The University of Adelaide
You are here
Text size: S | M | L
Printer Friendly Version
August 2019
MTWTFSS
   1234
567891011
12131415161718
19202122232425
262728293031 
       

Search the School of Mathematical Sciences

Find in People Courses Events News Publications

Courses matching "A fixed point theorem on noncompact manifolds"

Manifolds, lie groups and lie algebras

Lie groups and Lie algebras are fundamental concepts in both mathematics and theoretical physics. The theory of Lie groups and Lie algebras was developed in the late nineteenth century by Sophus Lie, Wilhelm Killing and others, when groups appeared as symmetries of differential equations. Soon it was realised that they can be treated by purely algebraic means yielding the concept of a Lie algebra. In physics Lie groups and Lie algebras are important in describing symmetries of physical systems and in gauge theories. As preparation for the theory of Lie groups the course will start off with an introduction to the basic notions of differential geometry, including smooth manifolds, tangent spaces and vector fields. This will enable us to understand the concept of a Lie group in a very general setting. The second part of the course will be an introduction the theory of Lie groups. I will focus mainly on the relation between Lie groups and Lie algebras and cover the following topics: the Lie algebra of a Lie group and the exponential map; Lie group homomorphisms; Lie subgroups and Cartan's theorem. The third part of the course is devoted to the structure theory of Lie algebras and will present the classification of finite dimensional complex semisimple Lie algebras. To this end we will cover the following topics: structure theory of Lie algebras: nilpotent, solvable and semi-­‐ simple Lie algebras; toral subalgebras; root systems and their classification by means of Dynkin diagrams. 1. Introduction, motivation and examples of matrix groups and algebras 2. Smooth manifolds and vector fields 3. Lie groups and their Lie algebras 4. Cartan's Theorem and the classical Lie groups  5. The Lie group - Lie algebras correspondence 6. Homogeneous spaces 7. Structure Theory of Lie algebras 8. Complex semisimple Lie algebras

More about this course...

Events matching "A fixed point theorem on noncompact manifolds"

Finite Geometries: Classical Problems and Recent Developments
15:10 Fri 20 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Joseph A. Thas :: Ghent University, Belgium

In recent years there has been an increasing interest in finite projective spaces, and important applications to practical topics such as coding theory, cryptography and design of experiments have made the field even more attractive. In my talk some classical problems and recent developments will be discussed. First I will mention Segre's celebrated theorem and ovals and a purely combinatorial characterization of Hermitian curves in the projective plane over a finite field here, from the beginning, the considered pointset is contained in the projective plane over a finite field. Next, a recent elegant result on semiovals in PG(2,q), due to Gács, will be given. A second approach is where the object is described as an incidence structure satisfying certain properties; here the geometry is not a priori embedded in a projective space. This will be illustrated by a characterization of the classical inversive plane in the odd case. Another quite recent beautiful result in Galois geometry is the discovery of an infinite class of hemisystems of the Hermitian variety in PG(3,q^2), leading to new interesting classes of incidence structures, graphs and codes; before this result, just one example for GF(9), due to Segre, was known.
An Introduction to invariant differential pairings
14:10 Tue 24 Jul, 2007 :: Mathematics G08 :: Jens Kroeske

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

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

Fermat's Last Theorem and modular elliptic curves
15:10 Wed 5 Sep, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Mark Kisin

Media...
I will give a historical talk, explaining the steps by which one can deduce Fermat's Last Theorem from a statement about modular forms and elliptic curves.
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/

Betti's Reciprocal Theorem for Inclusion and Contact Problems
15:10 Fri 1 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University

Enrico Betti (1823-1892) is recognized in the mathematics community for his pioneering contributions to topology. An equally important contribution is his formulation of the reciprocity theorem applicable to elastic bodies that satisfy the classical equations of linear elasticity. Although James Clerk Maxwell (1831-1879) proposed a law of reciprocal displacements and rotations in 1864, the contribution of Betti is acknowledged for its underlying formal mathematical basis and generality. The purpose of this lecture is to illustrate how Betti's reciprocal theorem can be used to full advantage to develop compact analytical results for certain contact and inclusion problems in the classical theory of elasticity. Inclusion problems are encountered in number of areas in applied mechanics ranging from composite materials to geomechanics. In composite materials, the inclusion represents an inhomogeneity that is introduced to increase either the strength or the deformability characteristics of resulting material. In geomechanics, the inclusion represents a constructed material region, such as a ground anchor, that is introduced to provide load transfer from structural systems. Similarly, contact problems have applications to the modelling of the behaviour of indentors used in materials testing to the study of foundations used to distribute loads transmitted from structures. In the study of conventional problems the inclusions and the contact regions are directly loaded and this makes their analysis quite straightforward. When the interaction is induced by loads that are placed exterior to the indentor or inclusion, the direct analysis of the problem becomes inordinately complicated both in terns of formulation of the integral equations and their numerical solution. It is shown by a set of selected examples that the application of Betti's reciprocal theorem leads to the development of exact closed form solutions to what would otherwise be approximate solutions achievable only through the numerical solution of a set of coupled integral equations.
On the Henstock-Kurzweil integral (along with concerns about general math education in Europe)
15:10 Fri 13 Feb, 2009 :: Napier LG28 :: Prof Jean-Pierre Demailly :: University of Grenoble, France

The talk will be the occasion to take a few minutes to describe the situation of math education in France and in Europe, to motivate the interest of the lecturer in trying to bring back rigorous proofs in integration theory. The remaining 45 minutes will be devoted to explaining the basics of Henstock-Kurzweil integration theory, which, although not a response to education problems, is a modern and elementary approach of a very strong extension of the Riemann integral, providing easy access to several fundamental results of Lebesgue theory (monotone convergence theorem, existence of Lebesgue measure, etc.).
The index theorem for projective families of elliptic operators
13:10 Fri 13 Mar, 2009 :: School Board Room :: Prof Mathai Varghese :: University of Adelaide

Classification and compact complex manifolds I
13:10 Fri 17 Apr, 2009 :: School Board Room :: A/Prof Nicholas Buchdahl :: 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).
Classification and compact complex manifolds II
13:10 Fri 24 Apr, 2009 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

Four classes of complex manifolds
13:10 Fri 8 May, 2009 :: School Board Room :: A/Prof Finnur Larusson :: University of Adelaide

We introduce the four classes of complex manifolds defined by having few or many holomorphic maps to or from the complex plane. Two of these classes have played an important role in complex geometry for a long time. A third turns out to be too large to be of much interest. The fourth class has only recently emerged from work of Abel Prize winner Mikhail Gromov.
Lagrangian fibrations on holomorphic symplectic manifolds I: Holomorphic Lagrangian fibrations
13:10 Fri 5 Jun, 2009 :: School Board Room :: Dr Justin Sawon :: Colorado State University

A compact K{\"a}hler manifold $X$ is a holomorphic symplectic manifold if it admits a non-degenerate holomorphic two-form $\sigma$. According to a theorem of Matsushita, fibrations on $X$ must be of a very restricted type: the fibres must be Lagrangian with respect to $\sigma$ and the generic fibre must be a complex torus. Moreover, it is expected that the base of the fibration must be complex projective space, and this has been proved by Hwang when $X$ is projective. The simplest example of these {\em Lagrangian fibrations\/} are elliptic K3 surfaces. In this talk we will explain the role of elliptic K3s in the classification of K3 surfaces, and the (conjectural) generalization to higher dimensions.
Chern-Simons classes on loop spaces and diffeomorphism groups
13:10 Fri 12 Jun, 2009 :: School Board Room :: Prof Steve Rosenberg :: Boston University

The loop space LM of a Riemannian manifold M comes with a family of Riemannian metrics indexed by a Sobolev parameter. We can construct characteristic classes for LM using the Wodzicki residue instead of the usual matrix trace. The Pontrjagin classes of LM vanish, but the secondary or Chern-Simons classes may be nonzero and may distinguish circle actions on M. There are similar results for diffeomorphism groups of manifolds.
Lagrangian fibrations on holomorphic symplectic manifolds II: Existence of Lagrangian fibrations
13:10 Fri 19 Jun, 2009 :: School Board Room :: Dr Justin Sawon :: Colorado State University

The Hilbert scheme ${\mathrm Hilb}^nS$ of points on a K3 surface $S$ is a well-known holomorphic symplectic manifold. When does ${\mathrm Hilb}^nS$ admit a Lagrangian fibration? The existence of a Lagrangian fibration places some conditions on the Hodge structure, since the pull back of a hyperplane from the base gives a special divisor on ${\mathrm Hilb}^nS$, and in turn a special divisor on $S$. The converse is more difficult, but using Fourier-Mukai transforms we will show that if $S$ admits a divisor of a certain degree then ${\mathrm Hilb}^nS$ admits a Lagrangian fibration.
Lagrangian fibrations on holomorphic symplectic manifolds III: Holomorphic coisotropic reduction
13:10 Fri 26 Jun, 2009 :: School Board Room :: Dr Justin Sawon :: Colorado State University

Given a certain kind of submanifold $Y$ of a symplectic manifold $(X,\omega)$ we can form its coisotropic reduction as follows. The null directions of $\omega|_Y$ define the characteristic foliation $F$ on $Y$. The space of leaves $Y/F$ then admits a symplectic form, descended from $\omega|_Y$. Locally, the coisotropic reduction $Y/F$ looks just like a symplectic quotient. This construction also work for holomorphic symplectic manifolds, though one of the main difficulties in practice is ensuring that the leaves of the foliation are compact. We will describe a criterion for compactness, and apply coisotropic reduction to produce a classification result for Lagrangian fibrations by Jacobians.
Generalizations of the Stein-Tomas restriction theorem
13:10 Fri 7 Aug, 2009 :: School Board Room :: Prof Andrew Hassell :: Australian National University

The Stein-Tomas restriction theorem says that the Fourier transform of a function in L^p(R^n) restricts to an L^2 function on the unit sphere, for p in some range [1, 2(n+1)/(n+3)]. I will discuss geometric generalizations of this result, by interpreting it as a property of the spectral measure of the Laplace operator on R^n, and then generalizing to the Laplace-Beltrami operator on certain complete Riemannian manifolds. It turns out that dynamical properties of the geodesic flow play a crucial role in determining whether a restriction-type theorem holds for these manifolds.
From linear algebra to knot theory
15:10 Fri 21 Aug, 2009 :: Badger Labs G13 Macbeth Lecture Theatre :: Prof Ross Street :: Macquarie University, Sydney

Vector spaces and linear functions form our paradigmatic monoidal category. The concepts underpinning linear algebra admit definitions, operations and constructions with analogues in many other parts of mathematics. We shall see how to generalize much of linear algebra to the context of monoidal categories. Traditional examples of such categories are obtained by replacing vector spaces by linear representations of a given compact group or by sheaves of vector spaces. More recent examples come from low-dimensional topology, in particular, from knot theory where the linear functions are replaced by braids or tangles. These geometric monoidal categories are often free in an appropriate sense, a fact that can be used to obtain algebraic invariants for manifolds.
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.
The proof of the Poincare conjecture
15:10 Fri 25 Sep, 2009 :: Napier 102 :: Prof Terrence Tao :: UCLA

In a series of three papers from 2002-2003, Grigori Perelman gave a spectacular proof of the Poincare Conjecture (every smooth compact simply connected three-dimensional manifold is topologically isomorphic to a sphere), one of the most famous open problems in mathematics (and one of the seven Clay Millennium Prize Problems worth a million dollars each), by developing several new groundbreaking advances in Hamilton's theory of Ricci flow on manifolds. In this talk I describe in broad detail how the proof proceeds, and briefly discuss some of the key turning points in the argument. About the speaker: Terence Tao was born in Adelaide, Australia, in 1975. He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal and SASTRA Ramanujan Prize in 2006, and the MacArthur Fellowship and Ostrowski Prize in 2007. Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society and the Australian Academy of Sciences (Corresponding Member).
Irreducible subgroups of SO(2,n)
13:10 Fri 16 Oct, 2009 :: School Board Room :: Dr Thomas Leistner :: University of Adelaide

