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Dr Pedram Hekmati
Adjunct Senior Lecturer


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Dr Peter Hochs
Lecturer in Pure Mathematics, Marie Curie Fellowship


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


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Dr Hang Wang
ARC DECRA Fellow


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Events matching "Localised index and L^2-Lefschetz fixed point form"

A Bivariate Zero-inflated Poisson Regression Model and application to some Dental Epidemiological data
14:10 Fri 27 Oct, 2006 :: G08 Mathematics Building University of Adelaide :: University Prof Sudhir Paul

Data in the form of paired (pre-treatment, post-treatment) counts arise in the study of the effects of several treatments after accounting for possible covariate effects. An example of such a data set comes from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Also, these data may show extra pairs of zeros than can be accounted for by a simpler model, such as, a bivariate Poisson regression model. In such situations we propose to use a zero-inflated bivariate Poisson regression (ZIBPR) model for the paired (pre-treatment, posttreatment) count data. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model and develop a procedure for testing treatment effects. The procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post-treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then compare our analysis, of the decayed, missing and filled teeth (DMFT) index data from the caries prevention study, based on the ZIBPR model with the analysis using a zero-inflated Poisson regression model in which the pre-treatment DMFT index is taken to be a covariate
Queues with Advance Reservations
15:10 Fri 21 Sep, 2007 :: G04 Napier Building University of Adelaide :: Prof. Peter Taylor :: Department of Mathematics and Statistics, University of Melbourne

Queues where, on "arrival", customers make a reservation for service at some time in the future are endemic. However there is surprisingly little about them in the literature. Simulations illustrate some interesting implications of the facility to make such reservations. For example introducing independent and identically distributed reservation periods into an Erlang loss system can either increase or decrease the blocking probability from that given by Erlang's formula, despite the fact that the process of 'reserved arrivals' is still Poisson. In this talk we shall discuss a number of ways of looking at such queues. In particular, we shall obtain various transient and stationary distributions associated with the "bookings diary" for the infinite server system. However, this does not immediately answer the question of how to calculate the above-mentioned blocking probabilities. We shall conclude with a few suggestions as to how this calculation might be carried out.
Similarity solutions for surface-tension driven flows
15:10 Fri 14 Mar, 2008 :: LG29 Napier Building University of Adelaide :: Prof John Lister :: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK

The breakup of a mass of fluid into drops is a ubiquitous phenomenon in daily life, the natural environment and technology, with common examples including a dripping tap, ocean spray and ink-jet printing. It is a feature of many generic industrial processes such as spraying, emulsification, aeration, mixing and atomisation, and is an undesirable feature in coating and fibre spinning. Surface-tension driven pinch-off and the subsequent recoil are examples of finite-time singularities in which the interfacial curvature becomes infinite at the point of disconnection. As a result, the flow near the point of disconnection becomes self-similar and independent of initial and far-field conditions. Similarity solutions will be presented for the cases of inviscid and very viscous flow, along with comparison to experiments. In each case, a boundary-integral representation can be used both to examine the time-dependent behaviour and as the basis of a modified Newton scheme for direct solution of the similarity equations.
Puzzle-based learning: Introduction to mathematics
15:10 Fri 23 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Zbigniew Michalewicz :: School of Computer Science, University of Adelaide

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

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

For further information see http://www.PuzzleBasedlearning.edu.au/

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

Sloshing in tanks of liquefied natural gas (LNG) vessels
15:10 Wed 22 Apr, 2009 :: Napier LG29 :: Prof. Frederic Dias :: ENS, Cachan

The last scientific conversation I had with Ernie Tuck was on liquid impact. As a matter of fact, we discussed the paper by J.H. Milgram, Journal of Fluid Mechanics 37 (1969), entitled "The motion of a fluid in a cylindrical container with a free surface following vertical impact." Liquid impact is a key issue in sloshing and in particular in sloshing in tanks of LNG vessels. Numerical simulations of sloshing have been performed by various groups, using various types of numerical methods. In terms of the numerical results, the outcome is often impressive, but the question remains of how relevant these results are when it comes to determining impact pressures. The numerical models are too simplified to reproduce the high variability of the measured pressures. In fact, for the time being, it is not possible to simulate accurately both global and local effects. Unfortunately it appears that local effects predominate over global effects when the behaviour of pressures is considered. Having said this, it is important to point out that numerical studies can be quite useful to perform sensitivity analyses in idealized conditions such as a liquid mass falling under gravity on top of a horizontal wall and then spreading along the lateral sides. Simple analytical models inspired by numerical results on idealized problems can also be useful to predict trends. The talk is organized as follows: After a brief introduction on the sloshing problem and on scaling laws, it will be explained to what extent numerical studies can be used to improve our understanding of impact pressures. Results on a liquid mass hitting a wall obtained by a finite-volume code with interface reconstruction as well as results obtained by a simple analytical model will be shown to reproduce the trends of experiments on sloshing. This is joint work with L. Brosset (GazTransport & Technigaz), J.-M. Ghidaglia (ENS Cachan) and J.-P. Braeunig (INRIA).
Defect formulae for integrals of pseudodifferential symbols: applications to dimensional regularisation and index theory
13:10 Fri 4 Sep, 2009 :: School Board Room :: Prof Sylvie Paycha :: Universite Blaise Pascal, Clermont-Ferrand, France

The ordinary integral on L^1 functions on R^d unfortunately does not extend to a translation invariant linear form on the whole algebra of pseudodifferential symbols on R^d, forcing to work with ordinary linear extensions which fail to be translation invariant. Defect formulae which express the difference between various linear extensions, show that they differ by local terms involving the noncommutative residue. In particular, we shall show how integrals regularised by a "dimensional regularisation" procedure familiar to physicists differ from Hadamard finite part (or "cut-off" regularised) integrals by a residue. When extended to pseudodifferential operators on closed manifolds, these defect formulae express the zeta regularised traces of a differential operator in terms of a residue of its logarithm. In particular, we shall express the index of a Dirac type operator on a closed manifold in terms of a logarithm of a generalized Laplacian, thus giving an a priori local description of the index and shall discuss further applications.
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.
Integrable systems: noncommutative versus commutative
14:10 Thu 4 Mar, 2010 :: School Board Room :: Dr Cornelia Schiebold :: Mid Sweden University

After a general introduction to integrable systems, we will explain an approach to their solution theory, which is based on Banach space theory. The main point is first to shift attention to noncommutative integrable systems and then to extract information about the original setting via projection techniques. The resulting solution formulas turn out to be particularly well-suited to the qualitative study of certain solution classes. We will show how one can obtain a complete asymptotic description of the so called multiple pole solutions, a problem that was only treated for special cases before.
Random walk integrals
13:10 Fri 16 Apr, 2010 :: School Board Room :: Prof Jonathan Borwein :: University of Newcastle

