
Search the School of Mathematical SciencesPeople matching "Generalized complex geometry" 
Professor Mathai Varghese Elder Professor of Mathematics, Australian Laureate Fellow, Fellow of the Australian Academy of Scie
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Courses matching "Generalized complex geometry" 
Complex Analysis III When the real numbers are replaced by the complex numbers in the definition of the derivative of a function, the resulting (complex)differentiable functions turn out to have many remarkable properties not enjoyed by their real analogues. These functions, usually known as holomorphic functions, have numerous applications in areas such as engineering, physics, differential equations and number theory, to name just a few. The focus of this course is on the study of holomorphic functions and their most important basic properties. Topics covered are: Complex numbers and functions; complex limits and differentiability; elementary examples; analytic functions; complex line integrals; Cauchy's theorem and the Cauchy integral formula; Taylor's theorem; zeros of holomorphic functions; Rouche's Theorem; the Open Mapping theorem and Inverse Function theorem; Schwarz' Lemma; automorphisms of the ball, the plane and the Riemann sphere; isolated singularities and their classification; Laurent series; the Residue Theorem; calculation of definite integrals and evaluation of infinite series using residues; outlines of the Jordan Curve Theorem, Montel's Theorem and the Riemann Mapping Theorem.
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Finite Geometry III Projective geometry is one of the important modern geometries introduced in the 19th century. Projective geometry is more general than our usual Euclidean geometry, and it has useful applications in Information Security, Statistics, Computer Graphics and Computer Vision. The focus of this course will be primarily on projective planes.
This course will be taught every second year.
Topics covered are: projective planes, homogeneous coordinates, fields, field planes, collineations of projective planes, conics in field planes, projective geometry of general dimension.
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Multivariable and Complex Calculus The mathematics required to describe most "real life" systems involves functions of more than one variable, so the differential and integral calculus developed in a first course in Calculus must be extended to functions of more variables. In this course, the key results of onevariable calculus are extended to higher dimensions: differentiation, integration, and the link between them provided by the Fundamental Theorem of Calculus are all generalised. The machinery developed can be applied to another generalisation of onevariable Calculus, namely to complex calculus, and the course also provides an introduction to this subject. The material covered in this course forms the basis for mathematical analysis and application across an extremely broad range of areas, essential for anyone studying the hard sciences, engineering, or mathematical economics/finance. Topics covered are: introduction to multivariable calculus; differentiation of scalar and vectorvalued functions; higherorder derivatives, extrema, Lagrange multipliers and the implicit function theorem; integration over regions, volumes, paths and surfaces; Green's, Stokes' and Gauss's theorems; differential forms; curvilinear coordinates; an introduction to complex numbers and functions; complex differentiation; complex integration and Cauchy's theorems; and conformal mappings.
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Events matching "Generalized complex geometry" 
TBA 00:00 Wed 30 Nov, 0001 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide


TBA 00:00 Wed 30 Nov, 0001 :: Ingkarni Wardli B17 :: Steve Rosenberg :: University of Adelaide / Boston University
Media...TBA 

Homological algebra and applications  a historical survey 15:10 Fri 19 May, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Amnon Neeman
Homological algebra is a curious branch of
mathematics; it is a powerful tool which has been used in many diverse
places, without any clear understanding why it should be so useful.
We will give a list of applications, proceeding chronologically: first
to topology, then to complex analysis, then to algebraic geometry,
then to commutative algebra and finally (if we have time) to
noncommutative algebra. At the end of the talk I hope to be able to
say something about the part of homological algebra on which I have
worked, and its applications. That part is derived categories. 

Statistical convergence of sequences of complex numbers with application to Fourier series 15:10 Tue 27 Mar, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Ferenc Morics
Media...The concept of statistical convergence was introduced by Henry Fast and Hugo Steinhaus in 1951. But in fact, it was Antoni Zygmund who first proved theorems on the statistical convergence of Fourier series, using the term \"almost convergence\". A sequence $\\{x_k : k=1,2\\ldots\\}$ of complex numbers is said to be statistically convergent to $\\xi$ if for every $\\varepsilon >0$ we have $$\\lim_{n\\to \\infty} n^{1} \\{1\\le k\\le n: x_k\\xi > \\varepsilon\\} = 0.$$ We present the basic properties of statistical convergence, and extend it to multiple sequences. We also discuss the convergence behavior of Fourier series. 

Finite Geometries: Classical Problems and Recent Developments 15:10 Fri 20 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Joseph A. Thas :: Ghent University, Belgium
In recent years there has been an increasing interest in finite projective spaces, and important applications to practical topics such as coding theory, cryptography and design of experiments have made the field even more attractive. In my talk some classical problems and recent developments will be discussed. First I will mention Segre's celebrated theorem and ovals and a purely combinatorial characterization of Hermitian curves in the projective plane over a finite field here, from the beginning, the considered pointset is contained in the projective plane over a finite field. Next, a recent elegant result on semiovals in PG(2,q), due to GÃ¡cs, will be given. A second approach is where the object is described as an incidence structure satisfying certain properties; here the geometry is not a priori embedded in a projective space. This will be illustrated by a characterization of the classical inversive plane in the odd case. Another quite recent beautiful result in Galois geometry is the discovery of an infinite class of hemisystems of the Hermitian variety in PG(3,q^2), leading to new interesting classes of incidence structures, graphs and codes; before this result, just one example for GF(9), due to Segre, was known. 

Rubber Ballons  Prototypes of Hysteresis
15:10 Fri 16 Nov, 2007 :: G04 Napier Building University of Adelaide :: Emeritus Prof. Ingo Muller :: Technical University Berlin
Rubber balloons are characterized by a nonmonotone pressureradius relation which presages interesting nontrivial stability problems. A stability criterion is developed and exploited in order to show that the balloon may be stabilized at any radius by loading it with a piston under an elastic spring, if only the spring is hard enough.
If two connected balloons are subject to an inflationdeflation cycle, the pressureradius curve exhibits a fairly simple hysteresis loop. More complex hysteresis loops appear when more balloons are all inflated together. And if many balloons are inflated and deflated at the same time, the hysteresis loop assumes the form reminiscent of pseudoelasticity. Stability in those complex cases is determined by a simple suggestive argument.
References:
[1] W.Kitsche, I.Muller, P.Strehlow. Simulation of pseudoelastic behaviour in a system of rubber balloons. In: Metastability and Incompletely Posed Problems, S.Antman, J.L.Ericksen, D.Kinderlehrer, I.Muller (eds.) IMA Volume No.3, Springer Verlag, New York (1987)
[2] I.Muller, P.Strehlow, Rubber and Rubber Balloons, Springer Lecture Notes on Physics, Springer Verlag, Heidelberg (2004) 

Probabilistic models of human cognition 15:10 Fri 29 Aug, 2008 :: G03 Napier Building University of Adelaide :: Dr Daniel Navarro :: School of Psychology, University of Adelaide
Over the last 15 years a fairly substantial psychological literature has developed in which human reasoning and decisionmaking is viewed as the solution to a variety of statistical problems posed by the environments in which we operate. In this talk, I briefly outline the general approach to cognitive modelling that is adopted in this literature, which relies heavily on Bayesian statistics, and introduce a little of the current research in this field. In particular, I will discuss work by myself and others on the statistical basis of how people make simple inductive leaps and generalisations, and the links between these generalisations and how people acquire word meanings and learn new concepts. If time permits, the extensions of the work in which complex concepts may be characterised with the aid of nonparametric Bayesian tools such as Dirichlet processes will be briefly mentioned. 

Free surface Stokes flows with surface tension 15:10 Fri 5 Sep, 2008 :: G03 Napier Building University of Adelaide :: Prof. Darren Crowdy :: Imperial College London
In this talk, we will survey a number of different
free boundary problems involving slow viscous (Stokes) flows
in which surface tension is active on the free boundary. Both steady
and unsteady flows will be considered. Motivating applications
range from industrial processes such as viscous sintering (where
endproducts are formed as a result of the surfacetensiondriven densification
of a compact of smaller particles that are heated in order that they
coalesce) to biological phenomena such as understanding how
organisms swim (i.e. propel themselves) at low Reynolds numbers.
Common to our approach to all these problems will be an
analytical/theoretical treatment of model problems via complex variable methods 
techniques wellknown at infinite Reynolds numbers
but used much less often in the Stokes regime. These model
problems can give helpful insights into the behaviour of the true
physical systems. 

Mathematical modelling of blood flow in curved arteries 15:10 Fri 12 Sep, 2008 :: G03 Napier Building University of Adelaide :: Dr Jennifer Siggers :: Imperial College London
Atherosclerosis, characterised by plaques, is the most common arterial
disease. Plaques tend to develop in regions of low mean wall shear
stress, and regions where the wall shear stress changes direction during
the course of the cardiac cycle. To investigate the effect of the
arterial geometry and driving pressure gradient on the wall shear stress
distribution we consider an idealised model of a curved artery with
uniform curvature. We assume that the flow is fullydeveloped and seek
solutions of the governing equations, finding the effect of the
parameters on the flow and wall shear stress distribution. Most
previous work assumes the curvature ratio is asymptotically small;
however, many arteries have significant curvature (e.g. the aortic arch
has curvature ratio approx 0.25), and in this work we consider in
particular the effect of finite curvature.
We present an extensive analysis of curvedpipe flow driven by a steady
and unsteady pressure gradients. Increasing the curvature causes the
shear stress on the inside of the bend to rise, indicating that the risk
of plaque development would be overestimated by considering only the
weak curvature limit. 