Berger's classification of irreducibly represented Lie groups that can occur as holonomy groups of semi-Riemannian manifolds is a remarkable result of modern differential geometry. What is remarkable about it is that it is so short and that only so few types of geometry can occur. In Riemannian signature this is even more remarkable, taking into account that any representation of a compact Lie group admits a positive definite invariant scalar product. Hence, for any not too small n there is an abundance of irreducible subgroups of SO(n). We show that in other signatures the situation is quite different with, for example, SO(1,n) having no proper irreducible subgroups. We will show how this and the corresponding result about irreducible subgroups of SO(2,n) follows from the Karpelevich-Mostov theorem. (This is joint work with Antonio J. Di Scala, Politecnico di Torino.)
Manifold destiny: a talk on water, fire and life
15:10 Fri 6 Nov, 2009 :: MacBeth Lecture Theatre :: Dr Sanjeeva Balasuriya :: University of Adelaide

Manifolds are important entities in dynamical systems, and organise space into regions in which different motions occur. For example, intersections between stable and unstable manifolds in discrete systems result in chaotic motion. This talk will focus on manifolds and their locations in continuous dynamical systems, and in particular on Melnikov's method and its adaptations for determining the effect of perturbations on manifolds. The relevance of such adaptations to a surprising range of applications will be shown, in addition to recent theoretical developments inspired by such problems. The applications addressed in this talk include understanding the motion of fluid near oceanic eddies and currents, optimising mixing in nano-fluidic devices in order to improve reactions, computing the speed of a flame front, and finding the spreading rate of bacterial colonies.
Hartogs-type holomorphic extensions
13:10 Tue 15 Dec, 2009 :: School Board Room :: Prof Roman Dwilewicz :: Missouri University of Science and Technology

We will review holomorphic extension problems starting with the famous Hartogs extension theorem (1906), via Severi-Kneser-Fichera-Martinelli theorems, up to some recent (partial) results of Al Boggess (Texas A&M Univ.), Zbigniew Slodkowski (Univ. Illinois at Chicago), and the speaker. The holomorphic extension problems for holomorphic or Cauchy-Riemann functions are fundamental problems in complex analysis of several variables. The talk will be very elementary, with many figures, and accessible to graduate and even advanced undergraduate students.
Oka manifolds and Oka maps
13:10 Fri 29 Jan, 2010 :: Napier LG 23 :: Prof Franc Forstneric :: University of Ljubljana

In this survey lecture I will discuss a new class of complex manifolds and of holomorphic maps between them which I introduced in 2009 (F. Forstneric, Oka Manifolds, C. R. Acad. Sci. Paris, Ser. I, 347 (2009) 1017-1020). Roughly speaking, a complex manifold Y is said to be an Oka manifold if Y admits plenty of holomorphic maps from any Stein manifold (or Stein space) X to Y, in a certain precise sense. In particular, the inclusion of the space of holomorphic maps of X to Y into the space of continuous maps must be a weak homotopy equivalence. One of the main results is that this class of manifolds can be characterized by a simple Runge approximation property for holomorphic maps from complex Euclidean spaces C^n to Y, with approximation on compact convex subsets of C^n. This answers in the affirmative a question posed by M. Gromov in 1989. I will also discuss the Oka properties of holomorphic maps and their characterization by approximation properties.
A solution to the Gromov-Vaserstein problem
15:10 Fri 29 Jan, 2010 :: Engineering North N 158 Chapman Lecture Theatre :: Prof Frank Kutzschebauch :: University of Berne, Switzerland

Any matrix in $SL_n (\mathbb C)$ can be written as a product of elementary matrices using the Gauss elimination process. If instead of the field of complex numbers, the entries in the matrix are elements of a more general ring, this becomes a delicate question. In particular, rings of complex-valued functions on a space are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size $n$ of the matrix is at least 3. In the topological category, the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\mathbb C^m$, the problem was posed by Gromov in the 1980s. We report on a complete solution to Gromov's problem. A main tool is the Oka-Grauert-Gromov h-principle in complex analysis. Our main theorem can be formulated as follows: In the absence of obvious topological obstructions, the Gauss elimination process can be performed in a way that depends holomorphically on the matrix. This is joint work with Bj\"orn Ivarsson.
Proper holomorphic maps from strongly pseudoconvex domains to q-convex manifolds
13:10 Fri 5 Feb, 2010 :: School Board Room :: Prof Franc Forstneric :: University of Ljubljana

(Joint work with B. Drinovec Drnovsek, Amer. J. Math., in press.) I will discuss the existence of closed complex subvarieties of a complex manifold X that are proper holomorphic images of strongly pseudoconvex Stein domains. The main sufficient condition is expressed in terms of the Morse indices and of the number of positive Levi eigenvalues of an exhaustion function on X. Examples show that our condition cannot be weakened in general. I will describe optimal results for subvarieties of this type in complements of compact complex submanifolds with Griffiths positive normal bundle; in the projective case these generalize classical theorems of Remmert, Bishop and Narasimhan concerning proper holomorphic maps and embeddings to complex Euclidean spaces.
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.
Conformal structures with G_2 ambient metrics
13:10 Fri 19 Mar, 2010 :: School Board Room :: Dr Thomas Leistner :: University of Adelaide

The n-sphere considered as a conformal manifold can be viewed as the projectivisation of the light cone in n+2 Minkowski space. A construction that generalises this picture to arbitrary conformal classes is the ambient metric introduced by C. Fefferman and R. Graham. In the talk, I will explain the Fefferman-Graham ambient metric construction and how it detects the existence of certain metrics in the conformal class. Then I will present conformal classes of signature (3,2) for which the 7-dimensional ambient metric has the noncompact exceptional Lie group G_2 as its holonomy. This is joint work with P. Nurowski, Warsaw University.
Exploratory experimentation and computation
15:10 Fri 16 Apr, 2010 :: Napier LG29 :: Prof Jonathan Borwein :: University of Newcastle

Media...
The mathematical research community is facing a great challenge to re-evaluate the role of proof in light of the growing power of current computer systems, of modern mathematical computing packages, and of the growing capacity to data-mine on the Internet. Add to that the enormous complexity of many modern capstone results such as the Poincare conjecture, Fermat's last theorem, and the Classification of finite simple groups. As the need and prospects for inductive mathematics blossom, the requirement to ensure the role of proof is properly founded remains undiminished. I shall look at the philosophical context with examples and then offer some of five bench-marking examples of the opportunities and challenges we face.
Moduli spaces of stable holomorphic vector bundles II
13:10 Fri 30 Apr, 2010 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

In this talk, I shall briefly review the notion of stability for holomorphic vector bundles on compact complex manifolds as discussed in the first part of this talk (28 August 2009). Then I shall attempt to compute some explicit examples in simple situations, illustrating the use of basic algebraic-geometric tools. The level of the talk will be appropriate for graduate students, particularly those who have been taking part in the algebraic geometry reading group meetings.
The caloron transform
13:10 Fri 7 May, 2010 :: School Board Room :: Prof Michael Murray :: University of Adelaide

The caloron transform is a `fake' dimensional reduction which transforms a G-bundle over certain manifolds to a loop group of G bundle over a manifold of one lower dimension. This talk will review the caloron transform and show how it can be best understood using the language of pseudo-isomorphisms from category theory as well as considering its application to Bogomolny monopoles and string structures.
Holonomy groups
15:10 Fri 7 May, 2010 :: Napier LG24 :: Dr Thomas Leistner :: University of Adelaide

In the first part of the talk I will illustrate some basic concepts of differential geometry that lead to the notion of a holonomy group. Then I will explain Berger's classification of Riemannian holonomy groups and discuss questions that arose from it. Finally, I will focus on holonomy groups of Lorentzian manifolds and indicate briefly why all this is of relevance to present-day theoretical physics.
Moduli spaces of stable holomorphic vector bundles III
13:10 Fri 14 May, 2010 :: School Board Room :: A/Prof Nicholas Buchdahl :: University of Adelaide

This talk is a continuation of the talk on 30 April. The same abstract applies: In this talk, I shall briefly review the notion of stability for holomorphic vector bundles on compact complex manifolds as discussed in the first part of this talk (28 August 2009). Then I shall attempt to compute some explicit examples in simple situations, illustrating the use of basic algebraic-geometric tools. The level of the talk will be appropriate for graduate students, particularly those who have been taking part in the algebraic geometry reading group meetings.
Functorial 2-connected covers
13:10 Fri 21 May, 2010 :: School Board Room :: David Roberts :: University of Adelaide

The Whitehead tower of a topological space seeks to resolve that space by successively removing homotopy groups from the 'bottom up'. For a path-connected space with no 1-dimensional local pathologies the first stage in the tower can be chosen to be the universal (=1-connected) covering space. This construction also works in the category Diff of manifolds. However, further stages in the two known constructions of the Whitehead tower do not work in Diff, being purely topological - and one of these is non-functorial, depending on a large number of choices. This talk will survey results from my thesis which constructs a new, functorial model for the 2-connected cover which will lift to a generalised (2-)category of smooth objects. This talk contains joint work with Andrew Stacey of the Norwegian University of Science and Technology.
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.
A classical construction for simplicial sets revisited
13:10 Fri 27 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Danny Stevenson :: University of Glasgow

Simplicial sets became popular in the 1950s as a combinatorial way to study the homotopy theory of topological spaces. They are more robust than the older notion of simplicial complexes, which were introduced for the same purpose. In this talk, which will be as introductory as possible, we will review some classical functors arising in the theory of simplicial sets, some well-known, some not-so-well-known. We will re-examine the proof of an old theorem of Kan in light of these functors. We will try to keep all jargon to a minimum.
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.
Contraction subgroups in locally compact groups
13:10 Fri 17 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Prof George Willis :: University of Newcastle

For each automorphism, $\alpha$, of the locally compact group $G$ there is a corresponding {\sl contraction subgroup\/}, $\hbox{con}(\alpha)$, which is the set of $x\in G$ such that $\alpha^n(x)$ converges to the identity as $n\to \infty$. Contractions subgroups are important in representation theory, through the Mautner phenomenon, and in the study of convolution semigroups. If $G$ is a Lie group, then $\hbox{con}(\alpha)$ is automatically closed, can be described in terms of eigenvalues of $\hbox{ad}(\alpha)$, and is nilpotent. Since any connected group may be approximated by Lie groups, contraction subgroups of connected groups are thus well understood. Following a general introduction, the talk will focus on contraction subgroups of totally disconnected groups. A criterion for non-triviality of $\hbox{con}(\alpha)$ will be described (joint work with U.~Baumgartner) and a structure theorem for $\hbox{con}(\alpha)$ when it is closed will be presented (joint with H.~Gl\"oeckner).
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/
Complete quaternionic Kahler manifolds associated to cubic polynomials
13:10 Fri 11 Feb, 2011 :: Ingkarni Wardli B18 :: Prof Vicente Cortes :: University of Hamburg

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h = 1} defined by a homogeneous cubic polynomial h such that -\partial^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler manifold defines a complete quaternionic Kahler manifold of negative scalar curvature. We classify all complete quaternionic Kahler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.
Real analytic sets in complex manifolds I: holomorphic closure dimension
13:10 Fri 4 Mar, 2011 :: Mawson 208 :: Dr Rasul Shafikov :: University of Western Ontario

After a quick introduction to real and complex analytic sets, I will discuss possible notions of complex dimension of real sets, and then discuss a structure theorem for the holomorphic closure dimension which is defined as the dimension of the smallest complex analytic germ containing the real germ.
Real analytic sets in complex manifolds II: complex dimension
13:10 Fri 11 Mar, 2011 :: Mawson 208 :: Dr Rasul Shafikov :: University of Western Ontario