Following Pearson in 1905, we study the expected distance of a two-dimensional walk in the plane with unit steps in random directions---what Pearson called a "ramble". A series evaluation and recursions are obtained making it possible to explicitly determine this distance for small number of steps. Closed form expressions for all the moments of a 2-step and a 3-step walk are given, and a formula is conjectured for the 4-step walk. Heavy use is made of the analytic continuation of the underlying integral.
Topological chaos in two and three dimensions
15:10 Fri 18 Jun, 2010 :: Santos Lecture Theatre :: Dr Matt Finn :: School of Mathematical Sciences

Research into two-dimensional laminar fluid mixing has enjoyed a renaissance in the last decade since the realisation that the Thurston–Nielsen theory of surface homeomorphisms can assist in designing efficient "topologically chaotic" batch mixers. In this talk I will survey some tools used in topological fluid kinematics, including braid groups, train-tracks, dynamical systems and topological index formulae. I will then make some speculations about topological chaos in three dimensions.
Mathematica Seminar
15:10 Wed 28 Jul, 2010 :: Engineering Annex 314 :: Kim Schriefer :: Wolfram Research

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

Counting lattice points in polytopes arises in many areas of pure and applied mathematics. A basic counting problem is this: how many different ways can one give change of 1 dollar into 5,10, 20 and 50 cent coins? This problem counts lattice points in a tetrahedron, and if there also must be exactly 10 coins then it counts lattice points in a triangle. The number of lattice points in polytopes can be used to measure the robustness of a computer network, or in statistics to test independence of characteristics of samples. I will describe the general structure of lattice point counts and the difficulty of calculations. I will then describe a particular lattice point count in which the structure simplifies considerably allowing one to calculate easily. I will spend a brief time at the end describing how this is related to the moduli space of Riemann surfaces.
A spatial-temporal point process model for fine resolution multisite rainfall data from Roma, Italy
14:10 Thu 19 Aug, 2010 :: Napier G04 :: A/Prof Paul Cowpertwait :: Auckland University of Technology

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

The aim of the talk is to give an overview of the noncommutative geometry approach to index theory.
Index theory in Mathematics and Physics
15:10 Fri 20 Aug, 2010 :: Napier G04 :: Prof Alan Carey :: Australian National University

This lecture is a personal (and partly historical) overview in non-technical terms of the topic described in the title, from first year linear algebra to von Neumann algebras.
A polyhedral model for boron nitride nanotubes
15:10 Fri 3 Sep, 2010 :: Napier G04 :: Dr Barry Cox :: University of Adelaide

The conventional rolled-up model of nanotubes does not apply to the very small radii tubes, for which curvature effects become significant. In this talk an existing geometric model for carbon nanotubes proposed by the authors, which accommodates this deficiency and which is based on the exact polyhedral cylindrical structure, is extended to a nanotube structure involving two species of atoms in equal proportion, and in particular boron nitride nanotubes. This generalisation allows the principle features to be included as the fundamental assumptions of the model, such as equal bond length but distinct bond angles and radii between the two species. The polyhedral model is based on the five simple geometric assumptions: (i) all bonds are of equal length, (ii) all bond angles for the boron atoms are equal, (iii) all boron atoms lie at an equal distance from the nanotube axis, (iv) all nitrogen atoms lie at an equal distance from the nanotube axis, and (v) there exists a fixed ratio of pyramidal height H, between the boron species compared with the corresponding height in a symmetric single species nanotube. Working from these postulates, expressions are derived for the various structural parameters such as radii and bond angles for the two species for specific values of the chiral vector numbers (n,m). The new model incorporates an additional constant of proportionality H, which we assume applies to all nanotubes comprising the same elements and is such that H = 1 for a single species nanotube. Comparison with `ab initio' studies suggest that this assumption is entirely reasonable, and in particular we determine the value H = 0.56\pm0.04 for boron nitride, based on computational results in the literature. This talk relates to work which is a couple of years old and given time at the end we will discuss some newer results in geometric models developed with our former student Richard Lee (now also at the University of Adelaide as a post doc) and some work-in-progress on carbon nanocones. Note: pyramidal height is our own terminology and will be explained in the talk.
IGA-AMSI Workshop: Dirac operators in geometry, topology, representation theory, and physics
10:00 Mon 18 Oct, 2010 :: 7.15 Ingkarni Wardli :: Prof Dan Freed :: University of Texas, Austin

Lecture Series by Dan Freed (University of Texas, Austin). Dirac introduced his eponymous operator to describe electrons in quantum theory. It was rediscovered by Atiyah and Singer in their study of the index problem on manifolds. In these lectures we explore new theorems and applications. Several of these also involve K-theory in its recent twisted and differential variations. These lectures will be supplemented by additional talks by invited speakers. For more details, please see the conference webpage: http://www.iga.adelaide.edu.au/workshops/WorkshopOct2010/
The Cauchy integral formula
12:10 Mon 9 May, 2011 :: 5.57 Ingkarni Wardli :: Stephen Wade :: University of Adelaide

In this talk I will explain a simple method used for calculating the Hilbert transform of an analytic function, and provide some assurance that this isn't a bad thing to do in spite of the somewhat ominous presence of infinite areas. As it turns out this type of integral is not without an application, as will be demonstrated by one application to a problem in fluid mechanics.
Change detection in rainfall time series for Perth, Western Australia
12:10 Mon 16 May, 2011 :: 5.57 Ingkarni Wardli :: Farah Mohd Isa :: University of Adelaide

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

The Euler characteristic is a nice simple integer invariant that one can attach to a space. Unfortunately, it is not natural: maps between spaces do not induce maps between their Euler characteristics, because it makes no sense to talk of a map between integers. This shortcoming is fixed by homology. Maps between spaces induce maps between their homologies, with the Euler characteristic encoded inside the homology. Recently it has become possible to play the same game with knots and the Jones polynomial: the Khovanov homology of a knot both encodes the Jones polynomial and is a natural invariant of the knot. After saying what all this means, this talk will observe that Khovanov homology is just a special case of sheaf homology on a poset, and we will explore some of the ramifications of this observation. This is joint work with Paul Turner (Geneva/Fribourg).
Inference and optimal design for percolation and general random graph models (Part I)
09:30 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

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

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

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

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

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

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

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

Object oriented data analysis of tree-structured data objects
15:10 Fri 1 Jul, 2011 :: 7.15 Ingkarni Wardli :: Prof Steve Marron :: The University of North Carolina at Chapel Hill