Direct "delay" reductions of the Toda equation
13:10 Fri 23 Jan, 2009 :: School Board Room :: Prof Nalini Joshi :: University of Sydney
A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differentialdifference equations, sometimes referred to as
delaydifferential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated to this equation is obtained, also by reduction.


Noncommutative geometry of odddimensional quantum spheres 13:10 Fri 27 Feb, 2009 :: School Board Room :: Dr Partha Chakraborty :: University of Adelaide
We will report on our attempts to understand noncommutative geometry in the lights of the example of quantum spheres. We will see how to produce an equivariant fundamental class and also indicate some of the limitations of isospectral deformations. 

Bibundles 13:10 Fri 6 Mar, 2009 :: School Board Room :: Prof Michael Murray :: University of Adelaide


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


Geometric analysis on the noncommutative torus 13:10 Fri 20 Mar, 2009 :: School Board Room :: Prof Jonathan Rosenberg :: University of Maryland
Noncommutative geometry (in the sense of Alain Connes) involves
replacing a conventional space by a "space" in which the algebra of
functions is noncommutative. The simplest truly nontrivial
noncommutative manifold is the noncommutative 2torus, whose algebra
of functions is also called the irrational rotation algebra. I will
discuss a number of recent results on geometric analysis on the
noncommutative torus, including the study of nonlinear noncommutative
elliptic PDEs (such as the noncommutative harmonic map equation) and
noncommutative complex analysis (with noncommutative elliptic
functions). 

Understanding optimal linear transient growth in complexgeometry flows 15:00 Fri 27 Mar, 2009 :: Napier LG29 :: Associate Prof Hugh Blackburn :: Monash University


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


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


String structures and characteristic classes for loop group bundles 13:10 Fri 1 May, 2009 :: School Board Room :: Mr Raymond Vozzo :: University of Adelaide
The ChernWeil homomorphism gives a geometric method for calculating characteristic classes for principal bundles. In infinite dimensions, however, the standard theory fails due to analytical problems. In this talk I shall give a geometric method for calculating characteristic classes for principal bundle with structure group the loop group of a compact group which sidesteps these complications. This theory is inspired in some sense by results on the string class (a certain cohomology class on the base of a loop group bundle) which I shall outline. 

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 nondegenerate holomorphic twoform $\sigma$. 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. 

ChernSimons 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 ChernSimons 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 wellknown 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 FourierMukai 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. 

Another proof of GaboriauPopa 13:10 Fri 3 Jul, 2009 :: School Board Room :: Prof Greg Hjorth :: University of Melbourne
Gaboriau and Popa showed that a nonabelian free group on finitely many generators has continuum many measure preserving, free, ergodic, actions on standard Borel probability spaces. The original proof used the notion of property (T). I will sketch how this can be replaced by an elementary, and apparently new, dynamical property. 

Generalizations of the SteinTomas restriction theorem 13:10 Fri 7 Aug, 2009 :: School Board Room :: Prof Andrew Hassell :: Australian National University
The SteinTomas 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 LaplaceBeltrami operator on
certain complete Riemannian manifolds. It turns out that dynamical
properties of the geodesic flow play a crucial role in determining whether
a restrictiontype theorem holds for these manifolds.


Asymmetric Cantor measures and sumsets 13:10 Fri 14 Aug, 2009 :: School Board Room :: Prof Gavin Brown :: Royal Institution of Australia and University of Adelaide


Weak Hopf algebras and Frobenius algebras 13:10 Fri 21 Aug, 2009 :: School Board Room :: Prof Ross Street :: Macquarie University
A basic example of a Hopf algebra is a group algebra: it is the vector space having the group as basis and having multiplication linearly extending that of the group. We can start with a category instead of a group, form the free vector space on the set of its morphisms, and define multiplication to be composition when possible and zero when not. The multiplication has an identity if the category has finitely many objects; this is a basic example of a weak bialgebra. It is a weak Hopf algebra when the category is a groupoid. Group algebras are also Frobenius algebras. We shall generalize weak bialgebras and Frobenius algebras to the context of monoidal categories and describe some of their theory using the geometry of string diagrams.


Moduli spaces of stable holomorphic vector bundles 13:10 Fri 28 Aug, 2009 :: School Board Room :: Dr Nicholas Buchdahl :: University of Adelaide


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, ClermontFerrand, 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 "cutoff" 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.


Covering spaces and algebra bundles 13:10 Fri 11 Sep, 2009 :: School Board Room :: Prof Keith Hannabuss :: University of Oxford
Bundles of C*algebras over a topological space M can be classified by a DixmierDouady obstruction in H^3(M,Z). This talk will describe some recent work with Mathai investigating the relationship between algebra bundles on M and on its covering space, where there can be no obstruction, particularly when there is a group acting on M. 

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

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


A FourierMukai transform for invariant differential cohomology 13:10 Fri 9 Oct, 2009 :: School Board Room :: Mr Richard Green :: University of Adelaide
FourierMukai transforms are a geometric analogue of integral transforms playing
an important role in algebraic geometry. Their name derives from the
construction of Mukai involving the Poincare line bundle associated to an
abelian variety. In this talk I will discuss recent work looking at an analogue
of this original FourierMukai transform in the context of differential
geometry, which gives an isomorphism between the invariant differential
cohomology of a real torus and its dual.


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 semiRiemannian 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 KarpelevichMostov theorem. (This is joint work with Antonio J. Di Scala, Politecnico di Torino.) 

Modelling and pricing for portfolio credit derivatives 15:10 Fri 16 Oct, 2009 :: MacBeth Lecture Theatre :: Dr Ben Hambly :: University of Oxford
The current financial crisis has been in part precipitated by the
growth of complex credit derivatives and their mispricing. This talk
will discuss some of the background to the `credit crunch', as well as
the models and methods used currently. We will then develop an alternative
view of large basket credit derivatives, as functions of a stochastic
partial differential equation, which addresses some of the shortcomings. 

Building centralisers in ~A_2 groups 13:10 Fri 23 Oct, 2009 :: School Board Room :: Prof Guyan Robertson :: University of Newcastle, UK


Analytic torsion for twisted de Rham complexes 13:10 Fri 30 Oct, 2009 :: School Board Room :: Prof Mathai Varghese :: University of Adelaide
We define analytic torsion for the twisted de Rham complex, consisting of differential forms on a compact Riemannian manifold X with coefficients in a flat vector bundle E, with a differential given by a flat connection on E plus a closed odd degree differential form on X. The definition in our case is more complicated than in the case discussed by RaySinger, as it uses pseudodifferential operators. We show that this analytic torsion is independent of the choice of metrics on X and E, establish some basic functorial properties, and compute it in many examples. We also establish the relationship of an invariant version of analytic torsion for Tdual circle bundles with closed 3form flux. This is joint work with Siye Wu. 

Upper bounds for the essential dimension of the moduli stack of SL_nbundles over a curve 11:10 Mon 14 Dec, 2009 :: School Board Room :: Dr Nicole Lemire :: University of Western Ontario, Canada
In joint work with Ajneet Dhillon, we find upper bounds for the essential dimension of various moduli stacks of SL_nbundles over a curve. When n is a prime power, our calculation computes the essential dimension of the moduli stack of stable bundles exactly and the essential dimension is not equal to the dimension in this case.


Critical sets of products of linear forms 13:10 Mon 14 Dec, 2009 :: School Board Room :: Dr Graham Denham :: University of Western Ontario, Canada
Suppose $f_1,f_2,\ldots,f_n$ are linear polynomials in $\ell$
variables and $\lambda_1,\lambda_2,\ldots,\lambda_n$ are nonzero complex numbers. The product
$$
\Phi_\lambda=\Prod_{i=1}^n f_1^{\lambda_i},
$$
called a master function,
defines a (multivalued) function on $\ell$dimensional complex space, or more precisely, on the complement of a set of hyperplanes. Then it is easy to ask (but harder to answer) what the set of critical points of a master function looks like, in terms of some properties of the input polynomials and $\lambda_i$'s.
In my talk I will describe the motivation for considering such a question. Then I will indicate how the geometry and combinatorics of hyperplane arrangements can be used to provide at least a partial answer. 

Hartogstype 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 SeveriKneserFicheraMartinelli 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 CauchyRiemann 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. 

Group actions in complex geometry, I and II 13:10 Fri 8 Jan, 2010 :: School Board Room :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne
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Group actions in complex geometry, III and IV 10:10 Fri 15 Jan, 2010 :: School Board Room :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne
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Group actions in complex geometry, V and VI 10:10 Fri 22 Jan, 2010 :: School Board Room :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne
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Group actions in complex geometry, VII and VIII 10:10 Fri 29 Jan, 2010 :: Napier LG 23 :: Prof Frank Kutzschebauch, IGA Lecturer :: University of Berne
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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) 10171020).
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 GromovVaserstein problem 15:10 Fri 29 Jan, 2010 :: Engineering North N 158 Chapman Lecture Theatre :: Prof Frank Kutzschebauch :: University of Berne, Switzerland
Any matrix in $SL_n (\mathbb C)$ can be written as a product of elementary matrices using the Gauss elimination process. If instead of the field of complex numbers, the entries in the matrix are elements of a more general ring, this becomes a delicate question. In particular, rings of complexvalued functions on a space are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size $n$ of the matrix is at least 3. In the topological category, the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\mathbb C^m$, the problem was posed by Gromov in the 1980s. We report on a complete solution to Gromov's problem. A main tool is the OkaGrauertGromov hprinciple in complex analysis. Our main theorem can be formulated as follows: In the absence of obvious topological obstructions, the Gauss elimination process can be performed in a way that depends holomorphically on the matrix. This is joint work with Bj\"orn Ivarsson. 