Given a real analytic set R, denote by A the subset of R of points through which there is a nontrivial complex variety contained in R, i.e., A consists of points in R of positive complex dimension. I will discuss the structure of the set A.
Lorentzian manifolds with special holonomy
13:10 Fri 25 Mar, 2011 :: Mawson 208 :: Mr Kordian Laerz :: Humboldt University, Berlin

A parallel lightlike vector field on a Lorentzian manifold X naturally defines a foliation of codimension 1 on X and a 1-dimensional subfoliation. In the first part we introduce Lorentzian metrics on the total space of certain circle bundles in order to construct weakly irreducible Lorentzian manifolds admitting a parallel lightlike vector field such that all leaves of the foliations are compact. Then we study which holonomy representations can be realized in this way. Finally, we consider the structure of arbitrary Lorentzian manifolds for which the leaves of the foliations are compact.
A strong Oka principle for embeddings of some planar domains into CxC*, I
13:10 Fri 6 May, 2011 :: Mawson 208 :: Mr Tyson Ritter :: University of Adelaide

The Oka principle refers to a collection of results in complex analysis which state that there are only topological obstructions to solving certain holomorphically defined problems involving Stein manifolds. For example, a basic version of Gromov's Oka principle states that every continuous map from a Stein manifold into an elliptic complex manifold is homotopic to a holomorphic map. In these two talks I will discuss a new result showing that if we restrict the class of source manifolds to circular domains and fix the target as CxC* we can obtain a much stronger Oka principle: every continuous map from a circular domain S into CxC* is homotopic to a proper holomorphic embedding. This result has close links with the long-standing and difficult problem of finding proper holomorphic embeddings of Riemann surfaces into C^2, with additional motivation from other sources.
A strong Oka principle for embeddings of some planar domains into CxC*, II
13:10 Fri 13 May, 2011 :: Mawson 208 :: Mr Tyson Ritter :: University of Adelaide

The Oka principle refers to a collection of results in complex analysis which state that there are only topological obstructions to solving certain holomorphically defined problems involving Stein manifolds. For example, a basic version of Gromov's Oka principle states that every continuous map from a Stein manifold into an elliptic complex manifold is homotopic to a holomorphic map. In these two talks I will discuss a new result showing that if we restrict the class of source manifolds to circular domains and fix the target as CxC* we can obtain a much stronger Oka principle: every continuous map from a circular domain S into CxC* is homotopic to a proper holomorphic embedding. This result has close links with the long-standing and difficult problem of finding proper holomorphic embeddings of Riemann surfaces into C^2, with additional motivation from other sources.
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.
Deformations of Oka manifolds
13:10 Fri 26 Aug, 2011 :: B.19 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

We discuss the behaviour of the Oka property with respect to deformations of compact complex manifolds. We have recently proved that in a family of compact complex manifolds, the set of Oka fibres corresponds to a G_delta subset of the base. We have also found a necessary and sufficient condition for the limit fibre of a sequence of Oka fibres to be Oka in terms of a new uniform Oka property. The special case when the fibres are tori will be considered, as well as the general case of holomorphic submersions with noncompact fibres.
Oka properties of some hypersurface complements
13:10 Fri 2 Sep, 2011 :: B.19 Ingkarni Wardli :: Mr Alexander Hanysz :: University of Adelaide

Oka manifolds can be viewed as the "opposite" of Kobayashi hyperbolic manifolds. Kobayashi conjectured that the complement of a generic algebraic hypersurface of sufficiently high degree is hyperbolic. Therefore it is natural to ask whether the complement is Oka for the case of low degree or non-algebraic hypersurfaces. We provide a complete answer to this question for complements of hyperplane arrangements, and some results for graphs of meromorphic functions.
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.
Applications of tropical geometry to groups and manifolds
13:10 Mon 21 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Stephan Tillmann :: University of Queensland

Tropical geometry is a young field with multiple origins. These include the work of Bergman on logarithmic limit sets of algebraic varieties; the work of the Brazilian computer scientist Simon on discrete mathematics; the work of Bieri, Neumann and Strebel on geometric invariants of groups; and, of course, the work of Newton on polynomials. Even though there is still need for a unified foundation of the field, there is an abundance of applications of tropical geometry in group theory, combinatorics, computational algebra and algebraic geometry. In this talk I will give an overview of (what I understand to be) tropical geometry with a bias towards applications to group theory and low-dimensional topology.
Noncritical holomorphic functions of finite growth on algebraic Riemann surfaces
13:10 Fri 3 Feb, 2012 :: B.20 Ingkarni Wardli :: Prof Franc Forstneric :: University of Ljubljana

Given a compact Riemann surface X and a point p in X, we construct a holomorphic function without critical points on the punctured (algebraic) Riemann surface R=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.)
Embedding circle domains into the affine plane C^2
13:10 Fri 10 Feb, 2012 :: B.20 Ingkarni Wardli :: Prof Franc Forstneric :: University of Ljubljana

We prove that every circle domain in the Riemann sphere admits a proper holomorphic embedding into the affine plane C^2. By a circle domain we mean a domain obtained by removing from the Riemann sphere a finite or countable family of pairwise disjoint closed round discs. Our proof also applies to some circle domains with punctures. The uniformization theorem of He and Schramm (1996) says that every domain in the Riemann sphere with at most countably many boundary components is conformally equivalent to a circle domain, so our theorem embeds all such domains properly holomorphically in C^2. (Joint work with Erlend F. Wold.)
The Lorentzian conformal analogue of Calabi-Yau manifolds
13:10 Fri 16 Mar, 2012 :: B.20 Ingkarni Wardli :: Prof Helga Baum :: Humboldt University

Calabi-Yau manifolds are Riemannian manifolds with holonomy group SU(m). They are Ricci-flat and Kahler and admit a 2-parameter family of parallel spinors. In the talk we will discuss the Lorentzian conformal analogue of this situation. If on a manifold a class of conformally equivalent metrics [g] is given, then one can consider the holonomy group of the conformal manifold (M,[g]), which is a subgroup of O(p+1,q+1) if the metric g has signature (p,q). There is a close relation between algebraic properties of the conformal holonomy group and the existence of Einstein metrics in the conformal class as well as to the existence of conformal Killing spinors. In the talk I will explain classification results for conformal holonomy groups of Lorentzian manifolds. In particular, I will describe Lorentzian manifolds (M,g) with conformal holonomy group SU(1,m), which can be viewed as the conformal analogue of Calabi-Yau manifolds. Such Lorentzian metrics g, known as Fefferman metrics, appear on S^1-bundles over strictly pseudoconvex CR spin manifolds and admit a 2-parameter family of conformal Killing spinors.
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 de Rham Complex
12:10 Mon 19 Mar, 2012 :: 5.57 Ingkarni Wardli :: Mr Michael Albanese :: University of Adelaide

Media...
The de Rham complex is of fundamental importance in differential geometry. After first introducing differential forms (in the familiar setting of Euclidean space), I will demonstrate how the de Rham complex elegantly encodes one half (in a sense which will become apparent) of the results from vector calculus. If there is time, I will indicate how results from the remaining half of the theory can be concisely expressed by a single, far more general theorem.
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.
Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds
13:10 Fri 4 May, 2012 :: Napier LG28 :: Dr Tyson Ritter :: University of Adelaide

In complex geometry a manifold is Stein if there are, in a certain sense, "many" holomorphic maps from the manifold into C^n. While this has long been well understood, a fruitful definition of the dual notion has until recently been elusive. In Oka theory, a manifold is Oka if it satisfies several equivalent definitions, each stating that the manifold has "many" holomorphic maps into it from C^n. Related to this is the geometric condition of ellipticity due to Gromov, who showed that it implies a complex manifold is Oka. We present recent contributions to three open questions involving elliptic and Oka manifolds. We show that affine quotients of C^n are elliptic, and combine this with an example of Margulis to construct new elliptic manifolds of interesting homotopy types. It follows that every open Riemann surface properly acyclically embeds into an elliptic manifold, extending an existing result for open Riemann surfaces with abelian fundamental group.
Index type invariants for twisted signature complexes
13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide

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.
The change of probability measure for jump processes
12:10 Mon 28 May, 2012 :: 5.57 Ingkarni Wardli :: Mr Ahmed Hamada :: University of Adelaide

Media...
In financial derivatives pricing theory, it is very common to change the probability measure from historical measure "real world" into a Risk-Neutral measure as a development of the non arbitrage condition. Girsanov theorem is the most known example of this technique and is used when prices randomness is modelled by Brownian motions. Other genuine candidates for modelling market randomness that have proved efficiency in recent literature are jump process, so how can a change of measure be performed for such processes? This talk will address this question by introducing the non arbitrage condition, discussing Girsanov theorem for diffusion and jump processes and presenting a concrete example.
Enhancing the Jordan canonical form
15:10 Fri 1 Jun, 2012 :: B.21 Ingkarni Wardli :: A/Prof Anthony Henderson :: The University of Sydney

Media...
In undergraduate linear algebra, we teach the Jordan canonical form theorem: that every similarity class of n x n complex matrices contains a special matrix which is block-diagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal, ones on the super-diagonal, and zeroes elsewhere). This is of course very useful for matrix calculations. After explaining some of the general context of this result, I will focus on a case which, despite its close proximity to the Jordan canonical form theorem, has only recently been worked out: the classification of pairs of a vector and a matrix.
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.
The Four Colour Theorem
11:10 Mon 23 Jul, 2012 :: B.17 Ingkarni Wardli :: Mr Vincent Schlegel :: University of Adelaide

Media...
Arguably the most famous problem in discrete mathematics, the Four Colour Theorem was first conjectured in 1852 by South African mathematician Francis Guthrie. For 124 years, it defied many attempts to prove and disprove it. I will talk briefly about some of the rich history of this result, including some of the graph-theoretic techniques used in the 1976 Appel-Haken proof.
The Banach-Tarski Paradox
11:10 Mon 30 Jul, 2012 :: G.07 Engineering Mathematics :: Mr William Crawford :: University of Adelaide

Media...
The Banach-Tarski Paradox is one of the most counter intuitive results in set theory. It states that a ball can be cut up into a finite number of pieces, which using just rotations and translations can be reassembled into two identical copies of the original ball. This contradicts our naive belief that cutting, rotating and translating objects in Euclidean space should preserve volume. However the construction of the "cutting" is heavily dependent on the axiom of choice, and the resultant pieces are non-measurable, i.e. no consistent notion of volume can be assigned to them. A stronger form of the theorem states that any two bounded subsets of R^3 with non-empty interior are equidecomposable, that is one can be disassembled and reassembled into the other. I'll be going through a brief proof of the theorem (and in doing so further alienate the pure mathematicians in the room from everybody else).
Geometry - algebraic to arithmetic to absolute
15:10 Fri 3 Aug, 2012 :: B.21 Ingkarni Wardli :: Dr James Borger :: Australian National University

Media...
Classical algebraic geometry is about studying solutions to systems of polynomial equations with complex coefficients. In arithmetic algebraic geometry, one digs deeper and studies the arithmetic properties of the solutions when the coefficients are rational, or even integral. From the usual point of view, it's impossible to go deeper than this for the simple reason that no smaller rings are available - the integers have no proper subrings. In this talk, I will explain how an emerging subject, lambda-algebraic geometry, allows one to do just this and why one might care.
The fundamental theorems of invariant theory, classical and quantum
15:10 Fri 10 Aug, 2012 :: B.21 Ingkarni Wardli :: Prof Gus Lehrer :: The University of Sydney