The field of Object Oriented Data Analysis has made a lot of progress on the statistical analysis of the variation in populations of complex objects. A particularly challenging example of this type is populations of tree-structured objects. Deep challenges arise, which involve a marriage of ideas from statistics, geometry, and numerical analysis, because the space of trees is strongly non-Euclidean in nature. These challenges, together with three completely different approaches to addressing them, are illustrated using a real data example, where each data point is the tree of blood arteries in one person's brain.
Boundaries of unsteady Lagrangian Coherent Structures
15:10 Wed 10 Aug, 2011 :: 5.57 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: Connecticut College, USA and the University of Adelaide

For steady flows, the boundaries of Lagrangian Coherent Structures are segments of manifolds connected to fixed points. In the general unsteady situation, these boundaries are time-varying manifolds of hyperbolic trajectories. Locating these boundaries, and attempting to meaningfully quantify fluid flux across them, is difficult since they are moving with time. This talk uses a newly developed tangential movement theory to locate these boundaries in nearly-steady compressible flows.
T-duality via bundle gerbes I
13:10 Fri 23 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

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

In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
Dirac operators on classifying spaces
13:10 Fri 28 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Pedram Hekmati :: University of Adelaide

The Dirac operator was introduced by Paul Dirac in 1928 as the formal square root of the D'Alembert operator. Thirty years later it was rediscovered in Euclidean signature by Atiyah and Singer in their seminal work on index theory. In this talk I will describe efforts to construct a Dirac type operator on the classifying space for odd complex K-theory. Ultimately the aim is to produce a projective family of Fredholm operators realising elements in twisted K-theory of a certain moduli stack.
Noncritical holomorphic functions of finite growth on algebraic Riemann surfaces
13:10 Fri 3 Feb, 2012 :: B.20 Ingkarni Wardli :: Prof Franc Forstneric :: University of Ljubljana

Given a compact Riemann surface X and a point p in X, we construct a holomorphic function without critical points on the punctured (algebraic) Riemann surface R=X-p which is of finite order at the point p. In the case at hand this improves the 1967 theorem of Gunning and Rossi to the effect that every open Riemann surface admits a noncritical holomorphic function, but without any particular growth condition. (Joint work with Takeo Ohsawa.)
Plurisubharmonic subextensions as envelopes of disc functionals
13:10 Fri 2 Mar, 2012 :: B.20 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

I will describe new joint work with Evgeny Poletsky. We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient is a complex manifold with a local biholomorphism to $X$, except it need not be Hausdorff. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension.
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 short-term load allocation and long-term planning for future generation facilities and transmission augmentation. Planners must adopt a probabilistic view of potential peak demand levels, therefore density forecasts (providing estimates of the full probability distributions of the possible future values of the demand) are more helpful than point forecasts, and are necessary for utilities to evaluate and hedge the financial risk accrued by demand variability and forecasting uncertainty. Electricity demand in a given season is subject to a range of uncertainties, including underlying population growth, changing technology, economic conditions, prevailing weather conditions (and the timing of those conditions), as well as the general randomness inherent in individual usage. It is also subject to some known calendar effects due to the time of day, day of week, time of year, and public holidays. I will describe a comprehensive forecasting solution designed to take all the available information into account, and to provide forecast distributions from a few hours ahead to a few decades ahead. We use semi-parametric additive models to estimate the relationships between demand and the covariates, including temperatures, calendar effects and some demographic and economic variables. Then we forecast the demand distributions using a mixture of temperature simulation, assumed future economic scenarios, and residual bootstrapping. The temperature simulation is implemented through a new seasonal bootstrapping method with variable blocks. The model is being used by the state energy market operators and some electricity supply companies to forecast the probability distribution of electricity demand in various regions of Australia. It also underpinned the Victorian Vision 2030 energy strategy.
The entropy of an overlapping dynamical system
15:10 Fri 23 Mar, 2012 :: Napier G03 :: Prof Michael Barnsley :: Australian National University

Media...
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence between these two classes of objects is used to: 1. find a necessary and sufficient condition for a fractal transformation from the attractor of one overlapping IFS to the attractor of another overlapping IFS to be a homeomorphism and 2. find a formula for the topological entropy of the dynamical system associated with an overlapping function. These results suggest a new method for analysing clocks, weather systems and prime numbers.
A Problem of Siegel
13:10 Fri 27 Apr, 2012 :: B.20 Ingkarni Wardli :: Dr Brent Everitt :: University of York

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

Media...
Spatial-point data sets, generated from a wide range of physical systems and mathematical models, can be analyzed by counting the number of objects in equally sized bins. We find that the bin counts are related to the Polya distribution. New indexes are developed which quantify whether or not a spatial data set is at its most evenly distributed state. Using three case studies (Lagrangian fluid particles in chaotic laminar flows, cellular automata agents in discrete models, and biological cells within colonies), we calculate the indexes and predict the spatial-state of the system.
Index type invariants for twisted signature complexes
13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide

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

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

There are many interesting and difficult algorithmic problems in low-dimensional topology. Here we study the problem of finding a taut structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting taut structures is "hard", in the sense that it is NP-complete. We also prove that detecting taut structures is "not too hard", by showing it to be fixed-parameter tractable. This is joint work with Jonathan Spreer.
On the full holonomy group of special Lorentzian manifolds
13:10 Fri 25 May, 2012 :: Napier LG28 :: Dr Thomas Leistner :: University of Adelaide

The holonomy group of a semi-Riemannian manifold is defined as the group of parallel transports along loops based at a point. Its connected component, the `restricted holonomy group', is given by restricting in this definition to contractible loops. The restricted holonomy can essentially be described by its Lie algebra and many classification results are obtained in this way. In contrast, the `full' holonomy group is a more global object and classification results are out of reach. In the talk I will describe recent results with H. Baum and K. Laerz (both HU Berlin) about the full holonomy group of so-called `indecomposable' Lorentzian manifolds. I will explain a construction method that arises from analysing the effects on holonomy when dividing the manifold by the action of a properly discontinuous group of isometries and present several examples of Lorentzian manifolds with disconnected holonomy groups.
K-theory and unbounded Fredholm operators
13:10 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Dr Jerry Kaminker :: University of California, Davis

There are several ways of viewing elements of K^1(X). One of these is via families of unbounded self-adjoint Fredholm operators on X. Each operator will have discrete spectrum, with infinitely many positive and negative eigenvalues of finite multiplicity. One can associate to such a family a geometric object, its graph, and the Chern character and other invariants of the family can be studied from this perspective. By restricting the dimension of the eigenspaces one may sometimes use algebraic topology to completely determine the family up to equivalence. This talk will describe the general framework and some applications to families on low-dimensional manifolds where the methods work well. Various notions related to spectral flow, the index gerbe and Berry phase play roles which will be discussed. This is joint work with Ron Douglas.
Geometry - algebraic to arithmetic to absolute
15:10 Fri 3 Aug, 2012 :: B.21 Ingkarni Wardli :: Dr James Borger :: Australian National University