Proper holomorphic maps from strongly pseudoconvex domains to qconvex 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. 

Conformal geometry of differential equations 13:10 Fri 12 Feb, 2010 :: School Board Room :: Dr Pawel Nurowski :: University of Warsaw


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 wellsuited 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. 

Convolution equations in A^{\infty} for convex domains 13:10 Fri 5 Mar, 2010 :: School Board Room :: Dr Le Hai Khoi :: Nanyang Technological University, Singapore


Holomorphic extension on complex spaces 14:10 Fri 5 Mar, 2010 :: School Board Room :: Prof Egmont Porten :: Mid Sweden University


Conformal structures with G_2 ambient metrics 13:10 Fri 19 Mar, 2010 :: School Board Room :: Dr Thomas Leistner :: University of Adelaide
The nsphere 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 FeffermanGraham 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 7dimensional ambient metric has the noncompact exceptional Lie group G_2 as its holonomy. This is joint work with P. Nurowski, Warsaw University. 

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

Random walk integrals 13:10 Fri 16 Apr, 2010 :: School Board Room :: Prof Jonathan Borwein :: University of Newcastle
Following Pearson in 1905, we study the expected distance of a twodimensional walk in the plane with unit steps in random directionswhat Pearson called a "ramble". A series evaluation and recursions are obtained making it possible to explicitly determine this distance for small number of steps. Closed form expressions for all the moments of a 2step and a 3step walk are given, and a formula is conjectured for the 4step walk. Heavy use is made of the analytic continuation of the underlying integral. 

Loop groups and characteristic classes 13:10 Fri 23 Apr, 2010 :: School Board Room :: Dr Raymond Vozzo :: University of Adelaide
Suppose $G$ is a compact Lie group, $LG$ its (free) loop group and $\Omega G \subseteq LG$ its based loop group. Let $P \to M$ be a principal bundle with structure group one of these loop groups. In general, differential form representatives of characteristic classes for principal bundles can be easily obtained using the ChernWeil homomorphism, however for infinitedimensional bundles such as $P$ this runs into analytical problems and classes are more difficult to construct. In this talk I will explain some new results on characteristic classes for loop group bundles which demonstrate how to construct certain classeswhich we call string classesfor such bundles. These are obtained by making heavy use of a certain $G$bundle associated to any loop group bundle (which allows us to avoid the problems of dealing with infinitedimensional bundles). We shall see that the free loop group case naturally involves equivariant cohomology. 

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 algebraicgeometric 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 Gbundle 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 pseudoisomorphisms
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 presentday 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 algebraicgeometric 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. 

Understanding convergence of meshless methods: Vortex methods and smoothed particle hydrodynamics 15:10 Fri 14 May, 2010 :: Santos Lecture Theatre :: A/Prof Lou Rossi :: University of Delaware
Meshless methods such as vortex methods (VMs) and smoothed particle
hydrodynamics (SPH) schemes offer many advantages in fluid flow computations.
Particlebased computations naturally adapt to complex flow geometries
and so provide a high degree of computational efficiency. Also, particle
based methods avoid CFL conditions because flow quantities are
integrated along characteristics. There are many approaches to
improving numerical methods, but one of the most effective routes
is quantifying the error through the direct estimate of residual
quantities. Understanding the residual for particle schemes requires
a different approach than for meshless schemes but the rewards are
significant. In this seminar, I will outline a general approach to
understanding convergence that has been effective in creating high
spatial accuracy vortex methods, and then I will discuss some recent
investigations in the accuracy of diffusion operators used in SPH
computations. Finally, I will provide some sample NavierStokes
computations of high Reynolds number flows using BlobFlow, an open
source implementation of the high precision vortex method. 

Functorial 2connected 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 pathconnected space with no 1dimensional local pathologies the first stage in the tower can be chosen to be the universal (=1connected) 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 nonfunctorial, depending on a large number of choices. This talk will survey results from my thesis which constructs a new, functorial model for the 2connected 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. 

Interpolation of complex data using spatiotemporal compressive sensing 13:00 Fri 28 May, 2010 :: Santos Lecture Theatre :: A/Prof Matthew Roughan :: School of Mathematical Sciences, University of Adelaide
Many complex datasets suffer from missing data, and interpolating these missing
elements is a key task in data analysis. Moreover, it is often the case that we
see only a linear combination of the desired measurements, not the measurements
themselves. For instance, in network management, it is easy to count the traffic
on a link, but harder to measure the endtoend flows. Additionally, typical
interpolation algorithms treat either the spatial, or the temporal
components of data separately, but in many real datasets have strong
spatiotemporal structure that we would like to exploit in reconstructing the
missing data. In this talk I will describe a novel reconstruction algorithm that
exploits concepts from the growing area of compressive sensing to solve all of
these problems and more. The approach works so well on Internet traffic matrices
that we can obtain a reasonable reconstruction with as much as 98% of the
original data missing. 

On the uniqueness of almostKahler structures 13:10 Fri 28 May, 2010 :: School Board Room :: Dr PaulAndi Nagy :: University of Auckland
We show uniqueness up to sign of positive, orthogonal almostKahler structures on any nonscalar flat KahlerEinstein surface. This is joint work with A. J. di Scala.


Vertex algebras and variational calculus I 13:10 Fri 4 Jun, 2010 :: School Board Room :: Dr Pedram Hekmati :: University of Adelaide
A basic operation in calculus of variations is the EulerLagrange variational
derivative, whose kernel determines the extremals of functionals. There exists a
natural resolution of this operator, called the variational complex.
In this talk, I shall explain how to use tools from the theory of vertex
algebras
to explicitly construct the variational complex. This also provides a very
convenient language for classifying and constructing integrable Hamiltonian
evolution equations. 

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

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

On affine BMW algebras 13:10 Fri 25 Jun, 2010 :: Napier 208 :: Prof Arun Ram :: University of Melbourne
I will describe a family of algebras of tangles (which give rise to link invariants
following the methods of ReshetikhinTuraev and Jones) and describe some aspects of their
structure and their representation theory. The main goal will be to explain how to use
universal Verma modules for the symplectic group to compute the representation theory
of affine BMW (BirmanMurakamiWenzl) algebras. 

Introduction to mirror symmetry and the Fukaya category I 13:10 Thu 15 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category II 13:10 Fri 16 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category III 13:10 Mon 19 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category IV 13:10 Tue 20 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category V 13:10 Wed 21 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


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

EynardOrantin invariants and enumerative geometry 13:10 Fri 6 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Paul Norbury :: University of Melbourne
As a tool for studying enumerative problems in geometry Eynard and Orantin associate multilinear differentials to any plane curve. Their work comes from matrix models but does not require matrix models (for understanding or calculations). In some sense they describe deformations of complex structures of a curve and conjectural relationships to deformations of Kahler structures of an associated object. I will give an introduction to their invariants via explicit examples, mainly to do with the moduli space of Riemann surfaces, in which the plane curve has genus zero. 

Counting lattice points in polytopes and geometry 15:10 Fri 6 Aug, 2010 :: Napier G04 :: Dr Paul Norbury :: University of Melbourne
Counting lattice points in polytopes arises in many areas of pure and applied mathematics. A basic counting problem is this: how many different ways can one give change of 1 dollar into 5,10, 20 and 50 cent coins? This problem counts lattice points in a tetrahedron, and if there also must be exactly 10 coins then it counts lattice points in a triangle. The number of lattice points in polytopes can be used to measure the robustness of a computer network, or in statistics to test independence of characteristics of samples. I will describe the general structure of lattice point counts and the difficulty of calculations. I will then describe a particular lattice point count in which the structure simplifies considerably allowing one to calculate easily. I will spend a brief time at the end describing how this is related to the moduli space of Riemann surfaces. 

Index theory in the noncommutative world 13:10 Fri 20 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Prof Alan Carey :: Australian National University
The aim of the talk is to give an overview of the noncommutative geometry approach to index theory. 

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 wellknown, some notsowellknown. We will
reexamine the proof of an old theorem of Kan in light of these
functors. We will try to keep all jargon to a minimum. 

On some applications of higher Quillen K'theory 13:10 Fri 3 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Snigdhayan Mahanta :: University of Adelaide
In my previous talk I introduced a functor from the category of kalgebras (k field) to abelian groups, called KQtheory. In this talk I will explain its relationship with
topological (homological) Tdualities and twisted Ktheory. 

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 nontriviality 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). 

Some algebras associated with quantum gauge theories 13:10 Fri 15 Oct, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Keith Hannabuss :: Balliol College, Oxford
Classical gauge theories study sections of vector bundles and associated connections and curvature. The corresponding quantum gauge theories are normally written algebraically but can be understood as noncommutative geometries. This talk will describe one approach to the quantum gauge theories which uses braided categories. 