Media...
Let V = C^n, and let (-,-) be a non-degenerate bilinear form on V , which is either symmetric or anti-symmetric. Write G for the isometry group of (V , (-,-)); thus G = O_n (C) or Sp_n (C). The first fundamental theorem (FFT) provides a set of generators for End_G(V^{\otimes r} ) (r = 1, 2, . . . ), while the second fundamental theorem (SFT) gives all relations among the generators. In 1937, Brauer formulated the FFT in terms of his celebrated 'Brauer algebra' B_r (\pm n), but there has hitherto been no similar version of the SFT. One problem has been the generic non-semisimplicity of B_r (\pm n), which caused H Weyl to call it, in his work on invariants 'that enigmatic algebra'. I shall present a solution to this problem, which shows that there is a single idempotent in B_r (\pm n), which describes all the relations. The proof is through a new 'Brauer category', in which the fundamental theorems are easily formulated, and where a calculus of tangles may be used to prove these results. There are quantum analogues of the fundamental theorems which I shall also discuss. There are numerous applications in representation theory, geometry and topology. This is joint work with Ruibin Zhang.
Differential topology 101
13:10 Fri 17 Aug, 2012 :: Engineering North 218 :: Dr Nicholas Buchdahl :: University of Adelaide

Much of my recent research been directed at a problem in the theory of compact complex surfaces---trying to fill in a gap in the Enriques-Kodaira classification. Attempting to classify some collection of mathematical objects is a very common activity for pure mathematicians, and there are many well-known examples of successful classification schemes; for example, the classification of finite simple groups, and the classification of simply connected topological 4-manifolds. The aim of this talk will be to illustrate how techniques from differential geometry can be used to classify compact surfaces. The level of the talk will be very elementary, and the material is all very well known, but it is sometimes instructive to look back over simple cases of a general problem with the benefit of experience to gain greater insight into the more general and difficult cases.
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.)
Holomorphic flexibility properties of compact complex surfaces
13:10 Fri 31 Aug, 2012 :: Engineering North 218 :: A/Prof Finnur Larusson :: University of Adelaide

I will describe recent joint work with Franc Forstneric (arXiv, July 2012). We introduce a new property, called the stratified Oka property, which fits into a hierarchy of anti-hyperbolicity properties that includes the Oka property. We show that stratified Oka manifolds are strongly dominable by affine spaces. It follows that Kummer surfaces are strongly dominable. We determine which minimal surfaces of class VII are Oka (assuming the global spherical shell conjecture). We deduce that the Oka property and several other anti-hyperbolicity properties are in general not closed in families of compact complex manifolds. I will summarise what is known about how the Oka property fits into the Enriques-Kodaira classification of surfaces.
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 space of cubic rational maps
13:10 Fri 26 Oct, 2012 :: Engineering North 218 :: Mr Alexander Hanysz :: University of Adelaide

For each natural number d, the space of rational maps of degree d on the Riemann sphere has the structure of a complex manifold. The topology of these manifolds has been extensively studied. The recent development of Oka theory raises some new and interesting questions about their complex structure. We apply geometric invariant theory to the degree 3 case, studying a double action of the Mobius group on the space of cubic rational maps. We show that the categorical quotient is C, and that the space of cubic rational maps enjoys the holomorphic flexibility properties of strong dominability and C-connectedness.
Variation of Hodge structure for generalized complex manifolds
13:10 Fri 7 Dec, 2012 :: Ingkarni Wardli B20 :: Dr David Baraglia :: University of Adelaide

Generalized complex geometry combines complex and symplectic geometry into a single framework, incorporating also holomorphic Poisson and bi-Hermitian structures. The Dolbeault complex naturally extends to the generalized complex setting giving rise to Hodge structures in twisted cohomology. We consider the variations of Hodge structure and period mappings that arise from families of generalized complex manifolds. As an application we prove a local Torelli theorem for generalized Calabi-Yau manifolds.
Recent results on holomorphic extension of functions on unbounded domains in C^n
11:10 Fri 21 Dec, 2012 :: Ingkarni Wardli B19 :: Prof Roman Dwilewicz :: Missouri University of Science and Technology

In the talk there will be given a short review of holomorphic extension problems starting with the famous Hartogs theorem (1906) up to recent results on global holomorphic extensions for unbounded domains, obtained together with Al Boggess (Arizona State Univ.) and Zbigniew Slodkowski (Univ. Illinois at Chicago). There is an interesting geometry behind the extension problem for unbounded domains, namely (in some cases) it depends on the position of a complex variety in the closure of the domain. The extension problem appeared non-trivial and the work is in progress. However the talk will be illustrated by many figures and pictures and should be accessible also to graduate students.
Conformally Fedosov manifolds
12:10 Fri 8 Mar, 2013 :: Ingkarni Wardli B19 :: Prof Michael Eastwood :: Australian National University

Symplectic and projective structures may be compatibly combined. The resulting structure closely resembles conformal geometry and a manifold endowed with such a structure is called conformally Fedosov. This talk will present the basic theory of conformally Fedosov geometry and, in particular, construct a Cartan connection for them. This is joint work with Jan Slovak.
On the chromatic number of a random hypergraph
13:10 Fri 22 Mar, 2013 :: Ingkarni Wardli B21 :: Dr Catherine Greenhill :: University of New South Wales

A hypergraph is a set of vertices and a set of hyperedges, where each hyperedge is a subset of vertices. A hypergraph is r-uniform if every hyperedge contains r vertices. A colouring of a hypergraph is an assignment of colours to vertices such that no hyperedge is monochromatic. When the colours are drawn from the set {1,..,k}, this defines a k-colouring. We consider the problem of k-colouring a random r-uniform hypergraph with n vertices and cn edges, where k, r and c are constants and n tends to infinity. In this setting, Achlioptas and Naor showed that for the case of r = 2, the chromatic number of a random graph must have one of two easily computable values as n tends to infinity. I will describe some joint work with Martin Dyer (Leeds) and Alan Frieze (Carnegie Mellon), in which we generalised this result to random uniform hypergraphs. The argument uses the second moment method, and applies a general theorem for performing Laplace summation over a lattice. So the proof contains something for everyone, with elements from combinatorics, analysis and algebra.
A stability theorem for elliptic Harnack inequalities
15:10 Fri 5 Apr, 2013 :: B.18 Ingkarni Wardli :: Prof Richard Bass :: University of Connecticut

Media...
Harnack inequalities are an important tool in probability theory, analysis, and partial differential equations. The classical Harnack inequality is just the one you learned in your graduate complex analysis class, but there have been many extensions, to different spaces, such as manifolds, fractals, infinite graphs, and to various sorts of elliptic operators. A landmark result was that of Moser in 1961, where he proved the Harnack inequality for solutions to a class of partial differential equations. I will talk about the stability of Harnack inequalities. The main result says that if the Harnack inequality holds for an operator on a space, then the Harnack inequality will also hold for a large class of other operators on that same space. This provides a generalization of the result of Moser.
Kronecker-Weber Theorem
12:10 Mon 8 Apr, 2013 :: B.19 Ingkarni Wardli :: Konrad Pilch :: University of Adelaide

Media...
The Kronecker-Weber Theorem has a rich and inspiring history. Much like Fermat's Last Theorem, it can be expressed in a very simple way. Its many proofs often utilise heavy machinery and those who claim it can be solved using elementary means, have quite frankly redefined the meaning of elementary. It has inspired David Hilbert and many other mathematicians leading to a great amount of fantastic work in the area. In this talk, I will discuss this theorem, a 'fairly' simple proof of it as well as discuss how it is relevant to my work and the works of others.
The Mathematics of Secrets
14:10 Mon 8 Apr, 2013 :: 210 Napier Building :: Dr Naomi Benger :: School of Mathematical Sciences

Media...
One very important application of number theory is the implementation of public key cryptosystems that we use today. I will introduce elementary number theory, Fermat's theorem and use these to explain how ElGamal encryption and digital signatures work.
A glimpse at the Langlands program
15:10 Fri 12 Apr, 2013 :: B.18 Ingkarni Wardli :: Dr Masoud Kamgarpour :: University of Queensland

Media...
Abstract: In the late 1960s, Robert Langlands made a series of surprising conjectures relating fundamental concepts from number theory, representation theory, and algebraic geometry. Langlands' conjectures soon developed into a high-profile international research program known as the Langlands program. Many fundamental problems, including the Shimura-Taniyama-Weil conjecture (partially settled by Andrew Wiles in his proof of the Fermat's Last Theorem), are particular cases of the Langlands program. In this talk, I will discuss some of the motivation and results in this program.
Conformal Killing spinors in Riemannian and Lorentzian geometry
12:10 Fri 19 Apr, 2013 :: Ingkarni Wardli B19 :: Prof Helga Baum :: Humboldt University

Conformal Killing spinors are the solutions of the conformally covariant twistor equation on spinors. Special cases are parallel and Killing spinors, the latter appear as eigenspinors of the Dirac operator on compact Riemannian manifolds of positive scalar curvature for the smallest possible positive eigenvalue. In the talk I will discuss geometric properties of manifolds admitting (conformal) Killing spinors. In particular, I will explain a local classification of the special geometric structures admitting conformal Killing spinors without zeros in the Riemannian as well as in the Lorentzian setting.
An Oka principle for equivariant isomorphisms
12:10 Fri 3 May, 2013 :: Ingkarni Wardli B19 :: A/Prof Finnur Larusson :: University of Adelaide

I will discuss new joint work with Frank Kutzschebauch (Bern) and Gerald Schwarz (Brandeis). Let $G$ be a reductive complex Lie group acting holomorphically on Stein manifolds $X$ and $Y$, which are locally $G$-biholomorphic over a common categorical quotient $Q$. When is there a global $G$-biholomorphism $X\to Y$? In a situation that we describe, with some justification, as generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that $X$ and $Y$ are $G$-biholomorphic if $X$ is $K$-contractible, where $K$ is a maximal compact subgroup of $G$, or if there is a $G$-diffeomorphism $X\to Y$ over $Q$, which is holomorphic when restricted to each fibre of the quotient map $X\to Q$. When $G$ is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of $G$-biholomorphisms from $X$ to $Y$ over $Q$. This sheaf can be badly singular, even in simply defined examples. Our work is in part motivated by the linearisation problem for actions on $\C^n$. It follows from one of our main results that a holomorphic $G$-action on $\C^n$, which is locally $G$-biholomorphic over a common quotient to a generic linear action, is linearisable.
Diffeological spaces and differentiable stacks
12:10 Fri 10 May, 2013 :: Ingkarni Wardli B19 :: Dr David Roberts :: University of Adelaide

The category of finite-dimensional smooth manifolds gives rise to interesting structures outside of itself, two examples being mapping spaces and classifying spaces. Diffeological spaces are a notion of generalised smooth space which form a cartesian closed category, so all fibre products and all mapping spaces of smooth manifolds exist as diffeological spaces. Differentiable stacks are a further generalisation that can also deal with moduli spaces (including classifying spaces) for objects with automorphisms. This talk will give an introduction to this circle of ideas.
Crystallographic groups II: generalisations
12:10 Fri 24 May, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide

The theory of crystallographic groups acting cocompactly on Euclidean space can be extended and generalised in many different ways. For example, instead of studying discrete groups of Euclidean isometries, one can consider groups of isometries for indefinite inner products. These are the fundamental groups of compact flat pseudo-Riemannian manifolds. Still more generally, one might study group of affine transformation on n-space that are not required to preserve any bilinear form. Also, the condition of cocompactness can be dropped. In this talk, I will present some of the results obtained for these generalisations, and also discuss some of my own work on flat homogeneous pseudo-Riemannian spaces.
Heat kernel estimates on non-compact Riemannian manifolds: why and how?
15:10 Fri 7 Jun, 2013 :: B.18 Ingkarni Wardli :: Prof Thierry Coulhon :: Australian National University