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Classical algebraic geometry is about studying solutions to systems of polynomial equations with complex coefficients. In arithmetic algebraic geometry, one digs deeper and studies the arithmetic properties of the solutions when the coefficients are rational, or even integral. From the usual point of view, it's impossible to go deeper than this for the simple reason that no smaller rings are available - the integers have no proper subrings. In this talk, I will explain how an emerging subject, lambda-algebraic geometry, allows one to do just this and why one might care.
Noncommutative geometry and conformal geometry
13:10 Fri 24 Aug, 2012 :: Engineering North 218 :: Dr Hang Wang :: Tsinghua University

In this talk, we shall use noncommutative geometry to obtain an index theorem in conformal geometry. This index theorem follows from an explicit and geometric computation of the Connes-Chern character of the spectral triple in conformal geometry, which was introduced recently by Connes and Moscovici. This (twisted) spectral triple encodes the geometry of the group of conformal diffeomorphisms on a spin manifold. The crux of of this construction is the conformal invariance of the Dirac operator. As a result, the Connes-Chern character is intimately related to the CM cocycle of an equivariant Dirac spectral triple. We compute this equivariant CM cocycle by heat kernel techniques. On the way we obtain a new heat kernel proof of the equivariant index theorem for Dirac operators. (Joint work with Raphael Ponge.)
Geometric quantisation in the noncompact setting
13:10 Fri 14 Sep, 2012 :: Engineering North 218 :: Dr Peter Hochs :: Leibniz University, Hannover

Traditionally, the geometric quantisation of an action by a compact Lie group on a compact symplectic manifold is defined as the equivariant index of a certain Dirac operator. This index is a well-defined formal difference of finite-dimensional representations, since the Dirac operator is elliptic and the manifold and the group in question are compact. From a mathematical and physical point of view however, it is very desirable to extend geometric quantisation to noncompact groups and manifolds. Defining a suitable index is much harder in the noncompact setting, but several interesting results in this direction have been obtained. I will review the difficulties connected to noncompact geometric quantisation, and some of the solutions that have been proposed so far, mainly in connection to the "quantisation commutes with reduction" principle. (An introduction to this principle will be given in my talk at the Colloquium on the same day.)
The advection-diffusion-reaction equation on the surface of the sphere
12:10 Mon 24 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr Kale Davies :: University of Adelaide

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We aim to solve the advection-diffusion-reaction equation on the surface of a sphere. In order to do this we will be required to utilise spherical harmonics, a set of solutions to Laplace's equation in spherical coordinates. Upon solving the equations, we aim to find a set of parameters that cause a localised concentration to be maintained in the flow, referred to as a hotspot. In this talk I will discuss the techniques that are required to numerically solve this problem and the issues that occur/how to deal with these issues when searching for hotspot solutions.
Twistor theory and the harmonic hull
15:10 Fri 8 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Michael Eastwood :: Australian National University

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Harmonic functions are real-analytic and so automatically extend as functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated conformal geometry. Nothing will be supposed about such matters: I shall base the constructions on an elementary yet mysterious formula of Bateman from 1904. This is joint work with Feng Xu.
Fire-Atmosphere Models
12:10 Mon 29 Jul, 2013 :: B.19 Ingkarni Wardli :: Mika Peace :: University of Adelaide

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Fire behaviour models are increasingly being used to assist in planning and operational decisions for bush fires and fuel reduction burns. Rate of spread (ROS) of the fire front is a key output of such models. The ROS value is typically calculated from a formula which has been derived from empirical data, using very simple meteorological inputs. We have used a coupled fire-atmosphere model to simulate real bushfire events. The results show that complex interactions between a fire and the atmosphere can have a significant influence on fire spread, thus highlighting the limitations of a model that uses simple meteorological inputs.
Noncommutative geometry and conformal geometry
13:10 Mon 16 Sep, 2013 :: Ingkarni Wardli B20 :: Prof Raphael Ponge :: Seoul National University

In this talk we shall report on a program of using the recent framework of twisted spectral triples to study conformal geometry from a noncommutative geometric perspective. One result is a local index formula in conformal geometry taking into account the action of the group of conformal diffeomorphisms. Another result is a version of Vafa-Witten's inequality for twisted spectral triples. Geometric applications include a version of Vafa-Witten's inequality in conformal geometry. There are also noncommutative versions for spectral triples over noncommutative tori and duals of discrete cocompact subgroups of semisimple Lie groups satisfying the Baum-Connes conjecture. (This is joint work with Hang Wang.)
Random Wanderings on a Sphere...
11:10 Tue 17 Sep, 2013 :: Ingkarni Wardli Level 5 Room 5.57 :: A/Prof Robb Muirhead :: University of Adelaide

This will be a short talk (about 30 minutes) about the following problem. (Even if I tell you all I know about it, it won't take very long!) Imagine the earth is a unit sphere in 3-dimensions. You're standing at a fixed point, which we may as well take to be the North Pole. Suddenly you get moved to another point on the sphere by a random (uniform) orthogonal transormation. Where are you now? You're not at a point which is uniformly distributed on the surface of the sphere (so, since most of the earth's surface is water, you're probably drowning). But then you get moved again by the same orthogonal transformation. Where are you now? And what happens to your location it this happens repeatedly? I have only a partial answwer to this question, for 2 and 3 transformations. (There's nothing special about 3 dimensions here--results hold for all dimensions which are at least 3.) I don't know of any statistical application for this! This work was motivated by a talk I heard, given by Tom Marzetta (Bell Labs) at a conference at MIT. Although I know virtually nothing about signal processing, I gather Marzetta was trying to encode signals using powers of ranfom orthogonal matrices. After carrying out simulations, I think he decided it wasn't a good idea.
Lost in Space: Point Pattern Matching and Astrometry
12:35 Mon 14 Oct, 2013 :: B.19 Ingkarni Wardli :: Annie Conway :: University of Adelaide

Astrometry is the field of research that concerns the positions of objects in space. This can be useful for satellite tracking where we would like to know accurate positions of satellites at given times. Telescopes give us some idea of the position, but unfortunately they are not very precise. However, if a photograph of a satellite has stars in the background, we can use that information to refine our estimate of the location of the image, since the positions of stars are known to high accuracy and are readily available in star catalogues. But there are billions of stars in the sky so first we would need to determine which ones we're actually looking at. In this talk I will give a brief introduction to astrometry and walk through a point pattern matching algorithm for identifying stars in a photograph.
Localised index and L^2-Lefschetz fixed point formula
12:10 Fri 25 Oct, 2013 :: Ingkarni Wardli B19 :: Dr Hang Wang :: University of Adelaide