Principal Component Analysis Revisited 15:10 Fri 15 Oct, 2010 :: Napier G04 :: Assoc. Prof Inge Koch :: University of Adelaide
Since the beginning of the 20th century, Principal Component Analysis (PCA) has been an important tool in the analysis of multivariate data. The principal components summarise data in fewer than the original number of variables without losing essential information, and thus allow a split of the data into signal and noise components. PCA is a linear method, based on elegant mathematical theory.
The increasing complexity of data together with the emergence of fast computers in the later parts of the 20th century has led to a renaissance of PCA. The growing numbers of variables (in particular, highdimensional low sample size problems), nonGaussian data, and functional data (where the data are curves) are posing exciting challenges to statisticians, and have resulted in new research which extends the classical theory.
I begin with the classical PCA methodology and illustrate the challenges presented by the complex data that we are now able to collect. The main part of the talk focuses on extensions of PCA: the duality of PCA and the Principal Coordinates of Multidimensional Scaling, Sparse PCA, and consistency results relating to principal components, as the dimension grows. We will also look at newer developments such as Principal Component Regression and Supervised PCA, nonlinear PCA and Functional PCA.


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

Higher stacks and homotopy theory II: the motivic context 13:10 Thu 16 Dec, 2010 :: Ingkarni Wardli B21 :: Mr James Wallbridge :: University of Adelaide and Institut de mathematiques de Toulouse
In part I of this talk (JC seminar May 2008) we presented motivation
and the basic definitions for building homotopy theory into an arbitrary
category by introducing the notion of (higher) stacks. In part II we consider a
specific example on the category of schemes to illustrate how the machinery
works in practice. It will lead us into motivic territory (if we like it or
not). 

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 cmaps 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. 

Bioinspired computation in combinatorial optimization: algorithms and their computational complexity 15:10 Fri 11 Mar, 2011 :: 7.15 Ingkarni Wardli :: Dr Frank Neumann :: The University of Adelaide
Media...Bioinspired computation methods, such as evolutionary algorithms and ant colony
optimization, are being applied successfully to complex engineering and
combinatorial optimization problems. The computational complexity analysis of
this type of algorithms has significantly increased the theoretical
understanding of these successful algorithms. In this talk, I will give an
introduction into this field of research and present some important results
that we achieved for problems from combinatorial optimization. These results
can also be found in my recent textbook "Bioinspired Computation in
Combinatorial Optimization  Algorithms and Their Computational Complexity". 

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

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 1dimensional 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.


Operator algebra quantum groups 13:10 Fri 1 Apr, 2011 :: Mawson 208 :: Dr Snigdhayan Mahanta :: University of Adelaide
Woronowicz initiated the study of quantum groups using C*algebras. His framework enabled him to deal with compact (linear) quantum groups. In this talk we shall introduce a notion of quantum groups that can handle infinite dimensional examples like SU(\infty). We shall also study some quantum homogeneous spaces associated to this group and compute their Ktheory groups. This is joint work with V. Mathai. 

How round is your triangle, square, pentagon, ...? 12:10 Wed 6 Apr, 2011 :: Napier 210 :: Dr Barry Cox :: University of Adelaide
Media...Most of us are familiar with the problem of making circular holes in wood or other material. For smaller diameter holes we typically use a drill, and for larger diameter holes a spadebit, holesaw or plunge router may be used. However for some applications, like mortiseandtenon joints, what is needed is a tool that will produce a hole with a crosssection that is something other than a circle. In this talk we look at curves that may be used as the basis for a device that will produce holes with a crosssection of an equilateral triangle, square, or any regular polygon. Along the way we will touch on areas of engineering, algebra, geometry, calculus, Gothic art and architecture. 

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

Algebraic hypersurfaces arising from Gorenstein algebras 15:10 Fri 8 Apr, 2011 :: 7.15 Ingkarni Wardli :: Associate Prof Alexander Isaev :: Australian National University
Media...To every Gorenstein algebra of finite dimension greater than 1 over a field of characteristic zero, and a projection on its maximal ideal with range equal to the annihilator of the ideal, one can associate a certain algebraic hypersurface lying in the ideal. Such hypersurfaces possess remarkable properties. They can be used, for instance, to help decide whether two given Gorenstein algebras are isomorphic, which for the case of complex numbers leads to interesting consequences in singularity theory. Also, for the case of real numbers such hypersurfaces naturally arise in CRgeometry. In my talk I will discuss these hypersurfaces and some of their applications. 

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

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 longstanding 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 longstanding and difficult problem of finding proper holomorphic
embeddings of Riemann surfaces into C^2, with additional motivation
from other sources.


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). 

Lifting principal bundles and abelian extensions 13:10 Fri 27 May, 2011 :: Mawson 208 :: Prof Michael Murray :: School of Mathematical Sciences
I will review what it means to lift the structure group of a principal bundle
and the topological obstruction to this in the case of a central extension. I will then discuss
some new results in the case of abelian extensions. 

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

Natural operations on the Hochschild cochain complex 13:10 Fri 3 Jun, 2011 :: Mawson 208 :: Dr Michael Batanin :: Macquarie University
The Hochschild cochain complex of an associative algebra provides an important bridge between algebra and geometry.
Algebraically, this is the derived center of the algebra. Geometrically, the Hochschild cohomology of the algebra of smooth functions on a manifold is isomorphic to the graduate space of polyvector fields on this manifold.
There are many important operations acting on the Hochschild complex. It is, however, a tricky question to ask which operations are natural because the Hochschild complex is not a functor. In my talk I will explain how we can overcome this obstacle and compute all possible natural operations on the Hochschild complex. The result leads immediately to a proof of the Deligne conjecture on Hochschild cochains. 

Object oriented data analysis 14:10 Thu 30 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Steve Marron :: The University of North Carolina at Chapel Hill
Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly nonEuclidean spaces, such as Lie Groups and Symmetric Spaces, or of strongly nonEuclidean spaces, such as spaces of treestructured data objects. These new contexts for Object Oriented Data Analysis create several potentially large new interfaces between mathematics and statistics. Even in situations where Euclidean analysis makes sense, there are statistical challenges because of the High Dimension Low Sample Size problem, which motivates a new type of asymptotics leading to nonstandard mathematical statistics. 

Object oriented data analysis of treestructured 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 treestructured objects. Deep challenges arise,
which involve a marriage of ideas from statistics, geometry, and
numerical analysis, because the space of trees is strongly
nonEuclidean 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. 

What is... a tensor? 12:10 Mon 25 Jul, 2011 :: 5.57 Ingkarni Wardli :: Mr Michael Albanese :: School of Mathematical Sciences
Tensors are important objects that are frequently used in a
variety of fields including continuum mechanics, general relativity and
differential geometry. Despite their importance, they are often defined
poorly (if at all) which contributes to a lack of understanding. In this
talk, I will give a concrete definition of a tensor and provide some
familiar examples. For the remainder of the talk, I will discuss some
applications—here I mean applications in the pure maths sense (i.e. more
abstract nonsense, but hopefully still interesting). 

The (dual) local cyclic homology valued ChernConnes character for some infinite dimensional spaces 13:10 Fri 29 Jul, 2011 :: B.19 Ingkarni Wardli :: Dr Snigdhayan Mahanta :: School of Mathematical Sciences
I will explain how to construct a bivariant ChernConnes character on the category of sigmaC*algebras taking values in Puschnigg's local cyclic homology. Roughly, setting the first (resp. the second) variable to complex numbers one obtains the Ktheoretic (resp. dual Khomological) ChernConnes character in one variable. We shall focus on the dual Khomological ChernConnes character and investigate it in the example of SU(infty). 

Towards RogersRamanujan identities for the Lie algebra A_n 13:10 Fri 5 Aug, 2011 :: B.19 Ingkarni Wardli :: Prof Ole Warnaar :: University of Queensland
The RogersRamanujan identities are a pair of qseries identities proved by Leonard Rogers in 1894 which became famous two decades later as conjectures of Srinivasa Ramanujan. Since the 1980s it is known that the RogersRamanujan identities are in fact identities for characters of certain modules for the affine Lie algebra A_1. This poses the obvious question as to whether there exist RogersRamanujan identities for higher rank affine Lie algebras. In this talk I will describe some recent progress on this problem. I will also discuss a seemingly mysterious connection with the representation theory of quivers over finite fields. 

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

Horocycle flows at prime times 13:10 Wed 10 Aug, 2011 :: B.19 Ingkarni Wardli :: Prof Peter Sarnak :: Institute for Advanced Study, Princeton
The distribution of individual orbits of unipotent flows in homogeneous spaces are well
understood thanks to the work work of Marina Ratner. It is conjectured that this property
is preserved on restricting the times from the integers to primes, this being important in the study of prime numbers as well as in such dynamics. We review progress in understanding this conjecture, starting with Dirichlet (a finite system), Vinogradov (rotation of a circle or torus), Green and Tao (translation on a nilmanifold) and Ubis and Sarnak (horocycle flows in the semisimple case).


K3 surfaces: a crash course 13:10 Fri 12 Aug, 2011 :: B.19 Ingkarni Wardli :: A/Prof Nicholas Buchdahl :: University of Adelaide
Everything you have ever wanted to know about K3 surfaces! Two talks: 1:10 pm to 3:00 pm. 

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

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

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. 

Laplace's equation on multiplyconnected domains 12:10 Mon 29 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide
Various physical processes take place on multiplyconnected domains
(domains with some number of 'holes'), such as the stirring of a fluid
with paddles or the extrusion of material from a die. These systems may
be described by partial differential equations (PDEs). However, standard
numerical methods for solving PDEs are not wellsuited to such examples:
finite difference methods are difficult to implement on
multiplyconnected domains, especially when the boundaries are irregular
or moving, while finite element methods are computationally expensive.
In this talk I will describe a fast and accurate numerical method for
solving certain PDEs on twodimensional multiplyconnected domains,
considering Laplace's equation as an example. This method takes
advantage of complex variable techniques which allow the solution to be
found with spectral accuracy provided the boundary data is smooth. Other
advantages over traditional numerical methods will also be discussed. 