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

Media...
A central theme in 19th century mathematics was invariant theory, which was viewed as a bridge between geometry and algebra. David Hilbert revolutionized the field with two seminal papers in 1890 and 1893 with techniques such as Hilbert's basis theorem, Hilbert's Nullstellensatz and Hilbert's syzygy theorem that spawned the modern field of commutative algebra. After Hilbert's groundbreaking work, the field of invariant theory remained largely inactive until the 1960's when David Mumford revitalized the field by reinterpreting Hilbert's ideas in the context of algebraic geometry which ultimately led to the influential construction of the moduli space of smooth curves. Today invariant theory remains a vital research area with connections to various mathematical disciplines: representation theory, algebraic geometry, commutative algebra, combinatorics and nonlinear differential operators. The goal of this talk is to provide an introduction to invariant theory with an emphasis on Hilbert's and Mumford's contributions. Time permitting, I will explain recent research with Maksym Fedorchuk and David Smyth which exploits the ideas of Hilbert, Mumford as well as Kempf to answer a classical question concerning the stability of algebraic curves.
The Lowenheim-Skolem theorem
12:10 Mon 26 Aug, 2013 :: B.19 Ingkarni Wardli :: William Crawford :: University of Adelaide

Media...
For those of us who didn't do an undergrad course in logic, the foundations of set theory are pretty daunting. I will give a run down of some of the basics and then talk about a lesser known, but interesting result; the Lowenheim-Skolem theorem. One of the consequences of the theorem is that a set can be countable in one model of set theory, while being uncountable in another.
Group meeting
15:10 Fri 13 Sep, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Sanjeeva Balasuriya and Dr Michael Chen :: University of Adelaide

Talks: Nonautonomous control of invariant manifolds - Dr Sanjeeva Balasuriya :: Interface problems in viscous flow - Dr Michael Chen
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.
Symmetry gaps for geometric structures
15:10 Fri 20 Sep, 2013 :: B.18 Ingkarni Wardli :: Dr Dennis The :: Australian National University

Media...
Klein's Erlangen program classified geometries based on their (transitive) groups of symmetries, e.g. Euclidean geometry is the quotient of the rigid motion group by the subgroup of rotations. While this perspective is homogeneous, Riemann's generalization of Euclidean geometry is in general very "lumpy" - i.e. there exist Riemannian manifolds that have no symmetries at all. A common generalization where a group still plays a dominant role is Cartan geometry, which first arose in Cartan's solution to the equivalence problem for geometric structures, and which articulates what a "curved version" of a flat (homogeneous) model means. Parabolic geometries are Cartan geometries modelled on (generalized) flag varieties (e.g. projective space, isotropic Grassmannians) which are well-known objects from the representation theory of semisimple Lie groups. These curved versions encompass a zoo of interesting geometries, including conformal, projective, CR, systems of 2nd order ODE, etc. This interaction between differential geometry and representation theory has proved extremely fruitful in recent years. My talk will be an example-based tour of various types of parabolic geometries, which I'll use to outline some of the main aspects of the theory (suppressing technical details). The main thread throughout the talk will be the symmetry gap problem: For a given type of Cartan geometry, the maximal symmetry dimension is realized by the flat model, but what is the next possible ("submaximal") symmetry dimension? I'll sketch a recent solution (in joint work with Boris Kruglikov) for a wide class of parabolic geometries which gives a combinatorial recipe for reading the submaximal symmetry dimension from a Dynkin diagram.
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.
Geodesic completeness of compact pp-waves
12:10 Fri 18 Oct, 2013 :: Ingkarni Wardli B19 :: Dr Thomas Leistner :: University of Adelaide

A semi-Riemannian manifold is geodesically complete (or for short, complete) if all its maximal geodesics are defined on the real line. Whereas for Riemannian metrics the compactness of the manifold implies completeness, there are compact Lorentzian manifolds that are not complete (e.g. the Clifton-Pohl torus). Several rather strong conditions have been found in the literature under which a compact Lorentzian manifold is complete, including being homogeneous (Marsden) or of constant curvature (Carriere, Klingler), or admitting a timelike Killing vector field (Romero, Sanchez). We will consider pp-waves, which are Lorentzian manifold with a parallel null vector field and a highly degenerate curvature tensor, but which do not satisfy any of the above conditions. We will show that a compact pp-wave is universally covered by a vector space, determine the metric on the universal cover and consequently show that they are geodesically complete.
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.
IGA Lectures on Finsler geometry
13:30 Thu 31 Oct, 2013 :: Ingkarni Wardli 7.15 :: Prof Robert Bryant :: Duke University

Media...
13:30 Refreshments. 14:00 Lecture 1: The origins of Finsler geometry in the calculus of variations. 15:00 Lecture 2: Finsler manifolds of constant flag curvature.
Recent developments in special holonomy manifolds
12:10 Fri 1 Nov, 2013 :: Ingkarni Wardli 7.15 :: Prof Robert Bryant :: Duke University

One of the big classification results in differential geometry from the past century has been the classification of the possible holonomies of affine manifolds, with the major first step having been taken by Marcel Berger in his 1954 thesis. However, Berger's classification was only partial, and, in the past 20 years, an extensive research effort has been expended to complete this classification and extend it in a number of ways. In this talk, after recounting the major parts of the history of the subject, I will discuss some of the recent results and surprising new examples discovered as a by-product of research into Finsler geometry. If time permits, I will also discuss some of the open problems in the subject.
The density property for complex manifolds: a strong form of holomorphic flexibility
12:10 Fri 24 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Frank Kutzschebauch :: University of Bern

Compared with the real differentiable case, complex manifolds in general are more rigid, their groups of holomorphic diffeomorphisms are rather small (in general trivial). A long known exception to this behavior is affine n-space C^n for n at least 2. Its group of holomorphic diffeomorphisms is infinite dimensional. In the late 1980s Andersen and Lempert proved a remarkable theorem which stated in its generalized version due to Forstneric and Rosay that any local holomorphic phase flow given on a Runge subset of C^n can be locally uniformly approximated by a global holomorphic diffeomorphism. The main ingredient in the proof was formalized by Varolin and called the density property: The Lie algebra generated by complete holomorphic vector fields is dense in the Lie algebra of all holomorphic vector fields. In these manifolds a similar local to global approximation of Andersen-Lempert type holds. It is a precise way of saying that the group of holomorphic diffeomorphisms is large. In the talk we will explain how this notion is related to other more recent flexibility notions in complex geometry, in particular to the notion of a Oka-Forstneric manifold. We will give examples of manifolds with the density property and sketch applications of the density property. If time permits we will explain criteria for the density property developed by Kaliman and the speaker.
Integrability of infinite-dimensional Lie algebras and Lie algebroids
12:10 Fri 7 Feb, 2014 :: Ingkarni Wardli B20 :: Christoph Wockel :: Hamburg University

Lie's Third Theorem states that each finite-dimensional Lie algebra is the Lie algebra of a Lie group (we also say "integrates to a Lie group"). The corresponding statement for infinite-dimensional Lie algebras or Lie algebroids is false and we will explain geometrically why this is the case. The underlying pattern is that of integration of central extensions of Lie algebras and Lie algebroids. This also occurs in other contexts, and we will explain some aspects of string group models in these terms. In the end we will sketch how the non-integrability of Lie algebras and Lie algebroids can be overcome by passing to higher categorical objects (such as smooth stacks) and give a panoramic (but still conjectural) perspective on the precise relation of the various integrability problems.
Hormander's estimate, some generalizations and new applications
12:10 Mon 17 Feb, 2014 :: Ingkarni Wardli B20 :: Prof Zbigniew Blocki :: Jagiellonian University

Lars Hormander proved his estimate for the d-bar equation in 1965. It is one the most important results in several complex variables (SCV). New applications have emerged recently, outside of SCV. We will present three of them: the Ohsawa-Takegoshi extension theorem with optimal constant, the one-dimensional Suita Conjecture, and Nazarov's approach to the Bourgain-Milman inequality from convex analysis.
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

Media...
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

Media...
How does one define the boundary of the ozone hole, an oceanic eddy, or Jupiter's Great Red Spot? These occur in flows which are unsteady (nonautonomous), that is, which change with time, and therefore any boundary must as well. In steady (autonomous) flows, defining flow boundaries is straightforward: one first finds fixed points of the flow, and then determines entities in space which are attracted to or repelled from these points as time progresses. These are respectively the stable and unstable manifolds of the fixed points, and can be shown to partition space into regions of different types of flow. This talk will focus on the required modifications to this idea for determining flow barriers in the more realistic unsteady context. An application to maximising mixing in microfluidic devices will also be presented.
T-Duality and its Generalizations
12:10 Fri 11 Apr, 2014 :: Ingkarni Wardli B20 :: Jarah Evslin :: Theoretical Physics Center for Science Facilities, CAS

Given a manifold M with a torus action and a choice of integral 3-cocycle H, T-duality yields another manifold with a torus action and integral 3-cocyle. It induces a number of surprising automorphisms between structures on these manifolds. In this talk I will review T-duality and describe some work on two generalizations which are realized in string theory: NS5-branes and heterotic strings. These respectively correspond to non-closed 3-classes H and to principal bundles fibered over M.
CARRYING CAPACITY FOR FINFISH AQUACULTURE IN SPENCER GULF: RAPID ASSESSMENT USING HYDRODYNAMIC AND NEAR-FIELD, SEMI - ANALYTIC SOLUTIONS
15:10 Fri 11 Apr, 2014 :: 5.58 Ingkarni Wardli :: Associate Professor John Middleton :: SARDI Aquatic Sciences and University of Adelaide

Aquaculture farming involves daily feeding of finfish and a subsequent excretion of nutrients into Spencer Gulf. Typically, finfish farming is done in six or so 50m diameter cages and over 600m X 600m lease sites. To help regulate the industry, it is desired that the finfish feed rates and the associated nutrient flux into the ocean are determined such that the maximum nutrient concentration c does not exceed a prescribed value (say cP) for ecosystem health. The prescribed value cP is determined by guidelines from the E.P.A. The concept is known as carrying capacity since limiting the feed rates limits the biomass of the farmed finfish. Here, we model the concentrations that arise from a constant input flux (F) of nutrients in a source region (the cage or lease) using the (depth-averaged) two dimensional, advection diffusion equation for constant and sinusoidal (tides) currents. Application of the divergence theorem to this equation results in a new scale estimate of the maximum flux F (and thus feed rate) that is given by F= cP /T* (1) where cP is the maximum allowed concentration and T* is a new time scale of “flushing” that involves both advection and diffusion. The scale estimate (1) is then shown to compare favourably with mathematically exact solutions of the advection diffusion equation that are obtained using Green’s functions and Fourier transforms. The maximum nutrient flux and associated feed rates are then estimated everywhere in Spencer Gulf through the development and validation of a hydrodynamic model. The model provides seasonal averages of the mean currents U and horizontal diffusivities KS that are needed to estimate T*. The diffusivities are estimated from a shear dispersal model of the tides which are very large in the gulf. The estimates have been provided to PIRSA Fisheries and Aquaculture to assist in the sustainable expansion of finfish aquaculture.
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.
Estimates for eigenfunctions of the Laplacian on compact Riemannian manifolds
12:10 Fri 1 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Hassell :: Australian National University

I am interested in estimates on eigenfunctions, accurate in the high-eigenvalue limit. I will discuss estimates on the size (as measured by L^p norms) of eigenfunctions, on the whole Riemannian manifold, at the boundary, or at an interior hypersurface. The link between high-eigenvalue estimates, geometry, and the dynamics of geodesic flow will be emphasized.
Boundary-value problems for the Ricci flow
15:10 Fri 15 Aug, 2014 :: B.18 Ingkarni Wardli :: Dr Artem Pulemotov :: The University of Queensland

Media...
The Ricci flow is a differential equation describing the evolution of a Riemannian manifold (i.e., a "curved" geometric object) into an Einstein manifold (i.e., an object with a "constant" curvature). This equation is particularly famous for its key role in the proof of the Poincare Conjecture. Understanding the Ricci flow on manifolds with boundary is a difficult problem with applications to a variety of fields, such as topology and mathematical physics. The talk will survey the current progress towards the resolution of this problem. In particular, we will discuss new results concerning spaces with symmetries.
Quasimodes that do not Equidistribute
13:10 Tue 19 Aug, 2014 :: Ingkarni Wardli B17 :: Shimon Brooks :: Bar-Ilan University