In this talk we introduce a class of localised indices for the Dirac type operators on a complete Riemannian manifold, where a discrete group acts properly, co-compactly and isometrically. These localised indices, generalising the L^2-index of Atiyah, are obtained by taking Hattori-Stallings traces of the higher index for the Dirac type operators. We shall talk about some motivation and applications for working on localised indices. The talk is related to joint work with Bai-Ling Wang.
The structuring role of chaotic stirring on pelagic ecosystems
11:10 Fri 28 Feb, 2014 :: B19 Ingkarni Wardli :: Dr Francesco d'Ovidio :: Universite Pierre et Marie Curie (Paris VI)

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

Geometric quantisation is a way to construct quantum mechanical phase spaces (Hilbert spaces) from classical mechanical phase spaces (symplectic manifolds). In the presence of a group action, the quantisation commutes with reduction principle states that geometric quantisation should be compatible with the ways the group action can be used to simplify (reduce) the classical and quantum phase spaces. This has deep consequences for the link between symplectic geometry and representation theory. The quantisation commutes with reduction principle has been given explicit meaning, and been proved, in cases where the symplectic manifold and the group acting on it are compact. There have also been results where just the group, or the orbit space of the action, is assumed to be compact. These are important and difficult, but it is somewhat frustrating that they do not even apply to the simplest example from the physics point of view: a free particle in Rn. This talk is about a joint result with Mathai Varghese where the group, manifold and orbit space may all be noncompact.
Moduli spaces of contact instantons
12:10 Fri 28 Mar, 2014 :: Ingkarni Wardli B20 :: David Baraglia :: University of Adelaide

In dimensions greater than four there are several notions of higher Yang-Mills instantons. This talk concerns one such case, contact instantons, defined for 5-dimensional contact manifolds. The geometry transverse to the Reeb foliation turns out to be important in understanding the moduli space. For example, we show the dimension of the moduli space is the index of a transverse elliptic complex. This is joint work with Pedram Hekmati.
Aircraft flight dynamics and stability
12:10 Mon 31 Mar, 2014 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide

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In general, a stable plane is safer, more efficient and more comfortable than an unstable plane, however there are many design features that affect stability. In this talk I will discuss the dynamics of fixed wing aircraft in flight, with particular emphasis on stability. I will discuss some basic stability considerations, and how they influence aircraft design as well as some interesting modes of instability, and how they may be managed. Hopefully this talk will help to explain why planes to look the way they do.
Flow barriers and flux in unsteady flows
15:10 Fri 4 Apr, 2014 :: B.21 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: The University of Adelaide

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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.
Lefschetz fixed point theorem and beyond
12:10 Fri 2 May, 2014 :: Ingkarni Wardli B20 :: Hang Wang :: University of Adelaide

A Lefschetz number associated to a continuous map on a closed manifold is a topological invariant determined by the geometric information near the neighbourhood of fixed point set of the map. After an introduction of the Lefschetz fixed point theorem, we shall use the Dirac-dual Dirac method to derive the Lefschetz number on K-theory level. The method concerns the comparison of the Dirac operator on the manifold and the Dirac operator on some submanifold. This method can be generalised to several interesting situations when the manifold is not necessarily compact.
The Bismut-Chern character as dimension reduction functor and its twisting
12:10 Fri 4 Jul, 2014 :: Ingkarni Wardli B20 :: Fei Han :: National University of Singapore

The Bismut-Chern character is a loop space refinement of the Chern character. It plays an essential role in the interpretation of the Atiyah-Singer index theorem from the point of view of loop space. In this talk, I will first briefly review the construction of the Bismut-Chern character and show how it can be viewed as a dimension reduction functor in the Stolz-Teichner program on supersymmetric quantum field theories. I will then introduce the construction of the twisted Bismut-Chern character, which represents our joint work with Varghese Mathai.
Mathematics: a castle in the sky?
14:10 Mon 25 Aug, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. David Roberts :: School of Mathematical Sciences

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At university you are exposed to more rigorous mathematics than at school, exemplified by definitions such as those of real numbers individually or as a whole. However, what does mathematics ultimately rest on? Definitions depend on things defined earlier, and this process must stop at some point. Mathematicians expended a lot of energy in the late 19th and early 20th centuries trying to pin down the absolutely fundamental ideas of mathematics, with unexpected results. The results of these efforts are called foundations and are still an area of active research today. This talk will explain what foundations are, some of the historical setting in which they arose, and several of the various systems on which mathematics can be built -- and why most of the mathematics you will do only uses a tiny portion of it!
⌊ n!/e ⌉
14:10 Tue 9 Sep, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. David Butler :: Maths Learning Centre

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What is this formula? Why does it use those strangely mismatched brackets, and why does it use both factorial and the number e? What is it supposed to calculate? And why would someone love it so much that they put it on a t-shirt? In this seminar you will find out the answers to all of these questions, and also find out what derangements have to do with Taylor's theorem.
Exploration vs. Exploitation with Partially Observable Gaussian Autoregressive Arms
15:00 Mon 29 Sep, 2014 :: Engineering North N132 :: Julia Kuhn :: The University of Queensland & The University of Amsterdam

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We consider a restless bandit problem with Gaussian autoregressive arms, where the state of an arm is only observed when it is played and the state-dependent reward is collected. Since arms are only partially observable, a good decision policy needs to account for the fact that information about the state of an arm becomes more and more obsolete while the arm is not being played. Thus, the decision maker faces a tradeoff between exploiting those arms that are believed to be currently the most rewarding (i.e. those with the largest conditional mean), and exploring arms with a high conditional variance. Moreover, one would like the decision policy to remain tractable despite the infinite state space and also in systems with many arms. A policy that gives some priority to exploration is the Whittle index policy, for which we establish structural properties. These motivate a parametric index policy that is computationally much simpler than the Whittle index but can still outperform the myopic policy. Furthermore, we examine the many-arm behavior of the system under the parametric policy, identifying equations describing its asymptotic dynamics. Based on these insights we provide a simple heuristic algorithm to evaluate the performance of index policies; the latter is used to optimize the parametric index.
Topology Tomography with Spatial Dependencies
15:00 Tue 25 Nov, 2014 :: Engineering North N132 :: Darryl Veitch :: The University of Melbourne

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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.
The Mathematics behind the Ingkarni Wardli Quincunx
12:10 Mon 23 Mar, 2015 :: Napier LG29 :: Andrew Pfeiffer :: University of Adelaide