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 nonalgebraic hypersurfaces. We provide a complete answer to this question for complements of hyperplane arrangements, and some results for graphs of meromorphic functions. 

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

Twisted Morava Ktheory 13:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne
Morava's extraordinary Ktheories K(n) are a family of generalized cohomology theories which behave in some ways like Ktheory (indeed, K(1) is mod 2 Ktheory). Their construction exploits Quillen's description of cobordism in terms of formal group laws and LubinTate's methods in class field theory for constructing abelian extensions of number fields. Constructed from homotopytheoretic methods, they do not admit a geometric description (like deRham cohomology, Ktheory, or cobordism), but are nonetheless subtle, computable invariants of topological spaces. In this talk, I will give an introduction to these theories, and explain how it is possible to define an analogue of twisted Ktheory in this setting. Traditionally, Ktheory is twisted by a threedimensional cohomology class; in this case, K(n) admits twists by (n+2)dimensional classes. This work is joint with Hisham Sati. 

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

Cohomology of higherrank graphs and twisted C*algebras 13:10 Fri 16 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Aidan Sims :: University of Wollongong
Higherrank graphs and their $C^*$algebras were introduced by Kumjian and Pask in 2000. They have provided a rich source of tractable examples of $C^*$algebras, the most elementary of which are the commutative algebras $C(\mathbb{T}^k)$ of continuous functions on $k$tori. In this talk we shall describe how to define the homology and cohomology of a higherrank graph, and how to associate to each higherrank graph $\Lambda$ and $\mathbb{T}$valued cocycle on $\Lambda$ a twisted higherrank graph $C^*$algebra. As elementary examples, we obtain all noncommutative tori.
This is a preleminary report on ongoing joint work with Alex Kumjian and David Pask. 

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

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

On the role of mixture distributions in the modelling of heterogeneous data 15:10 Fri 14 Oct, 2011 :: 7.15 Ingkarni Wardli :: Prof Geoff McLachlan :: University of Queensland
Media...We consider the role that finite mixture distributions have played in the modelling of heterogeneous data, in particular for clustering continuous data via mixtures of normal distributions. A very brief history is given starting with the seminal papers by Day and Wolfe in the sixties before the appearance of the EM algorithm. It was the publication in 1977 of the latter algorithm by Dempster, Laird, and Rubin that greatly stimulated interest in the use of finite mixture distributions to model heterogeneous data. This is because the fitting of mixture models by maximum likelihood is a classic example of a problem that is simplified considerably by the EM's conceptual unification of maximum likelihood estimation from data that can be viewed as being incomplete. In recent times there has been a proliferation of applications in which the number of experimental units n is comparatively small but the underlying dimension p is extremely large as, for example, in microarraybased genomics and other highthroughput experimental approaches. Hence there has been increasing attention given not only in bioinformatics and machine learning, but also in mainstream statistics, to the analysis of complex data in this situation where n is small relative to p. The latter part of the talk shall focus on the modelling of such highdimensional data using mixture distributions. 

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

Dirac operators on classifying spaces 13:10 Fri 28 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Pedram Hekmati :: University of Adelaide
The Dirac operator was introduced by Paul Dirac in 1928 as the formal square
root of the D'Alembert operator. Thirty years later it was rediscovered in
Euclidean signature by Atiyah and Singer in their seminal work on index theory.
In this talk I will describe efforts to construct a Dirac type operator on the
classifying space for odd complex Ktheory. Ultimately the aim is to produce a
projective family of Fredholm operators realising elements in twisted Ktheory
of a certain moduli stack. 

Staircase to heaven 13:10 Fri 4 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Burkard Polster :: Monash University
Media...How much of an overhang can we produce by stacking identical rectangular blocks at the edge of a table? It has been known for at least 100 years that the overhang can be as large as desired: we arrange the blocks in the form of a staircase. With $n$ blocks of length 2 the overhang can be made to sum to $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\cdots+\frac{1}{n}$. Since the harmonic series diverges, it follows that the overhang can be arranged to be as large as desired, simply by using a suitably large number of blocks.
Recently, a number of interesting twists have been added to this paradoxical staircase. I'll be talking about some of these new developments and in particular about a continuous counterpart of the staircase that I've been pondering together with my colleagues David Treeby and Marty Ross. 

Metric geometry in data analysis 13:10 Fri 11 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Facundo Memoli :: University of Adelaide
The problem of object matching under invariances can be
studied using certain tools from metric geometry. The central idea is
to regard
objects as metric spaces (or metric measure spaces). The type of
invariance that one wishes to have in the matching is encoded by the
choice of the metrics with which one endows the objects. The standard
example is matching objects in Euclidean space under rigid isometries:
in this
situation one would endow the objects with the Euclidean metric. More
general scenarios are possible in which the desired invariance cannot
be reflected by the preservation of an ambient space metric. Several
ideas due to M. Gromov are useful for approaching this problem. The
GromovHausdorff distance is a natural candidate for doing this.
However, this metric leads to very hard combinatorial optimization
problems and it is difficult to relate to previously reported
practical approaches to the problem of object matching. I will discuss
different variations of these ideas, and in particular will show a
construction of an L^p version of the GromovHausdorff metric, called
the GromovWassestein distance, which is based on mass transportation
ideas. This new metric directly leads to quadratic optimization
problems on continuous variables with linear constraints.
As a consequence of establishing several lower bounds, it turns out
that several invariants of metric measure spaces turn out to be
quantitatively stable in the GW sense. These invariants provide
practical tools for the discrimination of shapes and connect the GW
ideas to a number of preexisting approaches. 

Oka theory of blowups 13:10 Fri 18 Nov, 2011 :: B.19 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide
This talk is a continuation of my talk last August. I will discuss the recentlyobtained answers to the open questions I described then. 

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

Space of 2D shapes and the WeilPetersson metric: shapes, ideal fluid and Alzheimer's disease 13:10 Fri 25 Nov, 2011 :: B.19 Ingkarni Wardli :: Dr Sergey Kushnarev :: National University of Singapore
The WeilPetersson metric is an exciting metric on a space of simple
plane curves. In this talk the speaker will introduce the shape space and
demonstrate the connection with the EulerPoincare equations on the group
of diffeomorphisms (EPDiff). A numerical method for finding geodesics
between two shapes will be demonstrated and applied to the surface of the hippocampus to study the effects of Alzheimer's disease. As another application the speaker will discuss how to do statistics on the shape space and what should be done to improve it. 

Fluid flows in microstructured optical fibre fabrication 15:10 Fri 25 Nov, 2011 :: B.17 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide
Optical fibres are used extensively in modern telecommunications as they allow the transmission of information at high speeds. Microstructured optical fibres are a relatively new fibre design in which a waveguide for light is created by a series of air channels running along the length of the material. The flexibility of this design allows optical fibres to be created with adaptable (and previously unrealised) optical properties. However, the fluid flows that arise during fabrication can greatly distort the geometry, which can reduce the effectiveness of a fibre or render it useless. I will present an overview of the manufacturing process and highlight the difficulties. I will then focus on surfacetension driven deformation of the macroscopic version of the fibre extruded from a reservoir of molten glass, occurring during fabrication, which will be treated as a twodimensional Stokes flow problem. I will outline two different complexvariable numerical techniques for solving this problem along with comparisons of the results, both to other models and to experimental data.


Collision and instability in a rotating fluidfilled torus 15:10 Mon 12 Dec, 2011 :: Benham Lecture Theatre :: Dr Richard Clarke :: The University of Auckland
The simple experiment discussed in this talk, first conceived by Madden and
Mullin (JFM, 1994) as part of their investigations into the nonuniqueness
of decaying turbulent flow, consists of a fluidfilled torus which is
rotated in an horizontal plane. Turbulence within the contained flow is
triggered through a rapid change in its rotation rate. The flow
instabilities which transition the flow to this turbulent state, however,
are truly fascinating in their own right, and form the subject of this
presentation. Flow features observed in both UK and Aucklandbased
experiments will be highlighted, and explained through both boundarylayer
analysis and full DNS. In concluding we argue that this flow regime, with
its compact geometry and lack of cumbersome flow entry effects, presents an
ideal regime in which to study many prototype flow behaviours, very much in
the same spirit as TaylorCouette flow. 

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=Xp
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.) 

Plurisubharmonic subextensions as envelopes of disc functionals 13:10 Fri 2 Mar, 2012 :: B.20 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide
I will describe new joint work with Evgeny Poletsky. We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient is a complex manifold with a local biholomorphism to $X$, except it need not be Hausdorff. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension. 

IGA Workshop: The mathematical implications of gaugestring dualities 09:30 Mon 5 Mar, 2012 :: 7.15 Ingkarni Wardli :: Prof Rajesh Gopakumar :: HarishChandra Research Institute
Media...Lecture series by Rajesh Gopakumar (HarishChandra Research Institute). The lectures will be supplemented by talks by other invited speakers. 

The Lorentzian conformal analogue of CalabiYau manifolds 13:10 Fri 16 Mar, 2012 :: B.20 Ingkarni Wardli :: Prof Helga Baum :: Humboldt University
CalabiYau manifolds are Riemannian manifolds with holonomy group SU(m). They are Ricciflat and Kahler and admit a 2parameter 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 CalabiYau manifolds. Such Lorentzian
metrics g, known as Fefferman metrics, appear on S^1bundles over strictly pseudoconvex CR spin manifolds and admit a 2parameter family of conformal Killing spinors.


