symmetric domains. In finite dimensions they are tightly related to moduli spaces for compact Kaehler manifolds and to representations of semisimple Lie groups; in infinite dimensions there are more problems than answers. Finally, time permitting, I'll indicate how some of this goes over to real and to quaternionic bounded symmetric domains.


Modelling Directionality in Stationary Geophysical Time Series 12:10 Mon 12 Oct, 2015 :: Benham Labs G10 :: Mohd Mahayaudin Mansor :: University of Adelaide
Media...Many time series show directionality inasmuch as plots against time and against timetogo are qualitatively different, and there is a range of statistical tests to quantify this effect. There are two strategies for allowing for directionality in time series models. Linear models are reversible if and only if the noise terms are Gaussian, so one strategy is to use linear models with nonGaussian noise. The alternative is to use nonlinear models. We investigate how nonGaussian noise affects directionality in a first order autoregressive process AR(1) and compare this with a threshold autoregressive model with two thresholds. The findings are used to suggest possible improvements to an AR(9) model, identified by an AIC criterion, for the average yearly sunspot numbers from 1700 to 1900. The improvement is defined in terms of onestepahead forecast errors from 1901 to 2014. 

ChernSimons classes on loop spaces and diffeomorphism groups 12:10 Fri 16 Oct, 2015 :: Ingkarni Wardli B17 :: Steve Rosenberg :: Boston University
Media...Not much is known about the topology of the diffeomorphism group Diff(M) of manifolds M of dimension four and higher. We'll show that for a class of manifolds of dimension 4k+1, Diff(M) has infinite fundamental group. This is proved by translating the problem into a question about ChernSimons classes on the tangent bundle to the loop space LM. To build the CS classes, we use a family of metrics on LM associated to a Riemannian metric on M. The curvature of these metrics takes values in an algebra of pseudodifferential operators. The main technical step in the CS construction is to replace the ordinary matrix trace in finite dimensions with the Wodzicki residue, the unique trace on this algebra. The moral is that some techniques in finite dimensional Riemannian geometry can be extended to some examples in infinite dimensional geometry.


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. 

Nearmotiontrapping in rings of cylinders (and why this is the worst possible wave energy device) 15:10 Fri 30 Oct, 2015 :: Ingkarni Wardli B21 :: Dr Hugh Wolgamot :: University of Western Australia
Motion trapping structures can oscillate indefinitely when floating in an ideal fluid. This talk discusses a simple structure which is predicted to have very close to perfect trapping behaviour, where the structure has been investigated numerically and (for the first time) experimentally. While endless oscillations were evidently not observed experimentally, remarkable differences between 'tuned' and 'detuned' structures were still apparent, and simple theory is sufficient to explain much of the behaviour. A connection with wave energy will be briefly explored, though the link is not fruitful! 

Ocean dynamics of Gulf St Vincent: a numerical study 12:10 Mon 2 Nov, 2015 :: Benham Labs G10 :: Henry Ellis :: University of Adelaide
Media...The aim of this research is to determine the physical dynamics of ocean circulation within Gulf St. Vincent, South Australia, and the exchange of momentum, nutrients, heat, salt and other water properties between the gulf and shelf via Investigator Strait and Backstairs Passage. The project aims to achieve this through the creation of highresolution numerical models, combined with new and historical observations from a moored instrument package, satellite data, and shipboard surveys.
The quasirealistic highresolution models are forced using boundary conditions generated by existing larger scale ROMS models, which in turn are forced at the boundary by a global model, creating a global to regional to local model network. Climatological forcing is done using European Centres for Medium range Weather Forecasting (ECMWF) data sets and is consistent over the regional and local models. A series of conceptual models are used to investigate the relative importance of separate physical processes in addition to fully forced quasirealistic models.
An outline of the research to be undertaken is given:
ÃÂ¢ÃÂÃÂ¢ Connectivity of Gulf St. Vincent with shelf waters including seasonal variation due to wind and thermoclinic patterns;
ÃÂ¢ÃÂÃÂ¢ The role of winter time cooling and formation of eddies in flushing the gulf;
ÃÂ¢ÃÂÃÂ¢ The formation of a temperature front within the gulf during summer time; and
ÃÂ¢ÃÂÃÂ¢ The connectivity and importance of nutrient rich, cool, water upwelling from the Bonney Coast with the gulf via Backstairs Passage during summer time. 

Modelling Coverage in RNA Sequencing 09:00 Mon 9 Nov, 2015 :: Ingkarni Wardli 5.57 :: Arndt von Haeseler :: Max F Perutz Laboratories, University of Vienna
Media...RNA sequencing (RNAseq) is the method of choice for measuring the expression of RNAs in a cell population. In an RNAseq experiment, sequencing the full length of larger RNA molecules requires fragmentation into smaller pieces to be compatible with limited read lengths of most deepsequencing technologies. Unfortunately, the issue of nonuniform coverage across a genomic feature has been a concern in RNAseq and is attributed to preferences for certain fragments in steps of library preparation and sequencing. However, the disparity between the observed nonuniformity of read coverage in RNAseq data and the assumption of expected uniformity elicits a query on the read coverage profile one should expect across a transcript, if there are no biases in the sequencing protocol. We propose a simple model of unbiased fragmentation where we find that the expected coverage profile is not uniform and, in fact, depends on the ratio of fragment length to transcript length. To compare the nonuniformity proposed by our model with experimental data, we extended this simple model to incorporate empirical attributes matching that of the sequenced transcript in an RNAseq experiment. In addition, we imposed an experimentally derived distribution on the frequency at which fragment lengths occur.
We used this model to compare our theoretical prediction with experimental data and with the uniform coverage model. If time permits, we will also discuss a potential application of our model. 