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

From a geometric point of view, branch groups are groups acting spherically transitively on a spherically homogeneous rooted tree. The applications of branch groups reach out to analysis, geometry, combinatorics, and probability. The early construction of branch groups were the Grigorchuk group and the Gupta-Sidki p-groups. Among its many claims to fame, the Grigorchuk group was the first example of a group of intermediate growth (i.e. neither polynomial nor exponential). Here we consider a generalisation of the family of Grigorchuk-Gupta-Sidki groups, and we examine the restricted occurrence of their maximal subgroups.
Dirac operators and Hamiltonian loop group action
12:10 Fri 24 Jul, 2015 :: Engineering and Maths EM212 :: Yanli Song :: University of Toronto

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

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

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For a proper action by a Lie group on a Spin-c manifold (both of which may be noncompact), we study an index of deformations of the Spin-c Dirac operator, acting on the space of spinors invariant under the group action. When applied to spinors that are square integrable transversally to orbits in a suitable sense, the kernel of this operator turns out to be finite-dimensional, under certain hypotheses of the deformation. This also allows one to show that the index has the quantisation commutes with reduction property (as proved by Meinrenken in the compact symplectic case, and by Paradan-Vergne in the compact Spin-c case), for sufficiently large powers of the determinant line bundle. Furthermore, this result extends to Spin-c Dirac operators twisted by vector bundles. A key ingredient of the arguments is the use of a family of inner products on the Lie algebra, depending on a point in the manifold. This is joint work with Mathai Varghese.
Quasi-isometry classification of certain hyperbolic Coxeter groups
11:00 Fri 23 Oct, 2015 :: Ingkarni Wardli Conference Room 7.15 (Level 7) :: Anne Thomas :: University of Sydney

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Let Gamma be a finite simple graph with vertex set S. The associated right-angled Coxeter group W is the group with generating set S, so that s^2 = 1 for all s in S and st = ts if and only if s and t are adjacent vertices in Gamma. Moussong proved that the group W is hyperbolic in the sense of Gromov if and only if Gamma has no "empty squares". We consider the quasi-isometry classification of such Coxeter groups using the local cut point structure of their visual boundaries. In particular, we find an algorithm for computing Bowditch's JSJ tree for a class of these groups, and prove that two such groups are quasi-isometric if and only if their JSJ trees are the same. This is joint work with Pallavi Dani (Louisiana State University).
A fixed point theorem on noncompact manifolds
12:10 Fri 12 Feb, 2016 :: Ingkarni Wardli B21 :: Peter Hochs :: University of Adelaide / Radboud University

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For an elliptic operator on a compact manifold acted on by a compact Lie group, the Atiyah-Segal-Singer fixed point formula expresses its equivariant index in terms of data on fixed point sets of group elements. This can for example be used to prove Weyl’s character formula. We extend the definition of the equivariant index to noncompact manifolds, and prove a generalisation of the Atiyah-Segal-Singer formula, for group elements with compact fixed point sets. In one example, this leads to a relation with characters of discrete series representations of semisimple Lie groups. (This is joint work with Hang Wang.)
Expanding maps
12:10 Fri 18 Mar, 2016 :: Eng & Maths EM205 :: Andy Hammerlindl :: Monash University

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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.
Counting periodic points of plane Cremona maps
12:10 Fri 1 Apr, 2016 :: Eng & Maths EM205 :: Tuyen Truong :: University of Adelaide

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In this talk, I will present recent results, join with Tien-Cuong Dinh and Viet-Anh Nguyen, on counting periodic points of plane Cremona maps (i.e. birational maps of P^2). The tools used include a Lefschetz fixed point formula of Saito, Iwasaki and Uehara for birational maps of surface whose fixed point set may contain curves; a bound on the arithmetic genus of curves of periodic points by Diller, Jackson and Sommerse; a result by Diller, Dujardin and Guedj on invariant (1,1) currents of meromorphic maps of compact Kahler surfaces; and a theory developed recently by Dinh and Sibony for non proper intersections of varieties. Among new results in the paper, we give a complete characterisation of when two positive closed (1,1) currents on a compact Kahler surface behave nicely in the view of Dinh and Sibony’s theory, even if their wedge intersection may not be well-defined with respect to the classical pluripotential theory. Time allows, I will present some generalisations to meromorphic maps (including an upper bound for the number of isolated periodic points which is sometimes overlooked in the literature) and open questions.
Some free boundary value problems in mean curvature flow and fully nonlinear curvature flows
12:10 Fri 27 May, 2016 :: Eng & Maths EM205 :: Valentina Wheeler :: University of Wollongong

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

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The main result I will discuss is non-vanishing of the image of the index map from the G-equivariant K-homology of a G-manifold X to the K-theory of the C*-algebra of the group G. The action of G on X is assumed to be proper and cocompact. Under the assumption that the Kronecker pairing of a K-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero. Neither discreteness of the locally compact group G nor freeness of the action of G on X are required. The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.
Geometry of pseudodifferential algebra bundles
12:10 Fri 16 Sep, 2016 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide

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I will motivate the construction of pseudodifferential algebra bundles arising in index theory, and also outline the construction of general pseudodifferential algebra bundles (and the associated sphere bundles), showing that there are many that are purely infinite dimensional that do not come from usual constructions in index theory. I will also discuss characteristic classes of such bundles. This is joint work with Richard Melrose.
Character Formula for Discrete Series
12:10 Fri 14 Oct, 2016 :: Ingkarni Wardli B18 :: Hang Wang :: University of Adelaide

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Weyl character formula describes characters of irreducible representations of compact Lie groups. This formula can be obtained using geometric method, for example, from the Atiyah-Bott fixed point theorem or the Atiyah-Segal-Singer index theorem. Harish-Chandra character formula, the noncompact analogue of the Weyl character formula, can also be studied from the point of view of index theory. We apply orbital integrals on K-theory of Harish-Chandra Schwartz algebra of a semisimple Lie group G, and then use geometric method to deduce Harish-Chandra character formulas for discrete series representations of G. This is work in progress with Peter Hochs.
Toroidal Soap Bubbles: Constant Mean Curvature Tori in S ^ 3 and R ^3
12:10 Fri 28 Oct, 2016 :: Ingkarni Wardli B18 :: Emma Carberry :: University of Sydney

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Constant mean curvature (CMC) tori in S ^ 3, R ^ 3 or H ^ 3 are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes and whether tori can be deformed. I will address these questions for the spherical and Euclidean cases, using Whitham deformations.
Diffeomorphisms of discs, harmonic spinors and positive scalar curvature
11:10 Fri 17 Mar, 2017 :: Engineering Nth N218 :: Diarmuid Crowley :: University of Melbourne