IGA Workshop: Dualities in field theories and the role of Ktheory 09:30 Mon 19 Mar, 2012 :: 7.15 Ingkarni Wardli :: Prof Jonathan Rosenberg :: University of Maryland
Media...Lecture series by Jonathan Rosenberg (University of Maryland). There will be additional talks by other invited speakers. 

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. 

Bundle gerbes and the FaddeevMickelssonShatashvili anomaly 13:10 Fri 30 Mar, 2012 :: B.20 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide
The FaddeevMickelssonShatashvili anomaly arises in the quantisation of fermions interacting with external gauge potentials. Mathematically, it can be described as a certain lifting problem for an extension of groups. The theory of bundle gerbes is very useful for studying lifting problems, however it only applies in the case of a central extension whereas in the study of the FMS anomaly the relevant extension is noncentral. In this talk I will explain how to describe this anomaly indirectly using bundle gerbes and how to use a generalisation of bundle gerbes to describe the (noncentral) lifting problem directly. This is joint work with Pedram Hekmati, Michael Murray and Danny Stevenson. 

New examples of totally disconnected, locally compact groups 13:10 Fri 20 Apr, 2012 :: B.20 Ingkarni Wardli :: Dr Murray Elder :: University of Newcastle
I will attempt to explain what a totally disconnected,
locally compact group is, and then describe some new work with George
Willis on an attempt to create new examples based on BaumslagSolitar
groups, which are well known, tried and tested
examples/counterexamples in geometric/combinatorial group theory. I
will describe how to compute invariants of scale and flat rank for
these groups. 

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 3manifolds were constructed by Weber,
Siefert, and Lobell in the early 1930's. In the subsequent decades the world
of hyperbolic nmanifolds 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 ndimensional hyperbolic manifolds,
for fixed n, look like a wellordered 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 nmanifold. 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). 

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.


Multiscale models of collective cell behaviour: Linear or nonlinear diffusion? 15:10 Fri 4 May, 2012 :: B.21 Ingkarni Wardli :: Dr Matthew Simpson :: Queensland University of Technology
Media...Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. There is no guidance available in the mathematical biology literature with regard to which approach is more appropriate. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. We provide a link between individualbased and continuum models using a multiscale approach in which we analyse the collective motion of a population of interacting agents in a generalized latticebased exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description is a linear diffusion equation, whereas for elongated rodshaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is a nonlinear diffusion equation related to the porous media equation. We show that there are several reasonable approaches for dealing with agent size effects, and that these different approaches are related mathematically through the concept of mean action time. We extend our results to consider proliferation and travelling waves where greater care must be taken to ensure that the continuum model replicates the discrete process. This is joint work with Dr Ruth Baker (Oxford) and Dr Scott McCue (QUT). 

Index type invariants for twisted signature complexes 13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide
AtiyahPatodiSinger proved an index theorem for nonlocal boundary conditions
in the 1970's that has been widely used in mathematics and mathematical physics.
A key application of their theory gives the index theorem for signature operators on
oriented manifolds with boundary. As a consequence, they defined certain secondary
invariants that were metric independent. I will discuss some recent work with Benameur
where we extend the APS theory to signature operators twisted by an odd degree closed
differential form, and study the corresponding secondary invariants. 

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


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

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 semiRiemannian 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 socalled `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.


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

Enhancing the Jordan canonical form 15:10 Fri 1 Jun, 2012 :: B.21 Ingkarni Wardli :: A/Prof Anthony Henderson :: The University of Sydney
Media...In undergraduate linear algebra, we teach the Jordan canonical form theorem:
that every similarity class of n x n complex matrices contains a special
matrix which is blockdiagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal,
ones on the superdiagonal, and zeroes elsewhere). This is of course very
useful for matrix calculations.
After explaining some of the general context of this result,
I will focus on a case which, despite its close proximity to the Jordan
canonical form theorem, has only recently been worked out: the classification
of pairs of a vector and a matrix.


Model turbulent floods based upon the Smagorinski large eddy closure 12:10 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Meng Cao :: University of Adelaide
Media...Rivers, floods and tsunamis are often very turbulent. Conventional models of such environmental fluids are typically based on depthaveraged inviscid irrotational flow equations. We explore changing such a base to the turbulent Smagorinski large eddy closure. The aim is to more appropriately model the fluid dynamics of such complex environmental fluids by using such a turbulent closure. Large changes in fluid depth are allowed. Computer algebra constructs the slow manifold of the flow in terms of the fluid depth h and the mean turbulent lateral velocities u and v. The major challenge is to deal with the nonlinear stress tensor in the Smagorinski closure. The model integrates the effects of inertia, selfadvection, bed drag, gravitational forcing and turbulent dissipation with minimal assumptions. Although the resultant model is close to established models, the real outcome is creating a sound basis for the modelling so others, in their modelling of more complex situations, can systematically include more complex physical processes. 

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

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

Notions of noncommutative metric spaces; why and how 15:10 Fri 15 Jun, 2012 :: B.21 Ingkarni Wardli :: Dr Ittay Weiss :: The University of the South Pacific
Media...The classical notion of metric space includes the axiom of symmetry: d(x,y)=d(y,x). Some applications of metric techniques to problems in computer graphics, concurrency, and physics (to mention a few) are seriously stressing the limitations imposed by symmetry, resulting in various relaxations of it. I will review some of the motivating problems that seem to require nonsymmetry and then review some of the suggested models to deal with the problem. My review will be critical to the topological implications (which are often unpleasant) of some of the models and I will present metric 1spaces, a new notion of generalized metric spaces. 

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


Complex geometry and operator theory 14:10 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Prof Ron Douglas :: Texas A&M University
In the study of bounded operators on Hilbert spaces of holomorphic functions, concepts and techniques from complex geometry are important. An antiholomorphic bundle exists on which one can define the Chern connection. Its curvature turns out to be a complete invariant and various operator notions can't be reframed in terms of geometrical ones which leads to the solution of some problems. We will discuss this approach with an emphasis on natural examples in the one and multivariable case.


Inquirybased learning: yesterday and today 15:30 Mon 9 Jul, 2012 :: Ingkarni Wardli B19 :: Prof Ron Douglas :: Texas A&M University
Media...The speaker will report on a project to develop and promote approaches to mathematics instruction closely related to the Moore method  methods which are called inquirybased learning  as well as on his personal experience of the Moore method. For background, see the speaker's article in the May 2012 issue of the Notices of the American Mathematical Society. To download the article, click on "Media" above. 

The motivic logarithm and its realisations 13:10 Fri 3 Aug, 2012 :: Engineering North 218 :: Dr James Borger :: Australian National University
When a complex manifold is defined by polynomial equations, its cohomology groups inherit extra structure. This was discovered by Hodge in the 1920s and 30s. When the defining polynomials have rational coefficients, there is some additional, arithmetic structure on the cohomology. This was discovered by Grothendieck and others in the 1960s. But here the situation is still quite mysterious because each cohomology group has infinitely many different arithmetic structures and while they are not directly comparable, they share many propertieswith each other and with the Hodge structure.
All written accounts of this that I'm aware of treat arbitrary varieties. They are beautifully abstract and nonexplicit. In this talk, I'll take the opposite approach and try to give a flavour of the subject by working out a perhaps the simplest nontrivial example, the cohomology of C* relative to a subset of two points, in beautifully concrete and explicit detail. Here the common motif is the logarithm. In Hodge theory, it is realised as the complex logarithm; in the crystalline theory, it's as the padic logarithm; and in the etale theory, it's as Kummer theory.
I'll assume you have some familiarity with usual, singular cohomology of topological spaces, but I won't assume that you know anything about these nontopological cohomology theories. 

Geometry  algebraic to arithmetic to absolute 15:10 Fri 3 Aug, 2012 :: B.21 Ingkarni Wardli :: Dr James Borger :: Australian National University
Media...Classical algebraic geometry is about studying solutions to systems of polynomial equations with complex coefficients. In arithmetic algebraic geometry, one digs deeper and studies the arithmetic properties of the solutions when the coefficients are rational, or even integral. From the usual point of view, it's impossible to go deeper than this for the simple reason that no smaller rings are available  the integers have no proper subrings. In this talk, I will explain how an emerging subject, lambdaalgebraic geometry, allows one to do just this and why one might care. 

The importance of being fractal 13:10 Tue 7 Aug, 2012 :: 7.15 Ingkarni Wardli :: Prof Tony Roberts :: School of Mathematical Sciences
Media...Euclid's geometry describes the world around us in terms of points, lines and planes. For two thousand years these have formed the limited repertoire of basic geometric objects with which to describe the universe. Fractals immeasurably enhance this worldview by providing a description of much around us that is rough and fragmentedof objects that have structure on many sizes.


Hodge numbers and cohomology of complex algebraic varieties 13:10 Fri 10 Aug, 2012 :: Engineering North 218 :: Prof Gus Lehrer :: University of Sydney
Let $X$ be a complex algebraic variety defined over the ring $\mathfrak{O}$ of integers in a number field $K$ and let $\Gamma$ be a group of $\mathfrak{O}$automorphisms of $X$. I shall discuss how the counting of rational points over reductions mod $p$ of $X$, and an analysis of the Hodge structure of the cohomology of $X$, may be used to determine the cohomology as a $\Gamma$module. This will include some joint work with Alex Dimca and with Mark Kisin, and some classical unsolved problems.