The QUE Conjecture of Rudnick-Sarnak asserts that eigenfunctions of the Laplacian on Riemannian manifolds of negative curvature should equidistribute in the large eigenvalue limit. For a number of reasons, it is expected that this property may be related to the (conjectured) small multiplicities in the spectrum. One way to study this relationship is to ask about equidistribution for "quasimodes"-or approximate eigenfunctions- in place of highly-degenerate eigenspaces. We will discuss the case of surfaces of constant negative curvature; in particular, we will explain how to construct some examples of sufficiently weak quasimodes that do not satisfy QUE, and show how they fit into the larger theory.
Mathematics: a castle in the sky?
14:10 Mon 25 Aug, 2014 :: Ingkarni Wardli 715 Conference Room :: Dr. David Roberts :: School of Mathematical Sciences

Media...
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

Media...
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.
To Complex Analysis... and beyond!
12:10 Mon 29 Sep, 2014 :: B.19 Ingkarni Wardli :: Brett Chenoweth :: University of Adelaide

Media...
In the undergraduate complex analysis course students learn about complex valued functions on domains in C (the complex plane). Several interesting and surprising results come about from this study. In my talk I will introduce a more general setting where complex analysis can be done, namely Riemann surfaces (complex manifolds of dimension 1). I will then prove that all non-compact Riemann surfaces are Stein; which loosely speaking means that their function theory is similar to that of C.
The Serre-Grothendieck theorem by geometric means
12:10 Fri 24 Oct, 2014 :: Ingkarni Wardli B20 :: David Roberts :: University of Adelaide

The Serre-Grothendieck theorem implies that every torsion integral 3rd cohomology class on a finite CW-complex is the invariant of some projective bundle. It was originally proved in a letter by Serre, used homotopical methods, most notably a Postnikov decomposition of a certain classifying space with divisible homotopy groups. In this talk I will outline, using work of the algebraic geometer Offer Gabber, a proof for compact smooth manifolds using geometric means and a little K-theory.
Extending holomorphic maps from Stein manifolds into affine toric varieties
12:10 Fri 14 Nov, 2014 :: Ingkarni Wardli B20 :: Richard Larkang :: University of Adelaide

One way of defining so-called Oka manifolds is by saying that they satisfy the following interpolation property (IP): Y satisfies the IP if any holomorphic map from a closed submanifold S of a Stein manifold X into Y which has a continuous extension to X also has a holomorphic extension. An ostensibly weaker property is the convex interpolation property (CIP), where S is assumed to be a contractible submanifold of X = C^n. By a deep theorem of Forstneric, these (and several other) properties are in fact equivalent. I will discuss a joint work with Finnur Larusson, where we consider the interpolation property when the target Y is a singular affine toric variety. We show that all affine toric varieties satisfy an interpolation property stronger than CIP, but that only in very special situations do they satisfy the full IP.
Topology Tomography with Spatial Dependencies
15:00 Tue 25 Nov, 2014 :: Engineering North N132 :: Darryl Veitch :: The University of Melbourne

Media...
There has been quite a lot of tomography inference work on measurement networks with a tree topology. Here observations are made, at the leaves of the tree, of `probes' sent down from the root and copied at each branch point. Inference can be performed based on loss or delay information carried by probes, and used in order to recover loss parameters, delay parameters, or the topology, of the tree. In all of these a strong assumption of spatial independence between links in the tree has been made in prior work. I will describe recent work on topology inference, based on loss measurement, which breaks that assumption. In particular I will introduce a new model class for loss with non trivial spatial dependence, the `Jump Independent Models', which are well motivated, and prove that within this class the topology is identifiable.
Nonlinear analysis over infinite dimensional spaces and its applications
12:10 Fri 6 Feb, 2015 :: Ingkarni Wardli B20 :: Tsuyoshi Kato :: Kyoto University

In this talk we develop moduli theory of holomorphic curves over infinite dimensional manifolds consisted by sequences of almost Kaehler manifolds. Under the assumption of high symmetry, we verify that many mechanisms of the standard moduli theory over closed symplectic manifolds also work over these infinite dimensional spaces. As an application, we study deformation theory of discrete groups acting on trees. There is a canonical way, up to conjugacy to embed such groups into the automorphism group over the infinite projective space. We verify that for some class of Hamiltonian functions, the deformed groups must be always asymptotically infinite.
Boundary behaviour of Hitchin and hypo flows with left-invariant initial data
12:10 Fri 27 Feb, 2015 :: Ingkarni Wardli B20 :: Vicente Cortes :: University of Hamburg

Hitchin and hypo flows constitute a system of first order pdes for the construction of Ricci-flat Riemannian mertrics of special holonomy in dimensions 6, 7 and 8. Assuming that the initial geometric structure is left-invariant, we study whether the resulting Ricci-flat manifolds can be extended in a natural way to complete Ricci-flat manifolds. This talk is based on joint work with Florin Belgun, Marco Freibert and Oliver Goertsches, see arXiv:1405.1866 (math.DG).
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.
Indefinite spectral triples and foliations of spacetime
12:10 Fri 8 May, 2015 :: Napier 144 :: Koen van den Dungen :: Australian National University

Motivated by Dirac operators on Lorentzian manifolds, we propose a new framework to deal with non-symmetric and non-elliptic operators in noncommutative geometry. We provide a definition for indefinite spectral triples, which correspond bijectively with certain pairs of spectral triples. Next, we will show how a special case of indefinite spectral triples can be constructed from a family of spectral triples. In particular, this construction provides a convenient setting to study the Dirac operator on a spacetime with a foliation by spacelike hypersurfaces. This talk is based on joint work with Adam Rennie (arXiv:1503.06916).
The twistor equation on Lorentzian Spin^c manifolds
12:10 Fri 15 May, 2015 :: Napier 144 :: Andree Lischewski :: University of Adelaide

In this talk I consider a conformally covariant spinor field equation, called the twistor equation, which can be formulated on any Lorentzian Spin^c manifold. Its solutions have become of importance in the study of supersymmetric field theories in recent years and were named "charged conformal Killing spinors". After a short review of conformal Spin^c geometry in Lorentzian signature, I will briefly discuss the emergence of charged conformal Killing spinors in supergravity. I will then focus on special geometric structures related to the twistor equation and use charged conformal Killing spinors in order to establish a link between conformal and CR geometry.
Big things are weird
12:10 Mon 25 May, 2015 :: Napier LG29 :: Luke Keating-Hughes :: University of Adelaide

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

Media...
Geometric quantisation has been an increasingly active area since before the 1980s, with links to physics, symplectic geometry, representation theory, index theory, and differential geometry and geometric analysis in general. In addition to its relevance as a field on its own, it acts as a focal point for the interaction between all of these areas, which has yielded 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

Media...
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.
Bezout's Theorem
12:10 Mon 7 Sep, 2015 :: Benham Labs G10 :: David Bowman :: University of Adelaide

Media...
Generically, a line intersects a parabola at two distinct points. Bezout’s theorem generalises this idea to the intersection of two arbitrary polynomial plane curves. We discuss exceptional cases and how they are corrected by introducing the notion of multiplicity and by extending the plane to projective space. We shall also discuss applications, time permitting.
Analytic complexity of bivariate holomorphic functions and cluster trees
12:10 Fri 2 Oct, 2015 :: Ingkarni Wardli B17 :: Timur Sadykov :: Plekhanov University, Moscow

The Kolmogorov-Arnold theorem yields a representation of a multivariate continuous function in terms of a composition of functions which depend on at most two variables. In the analytic case, understanding the complexity of such a representation naturally leads to the notion of the analytic complexity of (a germ of) a bivariate multi-valued analytic function. According to Beloshapka's local definition, the order of complexity of any univariate function is equal to zero while the n-th complexity class is defined recursively to consist of functions of the form a(b(x,y)+c(x,y)), where a is a univariate analytic function and b and c belong to the (n-1)-th complexity class. Such a represenation is meant to be valid for suitable germs of multi-valued holomorphic functions. A randomly chosen bivariate analytic functions will most likely have infinite analytic complexity. However, for a number of important families of special functions of mathematical physics their complexity is finite and can be computed or estimated. Using this, we introduce the notion of the analytic complexity of a binary tree, in particular, a cluster tree, and investigate its properties.
Real Lie Groups and Complex Flag Manifolds
12:10 Fri 9 Oct, 2015 :: Ingkarni Wardli B17 :: Joseph A. Wolf :: University of California, Berkeley

Media...
Let G be a complex simple direct limit group. Let G_R be a real form of G that corresponds to an hermitian symmetric space. I'll describe the corresponding bounded symmetric domain in the context of the Borel embedding, Cayley transforms, and the Bergman-Shilov boundary. Let Q be a parabolic subgroup of G. In finite dimensions this means that G/Q is a complex projective variety, or equivalently has a Kaehler metric invariant under a maximal compact subgroup of G. Then I'll show just how the bounded symmetric domains describe cycle spaces for open G_R orbits on G/Q. These cycle spaces include the complex bounded symmetric domains. In finite dimensions they are tightly related to moduli spaces for compact Kaehler manifolds and to representations of semisimple Lie groups; in infinite dimensions there are more problems than answers. Finally, time permitting, I'll indicate how some of this goes over to real and to quaternionic bounded symmetric domains.
Chern-Simons classes on loop spaces and diffeomorphism groups
12:10 Fri 16 Oct, 2015 :: Ingkarni Wardli B17 :: Steve Rosenberg :: Boston University

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

Media...
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).
Locally homogeneous pp-waves
12:10 Fri 6 Nov, 2015 :: Ingkarni Wardli B17 :: Thomas Leistner :: The University of Adelaide

Media...
For a certain type of Lorentzian manifolds, the so-called pp-waves, we study the conditions implied on the curvature by local homogeneity of the metric. We show that under some mild genericity assumptions, these conditions are quite strong, forcing the pp-wave to be a plane wave, and yielding a classification of homogeneous pp-waves. This also leads to a generalisation of a classical result by Jordan, Ehlers and Kundt about vacuum pp-waves in dimension 4 to arbitrary dimensions. Several examples show that our genericity assumptions are essential. This is joint work with W. Globke.
Oka principles and the linearization problem
12:10 Fri 8 Jan, 2016 :: Engineering North N132 :: Gerald Schwarz :: Brandeis University

Media...
Let G be a reductive complex Lie group (e.g., SL(n,C)) and let X and Y be Stein manifolds (closed complex submanifolds of some C^n). Suppose that G acts freely on X and Y. Then there are quotient Stein manifolds X/G and Y/G and quotient mappings p_X:X-> X/G and p_Y: Y-> Y/G such that X and Y are principal G-bundles over X/G and Y/G. Let us suppose that Q=X/G ~= Y/G so that X and Y have the same quotient Q. A map Phi: X\to Y of principal bundles (over Q) is simply an equivariant continuous map commuting with the projections. That is, Phi(gx)=g Phi(x) for all g in G and x in X, and p_X=p_Y o Phi. The famous Oka Principle of Grauert says that any Phi as above embeds in a continuous family Phi_t: X -> Y, t in [0,1], where Phi_0=Phi, all the Phi_t satisfy the same conditions as Phi does and Phi_1 is holomorphic. This is rather amazing. We consider the case where G does not necessarily act freely on X and Y. There is still a notion of quotient and quotient mappings p_X: X-> X//G and p_Y: Y-> Y//G where X//G and Y//G are now Stein spaces and parameterize the closed G-orbits in X and Y. We assume that Q~= X//G~= Y//G and that we have a continuous equivariant Phi such that p_X=p_Y o Phi. We find conditions under which Phi embeds into a continuous family Phi_t such that Phi_1 is holomorphic. We give an application to the Linearization Problem. Let G act holomorphically on C^n. When is there a biholomorphic map Phi:C^n -> C^n such that Phi^{-1} o g o Phi in GL(n,C) for all g in G? We find a condition which is necessary and sufficient for "most" G-actions. This is joint work with F. Kutzschebauch and F. Larusson.
A fixed point theorem on noncompact manifolds
12:10 Fri 12 Feb, 2016 :: Ingkarni Wardli B21 :: Peter Hochs :: University of Adelaide / Radboud University