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

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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

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A surface in the Euclidean space R^3 is said to be minimal if it is locally area-minimizing, meaning that every point in the surface admits a compact neighborhood with the least area among all the surfaces with the same boundary. Although the origin of minimal surfaces is in physics, since they can be realized locally as soap films, this family of surfaces lies in the intersection of many fields of mathematics. In particular, complex analysis in one and several variables plays a fundamental role in the theory. In this lecture we will discuss the influence of complex analysis in the study of minimal surfaces.
Compact pseudo-Riemannian homogeneous spaces
12:10 Fri 18 Aug, 2017 :: Engineering Sth S111 :: Wolfgang Globke :: University of Adelaide

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

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

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Modern data problems often involve data in very high dimensions. For example, gene expression profiles, used to develop cancer screening models, typically have at least 30,000 dimensions. When dealing with such data, it is natural to apply intuition from low dimensional cases. For example, in a sample of normal observations, a typical data point will be near the centre of the distribution with only a small number of points at the edges. In this talk, simple probability theory will be used to show that the geometry of data in high dimensional space is very different from what we can see in one and two-dimensional examples. We will show that the typical data point is at the edge of the distribution, a long way from its centre and even further from any other points.
Equivariant formality of homogeneous spaces
12:10 Fri 29 Sep, 2017 :: Engineering Sth S111 :: Alex Chi-Kwong Fok :: University of Adelaide

Equivariant formality, a notion in equivariant topology introduced by Goresky-Kottwitz-Macpherson, is a desirable property of spaces with group actions, which allows the application of localisation formula to evaluate integrals of any top closed forms and enables one to compute easily the equivariant cohomology. Broad classes of spaces of especial interest are well-known to be equivariantly formal, e.g., compact symplectic manifolds equipped with Hamiltonian compact Lie group actions and projective varieties equipped with linear algebraic torus actions, of which flag varieties are examples. Less is known about compact homogeneous spaces G/K equipped with the isotropy action of K, which is not necessarily of maximal rank. In this talk we will review previous attempts of characterizing equivariant formality of G/K, and present our recent results on this problem using an analogue of equivariant formality in K-theory. Part of the work presented in this talk is joint with Jeffrey Carlson.
End-periodic K-homology and spin bordism
12:10 Fri 20 Oct, 2017 :: Engineering Sth S111 :: Michael Hallam :: University of Adelaide

This talk introduces new "end-periodic" variants of geometric K-homology and spin bordism theories that are tailored to a recent index theorem for even-dimensional manifolds with periodic ends. This index theorem, due to Mrowka, Ruberman and Saveliev, is a generalisation of the Atiyah-Patodi-Singer index theorem for manifolds with odd-dimensional boundary. As in the APS index theorem, there is an (end-periodic) eta invariant that appears as a correction term for the periodic end. Invariance properties of the standard relative eta invariants are elegantly expressed using K-homology and spin bordism, and this continues to hold in the end-periodic case. In fact, there are natural isomorphisms between the standard K-homology/bordism theories and their end-periodic versions, and moreover these isomorphisms preserve relative eta invariants. The study is motivated by results on positive scalar curvature, namely obstructions and distinct path components of the moduli space of PSC metrics. Our isomorphisms provide a systematic method for transferring certain results on PSC from the odd-dimensional case to the even-dimensional case. This work is joint with Mathai Varghese.
A multiscale approximation of a Cahn-Larche system with phase separation on the microscale
15:10 Thu 22 Feb, 2018 :: Ingkarni Wardli 5.57 :: Ms Lisa Reischmann :: University of Augsberg

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

Credit card users can roughly be divided into `transactors', who pay off their balance each month, and `revolvers', who maintain an outstanding balance, on which they pay substantial interest. In this talk, we focus on modelling the behaviour of an individual transactor customer. Our motivation is to calculate an optimal credit limit from the bank's point of view. This requires an expression for the expected outstanding balance at the end of a payment period. We establish a connection with the classical newsvendor model. Furthermore, we derive the Laplace transform of the outstanding balance, assuming that purchases are made according to a marked point process and that there is a simplified balance control policy which prevents all purchases in the rest of the payment period when the credit limit is exceeded. We then use the newsvendor model and our modified model to calculate bounds on the optimal credit limit for the more realistic balance control policy that accepts all purchases that do not exceed the limit. We illustrate our analysis using a compound Poisson process example and show that the optimal limit scales with the distribution of the purchasing process, while the probability of exceeding the optimal limit remains constant. Finally, we apply our model to some real credit card purchase data.
Chaos in higher-dimensional complex dynamics
13:10 Fri 20 Apr, 2018 :: Barr Smith South Polygon Lecture theatre :: Finnur Larusson :: University of Adelaide

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

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Suppose M is a smooth Riemannian manifold on which a Lie group G acts properly and isometrically. In this talk I will explore properties of a particular class of G-invariant operators on M, called G-Callias-type operators. These are Dirac operators that have been given an additional Z_2-grading and a perturbation so as to be "invertible outside of a cocompact set in M". It turns out that G-Callias-type operators are equivariantly Fredholm and so have an index in the K-theory of the maximal group C*-algebra of G. This index can be expressed as a KK-product of a class in K-homology and a class in the K-theory of the Higson G-corona. In fact, one can show that the K-theory of the Higson G-corona is highly non-trivial, and thus the index theory of G-Callias-type operators is not obviously trivial. As an application of the index theory of G-Callias-type operators, I will mention an obstruction to the existence of G-invariant metrics of positive scalar curvature on M.
Cobordism maps on PFH induced by Lefschetz fibration over higher genus base
13:10 Fri 11 May, 2018 :: Barr Smith South Polygon Lecture theatre :: Guan Heng Chen :: University of Adelaide

In this talk, we will discuss the cobordism maps on periodic Floer homology(PFH) induced by Lefschetz fibration. Periodic Floer homology is a Gromov types invariant for three dimensional mapping torus and it is isomorphic to a version of Seiberg Witten Floer cohomology(SWF). Our result is to define the cobordism maps on PFH induced by certain types of Lefschetz fibration via using holomorphic curves method. Also, we show that the cobordism maps is equivalent to the cobordism maps on Seiberg Witten cohomology under the isomorphism PFH=SWF.
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 non-autonomous 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, well-known eigenvalue detector, the Evans function. If there is time, I will try to expand on how to generalise these ideas to systems of PDEs.
Equivariant Index, Traces and Representation Theory
11:10 Fri 10 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Hang Wang :: University of Adelaide

K-theory of C*-algebras associated to a semisimple Lie group can be understood both from the geometric point of view via Baum-Connes assembly map and from the representation theoretic point of view via harmonic analysis of Lie groups. A K-theory generator can be viewed as the equivariant index of some Dirac operator, but also interpreted as a (family of) representation(s) parametrised by the noncompact abelian part in the Levi component of a cuspidal parabolic subgroup. Applying orbital traces to the K-theory group, we obtain the equivariant index as a fixed point formula which, for each K-theory generators for (limit of) discrete series, recovers Harish-Chandra’s character formula on the representation theory side. This is a noncompact analogue of Atiyah-Segal-Singer fixed point theorem in relation to the Weyl character formula. This is joint work with Peter Hochs.
Exceptional quantum symmetries
11:10 Fri 5 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Scott Morrison :: Australian National University

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

News matching "Localised index and L^2-Lefschetz fixed point form"

Teaching Fellow Position

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

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

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

Please see the University web site for further details.