Weak globularity in homotopy theory and higher category theory 12:10 Thu 12 Nov, 2015 :: Ingkarni Wardli B19 :: Simona Paoli :: University of Leicester
Media...Spaces and homotopy theories are fundamental objects of study of algebraic topology. One way to study these objects is to break them into smaller components with the Postnikov decomposition. To describe such decomposition purely algebraically we need higher categorical structures. We describe one approach to modelling these structures based on a new paradigm to build weak higher categories, which is the notion of weak globularity. We describe some of their connections to both homotopy theory and higher category theory. 

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

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

A SemiMarkovian Modeling of Limit Order Markets 13:00 Fri 11 Dec, 2015 :: Ingkarni Wardli 5.57 :: Anatoliy Swishchuk :: University of Calgary
Media...R. Cont and A. de Larrard (SIAM J. Financial Mathematics, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by empirical observations, we extend their framework to 1) arbitrary distributions for book events interarrival times (possibly nonexponential) and 2) both the nature of a new book event and its corresponding interarrival time depend on the nature of the previous book event. We do so by resorting to Markov renewal processes to model the dynamics of the bid and ask queues. We keep analytical tractability via explicit expressions for the Laplace transforms of various quantities of interest. Our approach is justified and illustrated by calibrating the model to the five stocks Amazon, Apple, Google, Intel and Microsoft on June 21st 2012. As in Cont and Larrard, the bidask spread remains constant equal to one tick, only the bid and ask queues are modelled (they are independent from each other and get reinitialized after a price change), and all orders have the same size. (This talk is based on our joint paper with Nelson Vadori (Morgan Stanley)). 

Tduality for elliptic curve orientifolds 12:10 Fri 4 Mar, 2016 :: Ingkarni Wardli B17 :: Jonathan Rosenberg :: University of Maryland
Media...Orientifold string theories are quantum field theories based on the
geometry of a space with an involution. Tdualities are certain
relationships between such theories that look different
on the surface but give rise to the same observable physics.
In this talk I will not assume
any knowledge of physics but will concentrate on the associated
geometry, in the case where the underlying space is a (complex)
elliptic curve and the involution is either holomorphic or
antiholomorphic. The results blend algebraic topology
and algebraic geometry. This is mostly joint work with
Chuck Doran and Stefan MendezDiez. 

The parametric hprinciple for minimal surfaces in R^n and null curves in C^n 12:10 Fri 11 Mar, 2016 :: Ingkarni Wardli B17 :: Finnur Larusson :: University of Adelaide
Media... I will describe new joint work with Franc Forstneric (arXiv:1602.01529). This work brings together four diverse topics from differential geometry, holomorphic geometry, and topology; namely the theory of minimal surfaces, Oka theory, convex integration theory, and the theory of absolute neighborhood retracts. Our goal is to determine the rough shape of several infinitedimensional spaces of maps of geometric interest. It turns out that they all have the same rough shape. 

Expanding maps 12:10 Fri 18 Mar, 2016 :: Eng & Maths EM205 :: Andy Hammerlindl :: Monash University
Media...Consider a function from the circle to itself such that the derivative is
greater than one at every point. Examples are maps of the form f(x) = mx for
integers m > 1. In some sense, these are the only possible examples. This
fact and the corresponding question for maps on higher dimensional manifolds
was a major motivation for Gromov to develop pioneering results in the field
of geometric group theory.
In this talk, I'll give an overview of this and other results relating
dynamical systems to the geometry of the manifolds on which they act and
(time permitting) talk about my own work in the area.


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. 

How predictable are you? Information and happiness in social media. 12:10 Mon 21 Mar, 2016 :: Ingkarni Wardli Conference Room 715 :: Dr Lewis Mitchell :: School of Mathematical Sciences
Media...The explosion of ``Big Data'' coming from online social networks and the like has opened up the new field of ``computational social science'', which applies a quantitative lens to problems traditionally in the domain of psychologists, anthropologists and social scientists. What does it mean to be influential? How do ideas propagate amongst populations? Is happiness contagious? For the first time, mathematicians, statisticians, and computer scientists can provide insight into these and other questions. Using data from social networks such as Facebook and Twitter, I will give an overview of recent research trends in computational social science, describe some of my own work using techniques like sentiment analysis and information theory in this realm, and explain how you can get involved with this highly rewarding research field as well.


Counting periodic points of plane Cremona maps 12:10 Fri 1 Apr, 2016 :: Eng & Maths EM205 :: Tuyen Truong :: University of Adelaide
Media...In this talk, I will present recent results, join with TienCuong Dinh and VietAnh Nguyen, on counting periodic points of plane Cremona maps (i.e. birational maps of P^2). The tools used include a Lefschetz fixed point formula of Saito, Iwasaki and Uehara for birational maps of surface whose fixed point set may contain curves; a bound on the arithmetic genus of curves of periodic points by Diller, Jackson and Sommerse; a result by Diller, Dujardin and Guedj on invariant (1,1) currents of meromorphic maps of compact Kahler surfaces; and a theory developed recently by Dinh and Sibony for non proper intersections of varieties. Among new results in the paper, we give a complete characterisation of when two positive closed (1,1) currents on a compact Kahler surface behave nicely in the view of Dinh and SibonyÃÂ¢ÃÂÃÂs theory, even if their wedge intersection may not be welldefined with respect to the classical pluripotential theory. Time allows, I will present some generalisations to meromorphic maps (including an upper bound for the number of isolated periodic points which is sometimes overlooked in the literature) and open questions. 

What is your favourite (4 dimensional) shape? 12:10 Mon 4 Apr, 2016 :: Ingkarni Wardli Conference Room 715 :: Dr Raymond Vozzo :: School of Mathematical Sciences
Media...This is a circle, it lives in R^2:
[picture of a circle].
This is a sphere, it lives in R^3:
[picture of a sphere]
In this talk I will (attempt to) give you a picture of what the next shape in this sequence (in R^4) looks like. I will also explain how all of this is related to a very important area of modern mathematics called topology.