Media...
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

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

Media...
In this talk, I will present recent results, join with 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.
Sard Theorem for the endpoint map in sub-Riemannian manifolds
12:10 Fri 29 Apr, 2016 :: Eng & Maths EM205 :: Alessandro Ottazzi :: University of New South Wales

Media...
Sub-Riemannian geometries occur in several areas of pure and applied mathematics, including harmonic analysis, PDEs, control theory, metric geometry, geometric group theory, and neurobiology. We introduce sub-Riemannian manifolds and give some examples. Therefore we discuss some of the open problems, and in particular we focus on the Sard Theorem for the endpoint map, which is related to the study of length minimizers. Finally, we consider some recent results obtained in collaboration with E. Le Donne, R. Montgomery, P. Pansu and D. Vittone.
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

Media...
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.
Chern-Simons invariants of Seifert manifolds via Loop spaces
14:10 Tue 28 Jun, 2016 :: Ingkarni Wardli B17 :: Ryan Mickler :: Northeastern University

Over the past 30 years the Chern-Simons functional for connections on G-bundles over three-manfolds has lead to a deep understanding of the geometry of three-manfiolds, as well as knot invariants such as the Jones polynomial. Here we study this functional for three-manfolds that are topologically given as the total space of a principal circle bundle over a compact Riemann surface base, which are known as Seifert manifolds. We show that on such manifolds the Chern-Simons functional reduces to a particular gauge-theoretic functional on the 2d base, that describes a gauge theory of connections on an infinite dimensional bundle over this base with structure group given by the level-k affine central extension of the loop group LG. We show that this formulation gives a new understanding of results of Beasley-Witten on the computability of quantum Chern-Simons invariants of these manifolds as well as knot invariants for knots that wrap a single fiber of the circle bundle. A central tool in our analysis is the Caloron correspondence of Murray-Stevenson-Vozzo.
Calculus on symplectic manifolds
12:10 Fri 12 Aug, 2016 :: Ingkarni Wardli B18 :: Mike Eastwood :: University of Adelaide

Media...
One can use the symplectic form to construct an elliptic complex replacing the de Rham complex. Then, under suitable curvature conditions, one can form coupled versions of this complex. Finally, on complex projective space, these constructions give rise to a series of elliptic complexes with geometric consequences for the Fubini-Study metric and its X-ray transform. This talk, which will start from scratch, is based on the work of many authors but, especially, current joint work with Jan Slovak.
What is the best way to count votes?
13:10 Mon 12 Sep, 2016 :: Hughes 322 :: Dr Stuart Johnson :: School of Mathematical Sciences

Media...
Around the world there are many different ways of counting votes in elections, and even within Australia there are different methods in use in various states. Which is the best method? Even for the simplest case of electing one person in a single electorate there is no easy answer to this, in fact there is a famous result - Arrow's Theorem - which tells us that there is no perfect way of counting votes. I will describe a number of different methods along with their problems before giving a more precise statement of the theorem and outlining a proof
Character Formula for Discrete Series
12:10 Fri 14 Oct, 2016 :: Ingkarni Wardli B18 :: Hang Wang :: University of Adelaide

Media...
Weyl character formula describes characters of irreducible representations of compact Lie groups. This formula can be obtained using geometric method, for example, from the 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

Media...
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

Media...
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

Media...
Index theory is a link between topology, geometry and analysis. A typical theorem in index theory says that two numbers are equal: an analytic index and a topological index. The first theorem of this kind was the index theorem of Atiyah and Singer, which they proved in 1963. Index theorems have many applications in maths and physics. For example, they can be used to prove that a differential equation must have a solution. Also, they imply that the topology of a space like a sphere or a torus determines in what ways it can be curved. Topology is the study of geometric properties that do not change if we stretch or compress a shape without cutting or glueing. Curvature does change when we stretch something out, so it is surprising that topology can say anything about curvature. Index theory has many surprising consequences like this.
Minimal surfaces and complex analysis
12:10 Fri 24 Mar, 2017 :: Napier 209 :: Antonio Alarcon :: University of Granada

Media...
A surface in the Euclidean space R^3 is said to be minimal if it is locally 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.
Geometric structures on moduli spaces
12:10 Fri 31 Mar, 2017 :: Napier 209 :: Nicholas Buchdahl :: University of Adelaide

Media...
Moduli spaces are used to classify various kinds of objects, often arising from solutions of certain differential equations on manifolds; for example, the complex structures on a compact surface or the anti-self-dual Yang-Mills equations on an oriented smooth 4-manifold. Sometimes these moduli spaces carry important information about the underlying manifold, manifested most clearly in the results of Donaldson and others on the topology of smooth 4-manifolds. It is also the case that these moduli spaces themselves carry interesting geometric structures; for example, the Weil-Petersson metric on moduli spaces of compact Riemann surfaces, exploited to great effect by Maryam Mirzakhani. In this talk, I shall elaborate on the theme of geometric structures on moduli spaces, with particular focus on some recent-ish work done in conjunction with Georg Schumacher.
K-types of tempered representations
12:10 Fri 7 Apr, 2017 :: Napier 209 :: Peter Hochs :: University of Adelaide

Media...
Tempered representations of a reductive Lie group G are the irreducible unitary representations one needs in the Plancherel decomposition of L^2(G). They are relevant to harmonic analysis because of this, and also occur in the Langlands classification of the larger class of admissible representations. If K in G is a maximal compact subgroup, then there is a considerable amount of information in the restriction of a tempered representation to K. In joint work with Yanli Song and Shilin Yu, we give a geometric expression for the decomposition of such a restriction into irreducibles. The multiplicities of these irreducibles are expressed as indices of Dirac operators on reduced spaces of a coadjoint orbit of G corresponding to the representation. These reduced spaces are Spin-c analogues of reduced spaces in symplectic geometry, defined in terms of moment maps that represent conserved quantities. This result involves a Spin-c version of the quantisation commutes with reduction principle for noncompact manifolds. For discrete series representations, this was done by Paradan in 2003.
Hodge theory on the moduli space of Riemann surfaces
12:10 Fri 5 May, 2017 :: Napier 209 :: Jesse Gell-Redman :: University of Melbourne

Media...
The Hodge theorem on a closed Riemannian manifold identifies the deRham cohomology with the space of harmonic differential forms. Although there are various extensions of the Hodge theorem to singular or complete but non-compact spaces, when there is an identification of L^2 Harmonic forms with a topological feature of the underlying space, it is highly dependent on the nature of infinity (in the non-compact case) or the locus of incompleteness; no unifying theorem treats all cases. We will discuss work toward extending the Hodge theorem to singular Riemannian manifolds where the singular locus is an incomplete cusp edge. These can be pictured locally as a bundle of horns, and they provide a model for the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Joint with J. Swoboda and R. Melrose.
Holomorphic Legendrian curves
12:10 Fri 26 May, 2017 :: Napier 209 :: Franc Forstneric :: University of Ljubljana, Slovenia

Media...
I will present recent results on the existence and behaviour of noncompact holomorphic Legendrian curves in complex contact manifolds. We show that these curves are ubiquitous in \C^{2n+1} with the standard holomorphic contact form \alpha=dz+\sum_{j=1}^n x_jdy_j; in particular, every open Riemann surface embeds into \C^3 as a proper holomorphic Legendrian curves. On the other hand, for any integer n>= 1 there exist Kobayashi hyperbolic complex contact structures on \C^{2n+1} which do not admit any nonconstant Legendrian complex lines. Furthermore, we construct a holomorphic Darboux chart around any noncompact holomorphic Legendrian curve in an arbitrary complex contact manifold. As an application, we show that every bordered holomorphic Legendrian curve can be uniformly approximated by complete bounded Legendrian curves.
Quaternionic Kaehler manifolds of co-homogeneity one
12:10 Fri 16 Jun, 2017 :: Ligertwood 231 :: Vicente Cortes :: Universitat Hamburg

Media...
Quaternionic Kaehler manifolds form an important class of Riemannian manifolds of special holonomy. They provide examples of Einstein manifolds of non-zero scalar curvature. I will show how to construct explicit examples of complete quaternionic Kaehler manifolds of negative scalar curvature beyond homogeneous spaces. In particular, I will present a series of examples of co-homogeneity one, based on arXiv:1701.07882.
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

Media...
Modern data problems often involve data in very high dimensions. For example, gene expression profiles, used to develop cancer screening models, typically have at least 30,000 dimensions. When dealing with such data, it is natural to apply intuition from low dimensional cases. For example, in a sample of normal observations, a typical data point will be near the centre of the distribution with only a small number of points at the edges. In this talk, simple probability theory will be used to show that the geometry of data in high dimensional space is very different from what we can see in one and 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.
A Hecke module structure on the KK-theory of arithmetic groups
13:10 Fri 2 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Bram Mesland :: University of Bonn

Media...
Let $G$ be a locally compact group, $\Gamma$ a discrete subgroup and $C_{G}(\Gamma)$ the commensurator of $\Gamma$ in $G$. The cohomology of $\Gamma$ is a module over the Shimura Hecke ring of the pair $(\Gamma,C_G(\Gamma))$. This construction recovers the action of the Hecke operators on modular forms for $SL(2,\mathbb{Z})$ as a particular case. In this talk I will discuss how the Shimura Hecke ring of a pair $(\Gamma, C_{G}(\Gamma))$ maps into the $KK$-ring associated to an arbitrary $\Gamma$-C*-algebra. From this we obtain a variety of $K$-theoretic Hecke modules. In the case of manifolds the Chern character provides a Hecke equivariant transformation into cohomology, which is an isomorphism in low dimensions. We discuss Hecke equivariant exact sequences arising from possibly noncommutative compactifications of $\Gamma$-spaces. Examples include the Borel-Serre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the Bruhat-Tits tree of $SL(2,\mathbb{Z})$. This is joint work with M.H. Sengun (Sheffield).
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.
Family gauge theory and characteristic classes of bundles of 4-manifolds
13:10 Fri 16 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Hokuto Konno :: University of Tokyo

Media...
I will define a non-trivial characteristic class of bundles of 4-manifolds using families of Seiberg-Witten equations. The basic idea of the construction is to consider an infinite dimensional analogue of the Euler class used in the usual theory of characteristic classes. I will also explain how to prove the non-triviality of this characteristic class. If time permits, I will mention a relation between our characteristic class and positive scalar curvature metrics.
Computing trisections of 4-manifolds
13:10 Fri 23 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Stephen Tillmann :: University of Sydney

Media...
Gay and Kirby recently generalised Heegaard splittings of 3-manifolds to trisections of 4-manifolds. A trisection describes a 4–dimensional manifold as a union of three 4–dimensional handlebodies. The complexity of the 4–manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies. The minimal genus of such a surface is the trisection genus of the 4-manifold. After defining trisections and giving key examples and applications, I will describe an algorithm to compute trisections of 4–manifolds using arbitrary triangulations as input. This results in the first explicit complexity bounds for the trisection genus of a 4–manifold in terms of the number of pentachora (4–simplices) in a triangulation. This is joint work with Mark Bell, Joel Hass and Hyam Rubinstein. I will also describe joint work with Jonathan Spreer that determines the trisection genus for each of the standard simply connected PL 4-manifolds.
Complexity of 3-Manifolds
15:10 Fri 23 Mar, 2018 :: Horace Lamb 1022 :: A/Prof Stephan Tillmann :: University of Sydney