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

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

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 ConnesChern 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 ConnesChern 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 antihyperbolicity 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 antihyperbolicity 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 EnriquesKodaira classification of surfaces. 

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


Geometric quantisation in the noncompact setting 13:10 Fri 14 Sep, 2012 :: Engineering North 218 :: Dr Peter Hochs :: Leibniz University, Hannover
Traditionally, the geometric quantisation of an action by a compact Lie group on a compact symplectic manifold is defined as the equivariant index of a certain Dirac operator. This index is a welldefined formal difference of finitedimensional representations, since the Dirac operator is elliptic and the manifold and the group in question are compact. From a mathematical and physical point of view however, it is very desirable to extend geometric quantisation to noncompact groups and manifolds. Defining a suitable index is much harder in the noncompact setting, but several interesting results in this direction have been obtained. I will review the difficulties connected to noncompact geometric quantisation, and some of the solutions that have been proposed so far, mainly in connection to the "quantisation commutes with reduction" principle. (An introduction to this principle will be given in my talk at the Colloquium on the same day.)


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

Introduction to pairings in cryptography 13:10 Fri 21 Sep, 2012 :: Napier 209 :: Dr Naomi Benger :: University of Adelaide
From cryptanalysis to a powerful tool which made identity based cryptography possible, pairings have a range of applications in cryptography. I will present basic background (algebraic geometry) needed to understand pairings, hard problems associated with pairings and protocols which use pairings. 

Turbulent flows, semtex, and rainbows 12:10 Mon 8 Oct, 2012 :: B.21 Ingkarni Wardli :: Ms Sophie Calabretto :: University of Adelaide
Media...The analysis of turbulence in transient flows has applications across a broad range of fields. We use the flow of fluid in a toroidal container as a paradigm for studying the complex dynamics due to this turbulence. To explore the dynamics of our system, we exploit the numerical capabilities of semtex; a quadrilateral spectral element DNS code. Rainbows result. 

Complex analysis in low Reynolds number hydrodynamics 15:10 Fri 12 Oct, 2012 :: B.20 Ingkarni Wardli :: Prof Darren Crowdy :: Imperial College London
Media...It is a wellknown fact that the methods of complex analysis provide great advantage
in studying physical problems involving a harmonic field satisfying Laplace's equation.
One example is in ideal fluid mechanics (infinite Reynolds number)
where the absence of viscosity, and the
assumption of zero vorticity, mean that it is possible to introduce a socalled
complex potential  an analytic function from which all physical quantities of
interest can be inferred.
In the opposite limit of zero Reynolds number flows which are slow and viscous
and the governing fields are not harmonic
it is much less common to employ the methods of complex analysis
even though they continue to be relevant in certain circumstances.
This talk will give an overview of a variety of problems involving slow viscous Stokes
flows where complex analysis can be usefully employed to gain theoretical
insights. A number of example problems will be considered including
the locomotion of lowReynoldsnumber microorganisms and microrobots,
the friction properties of superhydrophobic surfaces in microfluidics and
problems of viscous sintering and the manufacture of microstructured optic fibres (MOFs). 

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

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

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

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

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


Twisted analytic torsion and adiabatic limits 13:10 Wed 5 Dec, 2012 :: Ingkarni Wardli B17 :: Mr Ryan Mickler :: University of Adelaide
We review MathaiWu's recent extension of RaySinger analytic torsion to supercomplexes. We explore some new results relating these two torsions, and how we can apply the adiabatic spectral sequence due to Forman and Farber's analytic deformation theory to compute some spectral invariants of the complexes involved, answering some questions that were posed in MathaiWu's paper.


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 biHermitian 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 CalabiYau manifolds. 

Hyperplane arrangements and tropicalization of linear spaces 10:10 Mon 17 Dec, 2012 :: Ingkarni Wardli B17 :: Dr Graham Denham :: University of Western Ontario
I will give an introduction to a sequence of ideas in tropical
geometry, the tropicalization of linear spaces. In the beginning, a construction due to De Concini and Procesi (wonderful models, 1995) gave a combinatorially explicit description of various iterated blowups of projective spaces along (proper transforms of) linear subspaces. A decade later, Tevelev's notion of tropical compactifications led to, in particular, a new view of the wonderful models and their intersection theory in terms of the theory of toric varieties (via work of FeichtnerSturmfels, FeichtnerYuzvinsky, ArdilaKlivans, and others). Recently, these ideas have played a role in Huh and Katz's proof of a longstanding conjecture in combinatorics. 

Stably Cayley groups over fields of characteristic 0 11:10 Mon 17 Dec, 2012 :: Ingkarni Wardli B17 :: Dr Nicole Lemire :: University of Western Ontario
A linear algebraic group is called a Cayley group if it is equivariantly
birationally isomorphic to its Lie algebra. It is stably Cayley
if the product of the group and some torus is Cayley. Cayley gave the first
examples of Cayley groups with his Cayley map back in 1846. Over an algebraically closed
field of characteristic 0, Cayley and stably Cayley simple groups were
classified by
Lemire, Popov and Reichstein in 2006.
In recent joint work with Blunk, Borovoi, Kunyavskii and Reichstein, we classify the simple stably Cayley groups over an arbitrary field of
characteristic 0. 

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 nontrivial 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. 

Twistor theory and the harmonic hull 15:10 Fri 8 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Michael Eastwood :: Australian National University
Media...Harmonic functions are realanalytic and so automatically extend as functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated conformal geometry. Nothing will be supposed about such matters: I shall base the constructions on an elementary yet mysterious formula of Bateman from 1904. This is joint work with Feng Xu. 

Twistor space for rolling bodies 12:10 Fri 15 Mar, 2013 :: Ingkarni Wardli B19 :: Prof Pawel Nurowski :: University of Warsaw
We consider a configuration space of two solids rolling on each other
without slipping or twisting, and identify it with an open subset U of
R^5, equipped with a generic distribution D of 2planes. We will discuss
symmetry properties of the pair (U,D) and will mention that, in the case
of the two solids being balls, when changing the ratio of their radii,
the dimension of the group of local symmetries unexpectedly jumps from 6
to 14. This occurs for only one such ratio, and in such case the local
group of symmetries of the pair (U,D) is maximal. It is maximal not only
among the balls with various radii, but more generally among all (U,D)s
corresponding to configuration spaces of two solids rolling on each
other without slipping or twisting. This maximal group is isomorphic to
the split real form of the exceptional Lie group G2.
In the remaining part of the talk we argue how to identify the space U
from the pair (U,D) defined above with the bundle T of totally null real
2planes over a 4manifold equipped with a split signature metric. We
call T the twistor bundle for rolling bodies. We show that the rolling
distribution D, can be naturally identified with an appropriately defined
twistor distribution on T. We use this formulation of the rolling system
to find more surfaces which, when rigidly rolling on each other without
slipping or twisting, have the local group of symmetries isomorphic to
the exceptional group G2. 

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

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 runiform 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
kcolouring.
We consider the problem of kcolouring a random runiform 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. 

Gauge groupoid cocycles and CheegerSimons differential characters 13:10 Fri 5 Apr, 2013 :: Ingkarni Wardli B20 :: Prof Jouko Mickelsson :: Royal Institute of Technology, Stockholm
Groups of gauge transformations in quantum field theory are typically
extended by a 2cocycle with values in a certain abelian group due to chiral symmetry breaking. For these extensions there exist a global explicit construction since the 1980's. I shall study the higher group cocycles following a recent paper by F. Wagemann and C. Wockel, but extending to the transformation groupoid
setting (motivated by QFT) and discussing potential obstructions in the
construction due to a nonvanishing of low dimensional homology groups
of the gauge group. The resolution of the obstruction is obtained
by an application of the CheegerSimons differential characters. 

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. 

Mtheory and higher gauge theory 13:10 Fri 12 Apr, 2013 :: Ingkarni Wardli B20 :: Dr Christian Saemann :: HeriotWatt University
I will review my recent work on integrability of Mbrane configurations and
the description of Mbrane models in higher gauge theory. In particular, I
will discuss categorified analogues of instantons and present superconformal equations of motion for the nonabelian tensor multiplet in six dimensions. The latter are derived from considering nonabelian gerbes on certain twistor spaces. 

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

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 localtoglobal 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. 

Models of cellextracellular matrix interactions in tissue engineering 15:10 Fri 3 May, 2013 :: B.18 Ingkarni Wardli :: Dr Ed Green :: University of Adelaide
Media...Tissue engineers hope in future to be able to grow functional tissues in vitro to replace those that are damaged by injury, disease, or simple wear and tear. They use cell culture methods, such as seeding cells within collagen gels, that are designed to mimic the cells' environment in vivo. Amongst other factors, it is clear that mechanical interactions between cells and the extracellular matrix (ECM) in which they reside play an important role in tissue development. However, the mechanics of the ECM is complex, and at present, its role is only partly understood. In this talk, I will present mathematical models of some simple cellECM interaction problems, and show how they can be used to gain more insight into the processes that regulate tissue development. 