Geometric analysis of gaplabelling 12:10 Fri 8 Apr, 2016 :: Eng & Maths EM205 :: Mathai Varghese :: University of Adelaide
Media...Using an earlier result, joint with Quillen, I will formulate a gap labelling conjecture for magnetic Schrodinger operators with smooth aperiodic potentials on Euclidean space. Results in low dimensions will be given, and the formulation of the same problem for certain nonEuclidean spaces will be given if time permits.
This is ongoing joint work with Moulay Benameur.


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.


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.


Algebraic structures associated to Brownian motion on Lie groups 13:10 Thu 16 Jun, 2016 :: Ingkarni Wardli B17 :: Steve Rosenberg :: University of Adelaide / Boston University
Media...In (1+1)d TQFT, products and coproducts are associated to pairs of pants decompositions of Riemann surfaces. We consider a toy model in dimension (0+1) consisting of specific broken paths in a Lie group. The products and coproducts are constructed by a Brownian motion average of holonomy along these paths with respect to a connection on an auxiliary bundle. In the trivial case over the torus, we (seem to) recover the Hopf algebra structure on the symmetric algebra. In the general case, we (seem to) get deformations of this Hopf algebra. This is a preliminary report on joint work with Michael Murray and Raymond Vozzo. 

Etale ideas in topological and algebraic dynamical systems 12:10 Fri 5 Aug, 2016 :: Ingkarni Wardli B18 :: Tuyen Truong :: University of Adelaide
Media...In etale topology, instead of considering open subsets of a space, we consider etale neighbourhoods lying over these open subsets. In this talk, I define an etale analog of dynamical systems: to understand a dynamical system f:(X,\Omega )>(X,\Omega ), we consider other dynamical systems lying over it. I then propose to use this to resolve the following two questions:
Question 1: What should be the topological entropy of a dynamical system (f,X,\Omega ) when (X,\Omega ) is not a compact space?
Question 2: What is the relation between topological entropy of a rational map or correspondence (over a field of arbitrary characteristic) to the pullback on cohomology groups and algebraic cycles?


Approaches to modelling cells and remodelling biological tissues 14:10 Wed 10 Aug, 2016 :: Ingkarni Wardli 5.57 :: Professor Helen Byrne :: University of Oxford
Biological tissues are complex structures, whose evolution is characterised by multiple biophysical processes that act across diverse space and time scales. For example, during normal wound healing, fibroblast cells located around the wound margin exert contractile forces to close the wound while those located in the surrounding tissue synthesise new tissue in response to local growth factors and mechanical stress created by wound contraction. In this talk I will illustrate how mathematical modelling can provide insight into such complex processes, taking my inspiration from recent studies of cell migration, vasculogenesis and wound healing. 

SIR epidemics with stages of infection 12:10 Wed 28 Sep, 2016 :: EM218 :: Matthieu Simon :: Universite Libre de Bruxelles
Media...This talk is concerned with a stochastic model for the spread of an epidemic in a closed homogeneously mixing population. The population is subdivided into three classes of individuals: the susceptibles, the infectives and the removed cases. In short, an infective remains infectious during a random period of time. While infected, it can contact all the susceptibles present, independently of the other infectives. At the end of the infectious period, it becomes a removed case and has no further part in the infection process.
We represent an infectious period as a set of different stages that an infective can go through before being removed. The transitions between stages are ruled by either a Markov process or a semiMarkov process. In each stage, an infective makes contaminations at the epochs of a Poisson process with a specific rate.
Our purpose is to derive closed expressions for a transform of different statistics related to the end of the epidemic, such as the final number of susceptibles and the area under the trajectories of all the infectives. The analysis is performed by using simple matrix analytic methods and martingale arguments. Numerical illustrations will be provided at the end of the talk. 

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. 

Some results on the stability of flat Stokes layers 15:10 Fri 14 Oct, 2016 :: Ingkarni Wardli 5.57 :: Professor Andrew Bassom :: University of Tasmania
The flat Stokes layer is one of the relatively few exact solutions of the incompressible NavierStokes equations. For that reason the temporal stability of the layer has attracted considerable interest over the years. Fortunately, not only is the issue one solely of academic curiosity, but some kind of Stokes layer is likely to be set up at the boundaries of any physical timeperiodic flow making its stability of practical interest as well. In this talk I shall review progress made in the understanding of the linear stability properties of the flow. In particular I will discuss the fact that theoretical predictions of critical conditions are wildly different from those observed in the laboratory. 

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. 

Segregation of particles in incompressible flows due to streamline topology and particleboundary interaction 15:10 Fri 2 Dec, 2016 :: Ingkarni Wardli 5.57 :: Professor Hendrik C. Kuhlmann :: Institute of Fluid Mechanics and Heat Transfer, TU Wien, Vienna, Austria
Media...The incompressible flow in a number of classical benchmark problems (e.g. liddriven cavity, liquid bridge) undergoes an instability from a twodimensional steady to a periodic threedimensional flow, which is steady or in form of a traveling wave, if the Reynolds number is increased. In the supercritical regime chaotic as well as regular (quasiperiodic) streamlines can coexist for a range of Reynolds numbers. The spatial structures of the regular regions in threedimensional NavierStokes flows has received relatively little attention, partly because of the high numerical effort required for resolving these structures. Particles whose density does not differ much from that of the liquid approximately follow the chaotic or regular streamlines in the bulk. Near the boundaries, however, their trajectories strongly deviate from the streamlines, in particular if the boundary (wall or free surface) is moving tangentially. As a result of this particleboundary interaction particles can rapidly segregate and be attracted to periodic or quasiperiodic orbits, yielding particle accumulation structures (PAS). The mechanism of PAS will be explained and results from experiments and numerical modelling will be presented to demonstrate the generic character of the phenomenon. 