In this talk, I will give a general introduction to complexity of 3-manifolds and explain the connections between combinatorics, algebra, geometry, and topology that arise in its study. The complexity of a 3-manifold is the minimum number of tetrahedra in a triangulation of the manifold. It was defined and first studied by Matveev in 1990. The complexity is generally difficult to compute, and various upper and lower bounds have been derived during the last decades using fundamental group, homology or hyperbolic volume. Effective bounds have only been found in joint work with Jaco, Rubinstein and, more recently, Spreer. Our bounds not only allowed us to determine the first infinite classes of minimal triangulations of closed 3-manifolds, but they also lead to a structure theory of minimal triangulations of 3-manifolds.
Chaos in higher-dimensional complex dynamics
13:10 Fri 20 Apr, 2018 :: Barr Smith South Polygon Lecture theatre :: Finnur Larusson :: University of Adelaide

Media...
I will report on new joint work with Leandro Arosio (University of Rome, Tor Vergata). Complex manifolds can be thought of as laid out across a spectrum characterised by rigidity at one end and flexibility at the other. On the rigid side, 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.
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.
Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory
13:10 Fri 25 May, 2018 :: Barr Smith South Polygon Lecture theatre :: David Baraglia :: University of Adelaide

Media...
Let X be a smooth, compact, oriented 4-manifold and consider the following problem. Let G be a group which acts on the second cohomology of X preserving the intersection form. Can this action of G on H^2(X) be lifted to an action of G on X by diffeomorphisms? We study a parametrised version of Seiberg-Witten theory for smooth families of 4-manifolds and obtain obstructions to the existence of such lifts. For example, we construct compact simply-connected 4-manifolds X and involutions on H^2(X) that can be realised by a continuous involution on X, or by a diffeomorphism, but not by an involutive diffeomorphism for any smooth structure on X.
The mass of Riemannian manifolds
13:10 Fri 1 Jun, 2018 :: Barr Smith South Polygon Lecture theatre :: Matthias Ludewig :: MPIM Bonn

We will define the mass of differential operators L on compact Riemannian manifolds. In odd dimensions, if L is a conformally covariant differential operator, then its mass is also conformally covariant, while in even dimensions, one has a more complicated transformation rule. In the special case that L is the Yamabe operator, its mass is related to the ADM mass of an associated asymptotically flat spacetime. In particular, one expects positive mass theorems in various settings. Here we highlight some recent results.
Hitchin's Projectively Flat Connection for the Moduli Space of Higgs Bundles
13:10 Fri 15 Jun, 2018 :: Barr Smith South Polygon Lecture theatre :: John McCarthy :: University of Adelaide

In this talk I will discuss the problem of geometrically quantizing the moduli space of Higgs bundles on a compact Riemann surface using Kahler polarisations. I will begin by introducing geometric quantization via Kahler polarisations for compact manifolds, leading up to the definition of a Hitchin connection as stated by Andersen. I will then describe the moduli spaces of stable bundles and Higgs bundles over a compact Riemann surface, and discuss their properties. The problem of geometrically quantizing the moduli space of stables bundles, a compact space, was solved independently by Hitchin and Axelrod, Del PIetra, and Witten. The Higgs moduli space is non-compact and therefore the techniques used do not apply, but carries an action of C*. I will finish the talk by discussing the problem of finding a Hitchin connection that preserves this C* action. Such a connection exists in the case of Higgs line bundles, and I will comment on the difficulties in higher rank.
Carleman approximation of maps into Oka manifolds.
11:10 Fri 3 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Brett Chenoweth :: University of Ljubljana

In 1927 Torsten Carleman proved a remarkable extension of the Stone-Weierstrass theorem. Carleman’s theorem is ostensibly the first result concerning the approximation of functions on unbounded closed subsets of C by entire functions. In this talk we introduce Carleman’s theorem and several of its recent generalisations including the titled generalisation which was proved by the speaker in arXiv:1804.10680.
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.
Interactive theorem proving for mathematicians
15:10 Fri 5 Oct, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University

Mathematicians use computers to write their proofs (LaTeX), and to do their calculations (Sage, Mathematica, Maple, Matlab, etc, as well as custom code for simulations or searches). However today we rarely use computers to help us to construct and understand proofs. There is a long tradition in computer science of interactive and automatic theorem proving; particularly today these are important tools in engineering correct software, as well as in optimisation and compilation. There have been some notable examples of formalisation of modern mathematics (e.g. the odd order theorem, the Kepler conjecture, and the four-colour theorem). Even in these cases, huge engineering efforts were required to translate the mathematics to a form a computer could understand. Moreover, in most areas of research there is a huge gap between the interests of human mathematicians and the abilities of computer provers. Nevertheless, I think it's time for mathematicians to start getting interested in interactive theorem provers! It's now possible to write proofs, and write tools that help write proofs, in languages which are expressive enough to encompass most of modern mathematics, and ergonomic enough to use for general purpose programming. I'll give an informal introduction to dependent type theory (the logical foundation of many modern theorem provers), some examples of doing mathematics in such a system, and my experiences working with mathematics students in these systems.
Twisted K-theory of compact Lie groups and extended Verlinde algebras
11:10 Fri 12 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Chi-Kwong Fok :: University of Adelaide

In a series of recent papers, Freed, Hopkins and Teleman put forth a deep result which identifies the twisted K -theory of a compact Lie group G with the representation theory of its loop group LG. Under suitable conditions, both objects can be enhanced to the Verlinde algebra, which appears in mathematical physics as the Frobenius algebra of a certain topological quantum field theory, and in algebraic geometry as the algebra encoding information of moduli spaces of G-bundles over Riemann surfaces. The Verlinde algebra for G with nice connectedness properties have been well-known. However, explicit descriptions of such for disconnected G are lacking. In this talk, I will discuss the various aspects of the Freed-Hopkins-Teleman Theorem and partial results on an extension of the Verlinde algebra arising from a disconnected G. The talk is based on work in progress joint with David Baraglia and Varghese Mathai.
Local Ricci flow and limits of non-collapsed regions whose Ricci curvature is bounded from below
11:10 Fri 26 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg

We use a local Ricci flow to obtain a bi-Holder correspondence between non-collapsed (possibly non-complete) 3-manifolds with Ricci curvature bounded from below and Gromov-Hausdorff limits of sequences thereof. This is joint work with Peter Topping and the proofs build on results and ideas from recent papers of Hochard and Topping+Simon.

News matching "A fixed point theorem on noncompact manifolds"

Stoneham Prize
The inaugural Stoneham Prize, awarded for the best poster by a graduate student in the first two years of their candidature, was awarded on the 4th of April. The winner was Ric Green, for his poster "What is Geometry?". Two Viewers' Choice prizes were also awarded to Ray Vozzo for his poster "The 7 Bridges of Koenigsberg - The 1st Theorem in Topology" and David Butler for his poster "The Queen of Hearts Plays Noughts and Crosses". Posted Sun 13 Apr 08.
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.
New Fellow of the Australian Academy of Science
Professor Mathai Varghese, Professor of Pure Mathematics and ARC Professorial Fellow within the School of Mathematical Sciences, was elected to the Australian Academy of Science. Professor Varghese's citation read "for his distinguished for his work in geometric analysis involving the topology of manifolds, including the Mathai-Quillen formalism in topological field theory.". Posted Tue 30 Nov 10.

Publications matching "A fixed point theorem on noncompact manifolds"

Publications
D-branes, RR-fields and duality on noncommutative manifolds
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Communications in Mathematical Physics 277 (643–706) 2008
Nonlinear dynamics on centre manifolds describing turbulent floods: k-omega model
Georgiev, D; Roberts, Anthony John; Strunin, D, Discrete and Continuous Dynamical Systems Supplement (419–428) 2007
Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds
Leistner, Thomas, Differential Geometry and its Applications 24 (458–478) 2006
On a generalised Connes-Hochschild-Kostant-Rosenberg theorem
Varghese, Mathai; Stevenson, Daniel, Advances in Mathematics 200 (303–335) 2006
Screen bundles of Lorentzian manifolds and some generalisations of pp-waves
Leistner, Thomas, Journal of Geometry and Physics 56 (2117–2134) 2006
Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
Kordyukov, Y; Varghese, Mathai; Shubin, M, Journal fur die Reine und Angewandte Mathematik 581 (193–236) 2005
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
Prolongations of linear overdetermined systems on affine and riemannian manifolds
Eastwood, Michael, Circolo Matmeatico di Palermo. Rendiconti 75 (89–108) 2005
Self-similar "stagnation point" boundary layer flows with suction or injection
King, J; Cox, Stephen, Studies in Applied Mathematics 115 (73–107) 2005
Smoothly parameterized ech cohomology of complex manifolds
Bailey, T; Eastwood, Michael; Gindikin, S, Journal of Geometric Analysis 15 (9–23) 2005
Smoothly parameterized Cech cohomology of complex manifolds
Bailey, T; Eastwood, Michael; Gindikin, S, Journal of Geometric Analysis 15 (9–23) 2005
Gerbes, Clifford Modules and the index theorem
Murray, Michael; Singer, Michael, Annals of Global Analysis and Geometry 26 (355–367) 2004
Memory, market stability and the nonlinear cobweb theorem
Gaffney, Janice; Pearce, Charles, The ANZIAM Journal 45 (547–555) 2004
Topology and H-flux of T-dual manifolds
Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Physical Review Letters 92 (181601-1–181601-3) 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
Two-zone model of shear dispersion in a channel using centre manifolds
Roberts, Anthony John; Strunin, D, Quarterly Journal of Mechanics and Applied Mathematics 57 (363–378) 2004
Edge of the wedge theory in hypo-analytic manifolds
Eastwood, Michael; Graham, C, Communications in Partial Differential Equations 28 (2003–2028) 2003
Modelling persistence in annual Australian point rainfall
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew, Hydrology and Earth System Sciences 7 (197–211) 2003
On the Clark-Ocone theorem for fractional Brownian motions with Hurst parameter bigger than a half
Bender, C; Elliott, Robert, Stochastics and Stochastic Reports 75 (391–405) 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
Two-point formulae of Euler type
Matic, M; Pearce, Charles; Pecaric, Josip, The ANZIAM Journal 44 (221–245) 2002
The Borel-Weil theorem for complex projective space
Eastwood, Michael; Sawon, J, chapter in Invitations to geometry and topology (Oxford University Press) 126–145, 2002
Lorentzian manifolds with special holonomy and parallel spinors
Leistner, Thomas, Supplemento ai Rendiconti del Circolo Matematico di Palermo II 69 (131–159) 2002
Commutative geometries are spin manifolds
Rennie, Adam, Reviews in Mathematical Physics 13 (409–464) 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
Poisson manifolds in generalised Hamiltonian biomechanics
Ivancevic, V; Pearce, Charles, Bulletin of the Australian Mathematical Society 64 (515–526) 2001
Complex Quaternionic Kahler Manifolds
Eastwood, Michael, chapter in Further advances in twistor theory. Vol. III, Curved twistor spaces (Chapman & Hall/CRC) 31–34, 2001
Introduction to Chern-Simons gauge theory on general 3-manifolds
Adams, David, chapter in Mathematical methods in physics (World Scientific Publishing) 1–43, 2000
A gerbe obstruction to quantization of fermions on odd-dimensional manifolds with boundary
Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 51 (145–160) 2000
More on the pizza theorem
Pearce, Charles, Australian Mathematical Society Gazette 27 (4–5) 2000

Advanced search options

You may be able to improve your search results by using the following syntax:

QueryMatches the following
Asymptotic EquationAnything with "Asymptotic" or "Equation".
+Asymptotic +EquationAnything with "Asymptotic" and "Equation".
+Stokes -"Navier-Stokes"Anything containing "Stokes" but not "Navier-Stokes".
Dynam*Anything containing "Dynamic", "Dynamical", "Dynamicist" etc.