Posted Wed 17 Sep 08.
IGA Lecture Series by Professor Dan Freed
The School of Mathematical Sciences will host a series of lectures by Professor Dan Freed (University of Texas, Austin) as part of an upcoming IGA/AMSI workshop, October 18-22, 2010. Details of the workshop can be found here. Posted Tue 5 Oct 10.
ARC Grant Success
Congratulations to the following staff who were successful in securing funding from the Australian Research Council Discovery Projects Scheme. Associate Professor Finnur Larusson awarded $270,000 for his project Flexibility and symmetry in complex geometry; Dr Thomas Leistner, awarded $303,464 for his project Holonomy groups in Lorentzian geometry, Professor Michael Murray Murray and Dr Daniel Stevenson (Glasgow), awarded $270,000 for their project Bundle gerbes: generalisations and applications; Professor Mathai Varghese, awarded $105,000 for his project Advances in index theory and Prof Anthony Roberts and Professor Ioannis Kevrekidis (Princeton) awarded $330,000 for their project Accurate modelling of large multiscale dynamical systems for engineering and scientific simulation and analysis Posted Tue 8 Nov 11.
Summer Research Scholarship Applications now Open
Applications for AMSI Vacation Scholarships and Adelaide Summer Research Scholarships are now OPEN.

Refer here for a list of possible Summer Research topics. See the links below for further information:

AMSI Vacation Scholarships: Closing date Tuesday 17th September
http://www.amsi.org.au/index.php/higher-education/vacation-research-scholarships
University of Adelaide Summer Research Scholarships: Closing date Friday 11th October.
http://www.adelaide.edu.au/scholarships/undergrad/asrs.html

Posted Thu 15 Aug 13.
Elder Professor Mathai Varghese Awarded Australian Laureate Fellowship
Professor Mathai Varghese, Elder Professor of Mathematics in the School of Mathematical Sciences, has been awarded an Australian Laureate Fellowship worth $1.64 million to advance Index Theory and its applications. The project is expected to enhance Australia’s position at the forefront of international research in geometric analysis. Posted Thu 15 Jun 17.

More information...

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

More information...

Publications matching "Localised index and L^2-Lefschetz fixed point form"

Publications
Equivariant and fractional index of projective elliptic operators
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 78 (465–473) 2008
A combinatorial formula for homogeneous moments
Eastwood, Michael; Romao, Nuno, Mathematical Proceedings of the Cambridge Philosophical Society 142 (153–160) 2007
The multivariate Faa di Bruno formula and multivariate Taylor expansions with explicit integral remainder term
Leipnik, R; Pearce, Charles, The ANZIAM Journal 48 (327–341) 2007
Fractional analytic index
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 74 (265–292) 2006
Estimating point-to-point and point-to-multipoint traffic matrices: An information-theoretic approach
Zhang, Y; Roughan, Matthew; Lund, C; Donoho, D, IEEE - ACM Transactions on Networking 13 (947–960) 2005
Self-similar "stagnation point" boundary layer flows with suction or injection
King, J; Cox, Stephen, Studies in Applied Mathematics 115 (73–107) 2005
The index of projective families of elliptic operators
Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 2005
Gerbes, Clifford Modules and the index theorem
Murray, Michael; Singer, Michael, Annals of Global Analysis and Geometry 26 (355–367) 2004
Method of best hybrid approximations for constructing fixed rank optimal estimators
Howlett, P; Pearce, Charles; Torokhti, Anatoli, World Congress of the Bernoulli Society for Mathematical Statistics and Probablility (6th: 2004), Barcelona, Spain 25/07/04
Geometric means, index mappings and entropy
Comanescu, D; Dragomir, S; Pearce, Charles, chapter in Inequality theory and applications - Volume 3 (Nova Science Publishers) 85–96, 2003
Geometric means, index mappings and supermultiplicativity
Pearce, Charles; Dragomir, S; Comanescu, D, chapter in Inequality theory and applications - Volume 2 (Nova Science Publishers) 193–201, 2003
An approximate formula for the stress intensity factor for the pressurized star crack
Clements, David; Widana, Inyoman, Mathematical and Computer Modelling 37 (689–694) 2003
Modelling persistence in annual Australian point rainfall
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew, Hydrology and Earth System Sciences 7 (197–211) 2003
Estimation of point-to-multipoint demands matrices from SNMP link traffic
Roughan, Matthew, Internet Traffic Matrices Estimation (Intimate 2003), Paris, France 16/08/03
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 lattice-gauge fields: a summary
Adams, Damian, Nuclear Physics B-Proceedings Supplements 109A (77–80) 2002
Two-point formulae of Euler type
Matic, M; Pearce, Charles; Pecaric, Josip, The ANZIAM Journal 44 (221–245) 2002
Direct computation of the performance index for an optimally controlled active suspension with preview applied to a half-car model
Thompson, A; Pearce, Charles, Vehicle System Dynamics 35 (121–137) 2001
Optimal fixed rank transform of the second degree
Torokhti, Anatoli; Howlett, P, IEEE Transactions on Circuits and Systems II - express briefs 48 (309–315) 2001
Performance index for a preview active suspension applied to a quarter-car model
Thompson, A; Pearce, Charles, Vehicle System Dynamics 35 (55–66) 2001
Twisted index theory on good orbifolds, II: Fractional quantum numbers
Marcolli, M; Varghese, Mathai, Communications in Mathematical Physics 217 (55–87) 2001
Hadamard and Dragomir-Agarwal inequalities, higher-order convexity and the Euler formula
Dedio, L; Pearce, Charles; Peoario, J, Journal of the Korean Mathematical Society (–) 2001
Dirac operator index and topology of lattice gauge fields
Adams, David, Chinese Journal of Physics 38 (633–646) 2000

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