An equivariant parametric Oka principle for bundles of homogeneous spaces 12:10 Fri 3 Mar, 2017 :: Napier 209 :: Finnur Larusson :: University of Adelaide
I will report on new joint work with Frank Kutzschebauch and Gerald Schwarz (arXiv:1612.07372). Under certain conditions, every continuous section of a holomorphic fibre bundle can be deformed to a holomorphic section. In fact, the inclusion of the space of holomorphic sections into the space of continuous sections is a weak homotopy equivalence. What if a complex Lie group acts on the bundle and its sections? We have proved an analogous result for equivariant sections. The result has a wide scope. If time permits, I will describe some interesting special cases and mention two applications. 

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. 

What is index theory? 12:10 Tue 21 Mar, 2017 :: Inkgarni Wardli 5.57 :: Dr Peter Hochs :: School of Mathematical Sciences
Media...Index theory is a link between topology, geometry and analysis. A typical theorem in index theory says that two numbers are equal: an analytic index and a topological index. The first theorem of this kind was the index theorem of Atiyah and Singer, which they proved in 1963. Index theorems have many applications in maths and physics. For example, they can be used to prove that a differential equation must have a solution. Also, they imply that the topology of a space like a sphere or a torus determines in what ways it can be curved. Topology is the study of geometric properties that do not change if we stretch or compress a shape without cutting or glueing. Curvature does change when we stretch something out, so it is surprising that topology can say anything about curvature. Index theory has many surprising consequences like this.


Minimal surfaces and complex analysis 12:10 Fri 24 Mar, 2017 :: Napier 209 :: Antonio Alarcon :: University of Granada
Media...A surface in the Euclidean space R^3 is said to be minimal if it is locally areaminimizing, meaning that every point in the surface admits a compact neighborhood with the least area among all the surfaces with the same boundary. Although the origin of minimal surfaces is in physics, since they can be realized locally as soap films, this family of surfaces lies in the intersection of many fields of mathematics. In particular, complex analysis in one and several variables plays a fundamental role in the theory. In this lecture we will discuss the influence of complex analysis in the study of minimal surfaces. 

Geometric structures on moduli spaces 12:10 Fri 31 Mar, 2017 :: Napier 209 :: Nicholas Buchdahl :: University of Adelaide
Media...Moduli spaces are used to classify various kinds of objects,
often arising from solutions of certain differential equations on
manifolds; for example, the complex structures on a compact
surface or the antiselfdual YangMills equations on an oriented
smooth 4manifold. Sometimes these moduli spaces carry important
information about the underlying manifold, manifested most
clearly in the results of Donaldson and others on the topology of
smooth 4manifolds. It is also the case that these moduli spaces
themselves carry interesting geometric structures; for example,
the WeilPetersson metric on moduli spaces of compact Riemann
surfaces, exploited to great effect by Maryam Mirzakhani. In this
talk, I shall elaborate on the theme of geometric structures on
moduli spaces, with particular focus on some recentish work done
in conjunction with Georg Schumacher. 

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. 

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

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

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. 

Curvature contraction of axially symmetric hypersurfaces in the sphere 12:10 Fri 4 Aug, 2017 :: Engineering Sth S111 :: James McCoy :: University of Wollongong
Media...We show that convex surfaces in an ambient threesphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of S^{n+1}. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature. 

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. 

Timereversal symmetric topology from physics 12:10 Fri 25 Aug, 2017 :: Engineering Sth S111 :: Guo Chuan Thiang :: University of Adelaide
Media...Timereversal plays a crucial role in experimentally discovered topological insulators (2008) and semimetals (2015). This is mathematically interesting because one is forced to use "Quaternionic" characteristic classes and differential topology  a previously illmotivated generalisation. Guided by physical intuition, an equivariant PoincareLefschetz duality, Euler structures, and a new type of monopole with torsion charge, will be introduced. 

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

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

Equivariant formality of homogeneous spaces 12:10 Fri 29 Sep, 2017 :: Engineering Sth S111 :: Alex ChiKwong Fok :: University of Adelaide
Equivariant formality, a notion in equivariant topology introduced by GoreskyKottwitzMacpherson, is a desirable property of spaces with group actions, which allows the application of localisation formula to evaluate integrals of any top closed forms and enables one to compute easily the equivariant cohomology. Broad classes of spaces of especial interest are wellknown to be equivariantly formal, e.g., compact symplectic manifolds equipped with Hamiltonian compact Lie group actions and projective varieties equipped with linear algebraic torus actions, of which flag varieties are examples. Less is known about compact homogeneous spaces G/K equipped with the isotropy action of K, which is not necessarily of maximal rank. In this talk we will review previous attempts of characterizing equivariant formality of G/K, and present our recent results on this problem using an analogue of equivariant formality in Ktheory. Part of the work presented in this talk is joint with Jeffrey Carlson. 

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. 

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. 

Springer correspondence for symmetric spaces 12:10 Fri 17 Nov, 2017 :: Engineering Sth S111 :: Ting Xue :: University of Melbourne
Media...The Springer theory for reductive algebraic groups plays an important role in representation theory. It relates nilpotent orbits in the Lie algebra to irreducible representations of the Weyl group. We develop a Springer theory in the case of symmetric spaces using Fourier transform, which relates nilpotent orbits in this setting to irreducible representations of Hecke algebras of various Coxeter groups with specified parameters. This in turn gives rise to character sheaves on symmetric spaces, which we describe explicitly in the case of classical symmetric spaces. A key ingredient in the construction is the nearby cycle sheaves associated to the adjoint quotient map. The talk is based on joint work with Kari Vilonen and partly based on joint work with Misha Grinberg and Kari Vilonen. 

Radial Toeplitz operators on bounded symmetric domains 11:10 Fri 9 Mar, 2018 :: Lower Napier LG11 :: Raul QuirogaBarranco :: CIMAT, Guanajuato, Mexico
Media...The Bergman spaces on a complex domain are defined as the space of holomorphic squareintegrable functions on the domain. These carry interesting structures both for analysis and representation theory in the case of bounded symmetric domains. On the other hand, these spaces have some bounded operators obtained as the composition of a multiplier operator and a projection. These operators are highly noncommuting between each other. However, there exist large commutative C*algebras generated by some of these Toeplitz operators very much related to Lie groups. I will construct an example of such C*algebras and provide a fairly explicit simultaneous diagonalization of the generating Toeplitz operators. 

Family gauge theory and characteristic classes of bundles of 4manifolds 13:10 Fri 16 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Hokuto Konno :: University of Tokyo
Media...I will define a nontrivial characteristic class of bundles of
4manifolds using families of SeibergWitten equations. The basic idea
of the construction is to consider an infinite dimensional
analogue of the Euler class used in the usual theory of characteristic
classes. I will also explain how to prove the nontriviality of this
characteristic class. If time permits, I will mention a relation between
our characteristic class and positive scalar curvature metrics. 

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. 

The topology and geometry of spaces of YangMillsHiggs flow lines 11:10 Fri 27 Jul, 2018 :: Barr Smith South Polygon Lecture theatre :: Graeme Wilkin :: National University of Singapore
Given a smooth complex vector bundle over a compact Riemann surface, one can define the space of Higgs bundles and an energy functional on this space: the YangMillsHiggs functional. The gradient flow of this functional resembles a nonlinear heat equation, and the limit of the flow detects information about the algebraic structure of the initial Higgs bundle (e.g. whether or not it is semistable). In this talk I will explain my work to classify ancient solutions of the YangMillsHiggs flow in terms of their algebraic structure, which leads to an algebrogeometric classification of YangMillsHiggs flow lines. Critical points connected by flow lines can then be interpreted in terms of the Hecke correspondence, which appears in Wittenâs recent work on Geometric Langlands. This classification also gives a geometric description of spaces of unbroken flow lines in terms of secant varieties of the underlying Riemann surface, and in the remaining time I will describe work in progress to relate the (analytic) Morse compactification of these spaces by broken flow lines to an algebrogeometric compactification by iterated blowups of secant varieties. 

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. 

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. 

An Introduction to Ricci Flow 11:10 Fri 19 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg
In these three talks we give an introduction to Ricci flow and present some applications thereof.
After introducing the Ricci flow we present some theorems and arguments from the theory of linear and nonlinear parabolic equations. We explain why this theory guarantees that there is always a solution to the Ricci flow for a short time for any given smooth initial metric on a compact manifold without boundary.
We calculate evolution equations for certain geometric quantities, and present some examples of maximum principle type arguments. In the last lecture we present some geometric results which are derived with the help of the Ricci flow. 

Some advances in the formulation of analytical methods for linear and nonlinear dynamics 15:10 Tue 20 Nov, 2018 :: EMG07 :: Dr Vladislav Sorokin :: University of Auckland
In the modern engineering, it is often necessary to solve problems involving strong parametric excitation and (or) strong nonlinearity. Dynamics of micro and nanoscale electromechanical systems, wave propagation in structures made of corrugated composite materials are just examples of those. Numerical methods, although able to predict systems behavior for specific sets of parameters, fail to provide an insight into underlying physics. On the other hand, conventional analytical methods impose severe restrictions on the problem parameters space and (or) on types of the solutions.
Thus, the quest for advanced tools to deal with linear and nonlinear structural dynamics still continues, and the lecture is concerned with an advanced formulation of an analytical method. The principal novelty aspect is that the presence of a small parameter in governing equations is not requested, so that dynamic problems involving strong parametric excitation and (or) strong nonlinearity can be considered. Another advantage of the method is that it is free from conventional restrictions on the excitation frequency spectrum and applicable for problems involving combined multiple parametric and (or) direct excitations with incommensurate frequencies, essential for some applications.
A use of the method will be illustrated in several examples, including analysis of the effects of corrugation shapes on dispersion relation and frequency bandgaps of structures and dynamics of nonlinear parametric amplifiers. 
News matching "Timereversal symmetric topology from physics" 
Stoneham Prize The inaugural Stoneham Prize, awarded for the best poster by a graduate student in the first two years of their candidature, was awarded on the 4th of April. The winner was Ric Green, for his poster "What is Geometry?". Two Viewers' Choice prizes were also awarded to Ray Vozzo for his poster "The 7 Bridges of Koenigsberg  The 1st Theorem in Topology" and David Butler for his poster "The Queen of Hearts Plays Noughts and Crosses". Posted Sun 13 Apr 08. 

Australian Research Council Discovery Project Successes Congratulations to the following members of the School for their
success in the ARC Discovery Grants which were announced recently.
 A/Prof M Roughan; Prof H Shen $315K Network Management in a World of Secrets
 Prof AJ Roberts; Dr D Strunin $315K
Effective and accurate model dynamics, deterministic and stochastic,
across multiple space and time scales
 A/Prof J Denier; Prof AP Bassom $180K A novel approach to controlling boundarylayer separation
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... 

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

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

ARC Future Fellowship success Associate Professor Zudi Lu has been awarded an ARC Future Fellowship. Associate Professor Lu, and Associate Professor in Statistics, will use the support provided by his Future Fellowship to further improve the theory and practice of econometric modelling of nonlinear spatial time series. Congratulations Zudi. Posted Thu 12 May 11. 

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

Noncommutative correspondences, duality and Dbranes in bivariant Ktheory Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009  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  Model dynamics across multiple length and time scales on a spatial multigrid Roberts, Anthony John, Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal 7 (1525–1548) 2009  Node localisation in wireless ad hoc networks using time difference of arrival Arnold, Jonathan; Bean, Nigel, 2nd International Conference on Signal Processing and Communication Systems, Gold Coast 15/12/08  A spacetime NeymanScott rainfall model with defined storm extent Leonard, Michael; Lambert, Martin; Metcalfe, Andrew; Cowpertwait, P, Water Resources Research 44 (9402–9402) 2008  Dbranes, KKtheory and duality on noncommutative spaces Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Journal of Physics: Conference Series (Print Edition) 103 (1–13) 2008  Dbranes, RRfields and duality on noncommutative manifolds Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Communications in Mathematical Physics 277 (643–706) 2008  Discretetime expectation maximization algorithms for Markovmodulated poisson processes Elliott, Robert; Malcolm, William, IEEE Transactions on Automatic Control 53 (247–256) 2008  Gene profiling for determining pluripotent genes in a time course microarray experiment Tuke, Simon; Glonek, Garique; Solomon, Patricia, Biostatistics 10 (80–93) 2008  Modelling survival in acute severe illness: Cox versus accelerated failure time models Moran, John; Bersten, A; Solomon, Patricia; Edibam, C; Hunt, T, Journal of Evaluation in Clinical Practice 14 (83–93) 2008  Robust adaptive synchronization of chaotic neural networks by slide technique Lou, X; Cui, B, Chinese Physics B 17 (520–528) 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 basic bundle gerbe on unitary groups Murray, Michael; Stevenson, Daniel, Journal of Geometry and Physics 58 (1571–1590) 2008  Topology of chaotic mixing patterns Thiffeault, J; Finn, Matthew; Gouillart, E; Hall, T, Chaos 18 (0331231–03312316) 2008  Unsteady fronts in the spindown of a fluidfilled torus del Pino, C; Hewitt, R; Clarke, Richard; Mullin, T; Denier, James, Physics of Fluids 20 (1241041–1241045) 2008  Normal form transforms separate slow and fast modes in stochastic dynamical systems Roberts, Anthony John, Physics Letters A 387 (12–38) 2008  The inertial dynamics of thin film flow of nonNewtonian fluids Roberts, Anthony John, Physics Letters A 372 (1607–1611) 2008  Model dynamics on a multigrid across multiple length and time scales Roberts, Anthony John,  Multicast Topology Inference and Its Applications Tian, Hui; Shen, Hong, chapter in Handbook of Approximation Alggorithms and Metaheuristics (Taylor & Francis) 691–6914, 2007  Topology reconstruction and characterisation of wireless ad hoc networks Arnold, Jonathan; Bean, Nigel; Kraetzl, Miro; Roughan, Matthew; Sorell, Matthew, 2007 IEEE International Conference on Communications, Glasgow, Scotland 24/06/07  Implementing a spacetime rainfall model for the Sydney region Leonard, Michael; Metcalfe, Andrew; Lambert, Martin; Kuczera, George, Water Science and Technology 55 (39–47) 2007  Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras Eastwood, Michael; Somberg, P; Soucek, V, Journal of Geometry and Physics 57 (2539–2546) 2007  Spectral curves and the mass of hyperbolic monopoles Norbury, Paul; Romao, Nuno, Communications in Mathematical Physics 270 (295–333) 2007  Statistics in review; Part 2: Generalised linear models, timetoevent and timeseries analysis, evidence synthesis and clinical trials Moran, John; Solomon, Patricia, Critical care and Resuscitation 9 (187–197) 2007  TDuality in type II string theory via noncommutative geometry and beyond Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007  Twodimensional Stokes flow driven by elliptical paddles Cox, Stephen; Finn, Matthew, Physics of Fluids 19 (1131021–11310212) 2007  Computer algebra models dynamics on a multigrid across multiple length and time scales Roberts, Anthony John,  Building an AStopology model that captures route diversity Muhlbauer, W; Feldmann, A; Maennel, Olaf; Roughan, Matthew; Uhlig, S, sigcomm 2006, Pisa, Italy 11/09/06  Can Dbranes wrap nonrepresentable cycles? Evslin, J; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 10 (WWW 1–WWW 10) 2006  Datarecursive smoother formulae for partially observed discretetime Markov chains Elliott, Robert; Malcolm, William, Stochastic Analysis and Applications 24 (579–597) 2006  Duality symmetry and the form fields of Mtheory Sati, Hicham, The Journal of High Energy Physics (Print Edition) 6 (0–10) 2006  Efficient simulation of a spacetime NeymanScott rainfall model Leonard, Michael; Metcalfe, Andrew; Lambert, Martin, Water Resources Research 42 (11503–11503) 2006  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  Nonassociative Tori and Applications to TDuality Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Communications in Mathematical Physics 264 (41–69) 2006  Optimal information transmission in nonlinear arrays through suprathreshold stochastic resonance McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Physics Letters A 352 (183–189) 2006  Quantum Hall effect and noncommutative geometry Carey, Alan; Hannabuss, K; Varghese, Mathai, Journal of Geometry and Symmetry in Physics 6 (16–36) 2006  Reduced models of chemical reaction in chaotic flows Vikhansky, A; Cox, Stephen, Physics of Fluids 18 (37102–37102) 2006  Screen bundles of Lorentzian manifolds and some generalisations of ppwaves Leistner, Thomas, Journal of Geometry and Physics 56 (2117–2134) 2006  Some Penrose transforms in complex differential geometry Anco, S; Bland, J; Eastwood, Michael, Science in China Series AMathematics Physics Astronomy 49 (1599–1610) 2006  Tduality for torus bundles with Hfluxes via noncommutative topology, II: the highdimensional case and the Tduality group Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 2006  The elliptic curves in gauge theory, string theory, and cohomology Sati, Hicham, The Journal of High Energy Physics (Print Edition) 3 (0–19) 2006  The many facets of Internet topology and traffic Alderson, D; Chang, H; Roughan, Matthew; Uhlig, S; Willinger, W, Networks and Heterogeneous Media 1 (569–600) 2006  YangMills theory for bundle gerbes Varghese, Mathai; Roberts, David, Journal of Physics A: Mathematical and Theoretical (Print Edition) 39 (6039–6044) 2006  Exact smoothers for discretetime hybrid stochastic systems Elliott, Robert; Malcolm, William; Dufour, F, The 44th IEEE Conference on Decision and Control and the European Control Conference, Seville, Spain 12/12/05  New Gaussian mixture state estimation schemes for discrete time hybrid GaussMarkov systems Elliott, Robert; Dufour, F; Malcolm, William, The 2005 American Control Conference, Portland, OR, USA 08/06/05  Arithmetic properties of eigenvalues of generalized harper operators on graphs Dodziuk, Josef; Varghese, Mathai; Yates, Stuart, Communications in Mathematical Physics 262 (269–297) 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  Dynamics of CP1 lumps on a cylinder Romao, Nuno, Journal of Geometry and Physics 54 (42–76) 2005  Examples of unbounded homogeneous domains in complex space Eastwood, Michael; Isaev, A, Science in China Series AMathematics Physics Astronomy 48 (248–261) 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  Hidden Markov filter estimation of the occurrence time of an event in a financial market Elliott, Robert; Tsoi, A, Stochastic Analysis and Applications 23 (1165–1177) 2005  Mtheory and characteristic classes Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (0201–0208) 2005  Risksensitive filtering and smoothing for continuoustime Markov processes Malcolm, William; Elliott, Robert; James, M, IEEE Transactions on Information Theory 51 (1731–1738) 2005  State and mode estimation for discretetime jump Markov systems Elliott, Robert; Dufour, F; Malcolm, William, Siam Journal on Control and Optimization 44 (1081–1104) 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  The dominant wave mode within a trailing line vortex Denier, James; Stott, Jillian, Physics of Fluids 17 (141011–141019) 2005  The index of projective families of elliptic operators Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 2005  Type II string theory and modularity Kriz, I; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (0381–03830) 2005  Type IIB string theory, Sduality, and generalized cohomology Kriz, I; Sati, Hicham, Nuclear Physics B 715 (639–664) 2005  Optimal nose shaping for delayed boundarylayer separation in laminar planesymmetric and axisymmetric flow Mattner, Trent; Tuck, Ernest; Denier, James, ANZIAM Applied Mathematics Conference (41st: 2005: Hawke's Bay, N.Z.), Napier, New Zealand 31/01/05  Dixmier traces as singular symmetric functionals and applications to measurable operators Lord, Steven; Sedaev, A; Sukochev, F, Journal of Functional Analysis 224 (72–106) 2005  Filtering, smoothing and Mary detection with discrete time poisson observations Elliott, Robert; Malcolm, William; Aggoun, L, Stochastic Analysis and Applications 23 (939–952) 2005  Finitedimensional filtering and control for continuoustime nonlinear systems Elliott, Robert; Aggoun, L; Benmerzouga, A, Stochastic Analysis and Applications 22 (499–505) 2005  Impinging laminar jets at moderate Reynolds numbers and separation distances Bergthorson, J; Sone, K; Mattner, Trent; Dimotakis, P; Goodwin, D; Meiron, D, Physical Review E. (Statistical, Nonlinear, and Soft Matter Physics) 72 (0663071–06630712) 2005  Optimal nose shaping for delayed boundarylayer separation in laminar planesymmetric and axisymmetric flow Mattner, Trent; Tuck, Ernest; Denier, James, 15th Australasian Fluid Mechanics Conference 2004, Sydney, Australia 13/12/04  A sufficient condition for the uniform exponential stability of timevarying systems with noise Grammel, G; Maizurna, Isna, Nonlinear AnalysisTheory Methods & Applications 56 (951–960) 2004  Factorial and time course designs for cDNA microarray experiments Glonek, Garique; Solomon, Patricia, Biostatistics 5 (89–111) 2004  Holonomy on Dbranes Carey, Alan; Johnson, Stuart; Murray, Michael, Journal of Geometry and Physics 52 (186–216) 2004  Mtheory, type IIA superstrings, and elliptic cohomology Kriz, I; Sati, Hicham, Advances in Theoretical and Mathematical Physics 8 (345–394) 2004  Quantum discontinuity for massive spin3/2 with a L term Duff, M; Liu, J; Sati, Hicham, Nuclear Physics B 680 (117–130) 2004  Some relations between twisted Ktheory and E8 gauge theory Varghese, Mathai; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 22) 2004  SwiftHohenberg model for magnetoconvection Cox, Stephen; Matthews, P; Pollicott, S, Physical Review E. (Statistical, Nonlinear, and Soft Matter Physics) 69 (0663141–06631414) 2004  Tduality for principal torus bundles Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 10) 2004  Tduality: Topology change from Hflux Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Communications in Mathematical Physics 249 (383–415) 2004  The envelope of a onedimensional pattern in the presence of a conserved quantity Cox, Stephen, Physics Letters A 333 (91–101) 2004  Topology and Hflux of Tdual manifolds Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Physical Review Letters 92 (1816011–1816013) 2004  Development of NonHomogeneous and Hierarchical Hidden Markov Models for Modelling Monthly Rainfall and Streamflow Time Series Whiting, Julian; Lambert, Martin; Metcalfe, Andrew; Kuczera, George, World Water and Environmental Resources Congress (2004), Salt Lake City, Utah, USA 27/06/04  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  Robust Mary detection filters and smoothers for continuoustime jump Markov systems Elliott, Robert; Malcolm, William, IEEE Transactions on Automatic Control 49 (1046–1055) 2004  Some relations between twisted Ktheory and E8 gauge theory Mathai, V; Sati, Hicham, The Journal of High Energy Physics (Online Editions) (WWW1–WWW22) 2004  Arborescences, matrixtrees and the accumulated sojourn time in a Markov process Pearce, Charles; Falzon, L, chapter in Stochastic analysis and applications Volume 3 (Nova Science Publishers) 147–168, 2003  A note on monopole moduli spaces Murray, Michael; Singer, Michael, Journal of Mathematical Physics 44 (3517–3531) 2003  Chern character in twisted Ktheory: Equivariant and holomorphic cases Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003  Higgs fields, bundle gerbes and string structures Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 243 (541–555) 2003  Type1 Dbranes in an Hflux and twisted KOtheory Varghese, Mathai; Murray, Michael; Stevenson, Daniel, The Journal of High Energy Physics (Online Editions) 11 (www 1–www 22) 2003  On the numerical stability of timediscretised state estimation via Clark transformations Malcolm, William; Elliott, Robert; Van Der Hoek, John, 42nd IEEE Conference on Decision and Control (2003), Maui, Hawaii 09/12/03  Traffic matrices and network topology Roughan, Matthew, UCLA IPAM Workshop (2003: Lake Arrowhead, CA, USA), Los Angeles, CA, USA 28/09/03  The geometry and physics of the SeibergWitten equations Wu, Siye, chapter in Geometric analysis and applications to quantum field theory (Birkhauser) 157–203, 2002  Axial anomaly and topological charge in lattice gauge theory with overlap dirac operator Adams, Damian, Annals of Physics 296 (131–151) 2002  Families index theory for Overlap lattice Dirac operator. I Adams, Damian, Nuclear Physics B 624 (469–484) 2002  Families index theory, gauge fixing, and topology of the space of latticegauge fields: a summary Adams, Damian, Nuclear Physics BProceedings Supplements 109A (77–80) 2002  Online almostsure parameter estimation for partially observed discretetime linear systems with known noise characteristics Elliott, Robert; Ford, J; Moore, J, International Journal of Adaptive Control and Signal Processing 16 (435–453) 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  Robust continuoustime smoothers without twosided stochastic integrals Krishnamurthy, V; Elliott, Robert, IEEE Transactions on Automatic Control 47 (1824–1841) 2002  Improved smoother dynamics for discrete time HMM parameter estimation Elliott, Robert; Malcolm, William, The 40th IEEE Conference on Decision and Control (CDC), Orlando, Florida 04/12/01  Robust Mary detection filters for continuoustime jump Markov systems Elliott, Robert; Malcolm, William, The 40th IEEE Conference on Decision and Control (CDC), Orlando, Florida 04/12/01  A proof of Atiyah's conjecture on configurations of four points in Euclidean threespace Eastwood, Michael; Norbury, Paul, Geometry & Topology 5 (885–893) 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  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 the continuum limit of fermionic topological charge in lattice gauge theory Adams, David, Journal of Mathematical Physics 42 (5522–5533) 2001  Regularizing the KdV equation near a blowup surface Joshi, Nalini, Theoretical and Mathematical Physics 127 (744–750) 2001  Twisted index theory on good orbifolds, II: Fractional quantum numbers Marcolli, M; Varghese, Mathai, Communications in Mathematical Physics 217 (55–87) 2001  Formal thickenings of ambitwistors for curved spacetime Eastwood, Michael, chapter in Further advances in twistor theory. Vol. III, Curved twistor spaces (Chapman & Hall/CRC) 117–123, 2001  Hidden state Markov chain time series models for arid zone hydrology Cigizoglu, K; Adamson, Peter; Lambert, Martin; Metcalfe, Andrew, International Symposium on Water Resources and Environmental Impact Assessment (2001), Istanbul, Turkey 11/07/01  Modelling Service Time Distribution in Cellular Networks Using PhaseType Service Distributions Green, David; Asenstorfer, J; Jayasuriya, A,  A continuous time kronecker's lemma and martingale convergence Elliott, Robert, Stochastic Analysis and Applications 19 (433–437) 2001  Information entropy and Parrondo's discretetime ratchet Harmer, Gregory; Abbott, Derek; Taylor, Peter; Pearce, Charles; Parrondo, J, Stochastic and Chaotic Dynamics in the Lakes  STOCHAOS, Ambleside, Cumbria, UK 01/08/99  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 gerbe obstruction to quantization of fermions on odddimensional manifolds with boundary Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 51 (145–160) 2000  A remark of Schwarz's topological field theory Adams, David; Prodanov, E, Letters in Mathematical Physics 51 (249–255) 2000  Bundle gerbes applied to quantum field theory Carey, Alan; Mickelsson, J; Murray, Michael, Reviews in Mathematical Physics 12 (65–90) 2000  DBranes, BFields and twisted Ktheory Bouwknegt, Pier; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (1–11) 2000  Dirac operator index and topology of lattice gauge fields Adams, David, Chinese Journal of Physics 38 (633–646) 2000  Global obstructions to gaugeinvariance in chiral gauge theory on the lattice Adams, David, Nuclear Physics B 589 (633–656) 2000  Length isn't everything  use of the Macedonian sarissa in the time of Alexander the Great Dickinson, Rowland, Journal of Battlefield Technology 3 (51–62) 2000  On a Schwarzian PDE associated with the KdV hierarchy Nijhoff, F; Hone, Andrew; Joshi, Nalini, Physics Letters A 267 (147–156) 2000  On the complete integrability of the discrete Nahm equations Murray, Michael; Singer, Michael, Communications in Mathematical Physics 210 (497–519) 2000  On the discrete and continuous Miura chain associated with the sixth Painlev equation Nijhoff, F; Joshi, Nalini; Hone, Andrew, Physics Letters A 264 (396–406) 2000  Unsteady stenosis flow prediction: a comparative study of nonNewtonian models with operator splitting scheme Siauw, W; Ng, E; Mazumdar, Jagan, Medical Engineering & Physics 22 (265–277) 2000 
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