Diffeological spaces and differentiable stacks 12:10 Fri 10 May, 2013 :: Ingkarni Wardli B19 :: Dr David Roberts :: University of Adelaide
The category of finitedimensional 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 I: the classical theory 12:10 Fri 17 May, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide
A discrete isometry group acting properly discontinuously on the ndimensional
Euclidean space with compact quotient is called a crystallographic group.
This name reflects the fact that in dimension n=3 their compact fundamental
domains resemble a spacefilling crystal pattern.
For higher dimensions, Hilbert posed his famous 18th problem:
"Is there in ndimensional Euclidean space only a finite number of essentially
different kinds of groups of motions with a [compact] fundamental region?"
This problem was solved by Bieberbach when he proved that in every
dimension n there exists only a finite number of isomorphic crystallographic groups
and also gave a description of these groups.
From the perspective of differential geometry these results are of major importance,
as crystallographic groups are precisely the fundamental groups of
compact flat Riemannian orbifolds.
The quotient is even a manifold if the fundamental group is required to be torsionfree,
in which case it is called a Bieberbach group.
Moreover, for a flat manifold the fundamental group completely determines the
holonomy group.
In this talk I will discuss the properties of crystallographic groups, study examples in
dimension n=2 and n=3, and present the three Bieberbach theorems on the
structure of crystallographic groups.


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 pseudoRiemannian manifolds.
Still more generally, one might study group of affine transformation on nspace
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 pseudoRiemannian
spaces. 

A strong Oka principle for proper immersions of finitely connected planar domains into CxC* 12:10 Fri 31 May, 2013 :: Ingkarni Wardli B19 :: Dr Tyson Ritter :: University of Adelaide
Gromov, in his seminal 1989 paper on the Oka principle, proved that every continuous map from a Stein manifold into an elliptic manifold is homotopic to a holomorphic map. In previous work we showed that, given a continuous map from X to the elliptic manifold CxC*, where X is a finitely connected planar domain without isolated boundary points, a stronger Oka property holds whereby the map is homotopic to a proper holomorphic embedding. If the planar domain is additionally permitted to have isolated boundary points the problem becomes more difficult, and it is not yet clear whether a strong Oka property for embeddings into CxC* continues to hold. We will discuss recent results showing that every continuous map from a finitely connected planar domain into CxC* is homotopic to a proper immersion that, in most cases, identifies at most finitely many pairs of distinct points. This is joint work with Finnur Larusson. 

A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces 12:10 Fri 7 Jun, 2013 :: Ingkarni Wardli B19 :: Prof Thierry Coulhon :: Australian National University
On doubling metric measure spaces endowed with a Dirichlet form and satisfying the DaviesGaffney estimate, we show some characterisations of pointwise upper bounds
of the heat kernel in terms of oneparameter weighted inequalities which correspond respectively to the Nash inequality and to a GagliardoNirenberg type inequality when the volume growth is polynomial. This yields a new and simpler proof of the wellknown equivalence between classical heat kernel upper bounds and the relative FaberKrahn inequalities. We are also able to treat more general pointwise estimates where the heat kernel rate of decay is not necessarily governed by the volume growth. This is a joint work with Salahaddine Boutayeb and Adam Sikora. 

Heat kernel estimates on noncompact Riemannian manifolds: why and how? 15:10 Fri 7 Jun, 2013 :: B.18 Ingkarni Wardli :: Prof Thierry Coulhon :: Australian National University
Media...We will describe what is known and remains to be known about the connection between the large scale geometry of noncompact Riemannian manifolds
(and more general metric measure spaces) and large time estimates of their heat kernel. We will show how some of these estimates can be characterised in terms of Sobolev inequalities and give applications to the boundedness of Riesz transforms. 

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

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

IGA/AMSI Workshop: Representation theory and operator algebras 10:00 Mon 1 Jul, 2013 :: 7.15 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University
Media...This interdisciplinary workshop will be about aspects of representation theory (in the sense of HarishChandra), aspects of noncommutative geometry (in the sense of Alain Connes) and aspects of operator Ktheory (in the sense of Gennadi Kasparov). It features the renowned speaker, Professor Nigel Higson (Penn State University) http://www.iga.adelaide.edu.au/workshops/WorkshopJuly2013/ All are welcome. 

Khomology and the quantization commutes with reduction problem 12:10 Fri 5 Jul, 2013 :: 7.15 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University
The quantization commutes with reduction problem for Hamiltonian actions of compact Lie groups was solved by Meinrenken in the mid1990s using geometric techniques, and solved again shortly afterwards by Tian and Zhang using analytic methods. In this talk I shall outline some of the close links that exist between the problem, the two solutions, and the geometric and analytic versions of Khomology theory that are studied in noncommutative geometry. I shall try to make the case for Khomology as a useful conceptual framework for the solutions and (at least some of) their various generalizations. 

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

The search for the exotic  subfactors and conformal field theory 13:10 Fri 26 Jul, 2013 :: EngineeringMaths 212 :: Prof David E. Evans :: Cardiff University
Subfactor theory provides a framework for studying modular invariant partition functions in conformal field theory,
and candidates for exotic modular tensor categories. I will describe work with Terry Gannon on the search for exotic theories
beyond those from symmetries based on loop groups, WessZuminoWitten models and finite groups. 

FireAtmosphere Models 12:10 Mon 29 Jul, 2013 :: B.19 Ingkarni Wardli :: Mika Peace :: University of Adelaide
Media...Fire behaviour models are increasingly being used to assist in planning and operational decisions for bush fires and fuel reduction burns. Rate of spread (ROS) of the fire front is a key output of such models. The ROS value is typically calculated from a formula which has been derived from empirical data, using very simple meteorological inputs. We have used a coupled fireatmosphere model to simulate real bushfire events. The results show that complex interactions between a fire and the atmosphere can have a significant influence on fire spread, thus highlighting the limitations of a model that uses simple meteorological inputs. 

Subfactors and twisted equivariant Ktheory 12:10 Fri 2 Aug, 2013 :: Ingkarni Wardli B19 :: Prof David E. Evans :: Cardiff University
The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. FreedHopkinsTeleman have expressed the Verlinde ring for the CFTs associated to loop groups as twisted equivariant Ktheory. In joint work with Terry Gannon, we build on their work to express Ktheoretically the structures of full CFT. In particular, the modular invariant partition functions (which essentially parametrise the possible full CFTs) have a rich interpretation within von Neumann algebras (subfactors), which has led to the developments of structures of full CFT such as the full system (fusion ring of defect lines), nimrep (cylindrical partition function), alphainduction etc. 

Symplectic Lie groups 12:10 Fri 9 Aug, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide
A "symplectic Lie group" is a Lie group G with a symplectic form such that G acts by symplectic transformations on itself. Such a G cannot be semisimple, so the research focuses on solvable symplectic Lie groups. In the compact case, a classification of these groups is known. In many cases, a solvable symplectic Lie group G is a cotangent bundle of a flat Lie group H. Then H is a Lagrange subgroup of G, meaning its Lie algebra h is isotropic in the Lie algebra g of G. The existence of Lagrange subalgebras or ideals in g is an important question which relates to many problems in the general structure theory of symplectic Lie groups.
In my talk, I will give a brief overview of the known results in this field, ranging from the 1970s to a very recent structure theory. 

A survey of nonabelian cohomology 12:10 Fri 16 Aug, 2013 :: Ingkarni Wardli B19 :: Dr Danny Stevenson :: University of Adelaide
If G is a topological group, not necessarily abelian, then the set H^1(M,G)
has a natural interpretation in terms of principal Gbundles on the space
M. In this talk I will describe higher degree analogs of both the set H^1(M,G)
and the notion of a principal bundle (the latter is closely connected to the
subject of bundle gerbes). I will explain, following work of Joyal,
Jardine and many others, how the language of abstract homotopy theory
gives a very convenient framework for discussing these ideas. 

The Einstein equations with torsion, reduction and duality 12:10 Fri 23 Aug, 2013 :: Ingkarni Wardli B19 :: Dr David Baraglia :: University of Adelaide
We consider the Einstein equations for connections with skew torsion. After some general remarks we look at these equations on principal Gbundles, making contact with string structures and heterotic string theory in the process. When G is a torus the equations are shown to possess a symmetry not shared by the usual Einstein equations  Tduality. This is joint work with Pedram Hekmati. 

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

What are fusion categories? 12:10 Fri 6 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Scott Morrison :: Australian National University
Fusion categories are a common generalization of finite groups and quantum groups at roots of unity. I'll explain a little of their structure, mention their applications (to topological field theory and quantum computing), and then explore the ways in which they are in general similar to, or different from, the 'classical' cases. We've only just started exploring, and don't yet know what the exotic examples we've discovered signify about the landscape ahead. 

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

The logarithmic singularities of the Green functions of the conformal powers of the Laplacian 11:10 Mon 16 Sep, 2013 :: Ingkarni Wardli B20 :: Prof Raphael Ponge :: Seoul National University
Green functions play an important role in conformal geometry. In this talk, we shall explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators are the Yamabe and Paneitz operators, as well as the conformal fractional powers of the Laplacian arising from scattering theory for PoincareEinstein metrics. The results are formulated in terms of Weyl conformal invariants defined via the ambient metric of FeffermanGraham. 

Noncommutative geometry and conformal geometry 13:10 Mon 16 Sep, 2013 :: Ingkarni Wardli B20 :: Prof Raphael Ponge :: Seoul National University
In this talk we shall report on a program of using the recent framework of twisted spectral triples to study conformal geometry from a noncommutative geometric perspective. One result is a local index formula in conformal geometry taking into account the action of the group of conformal diffeomorphisms. Another result is a version of VafaWitten's inequality for twisted spectral triples. Geometric applications include a version of VafaWitten's inequality in conformal geometry. There are also noncommutative versions for spectral triples over noncommutative tori and duals of discrete cocompact subgroups of semisimple Lie groups satisfying the BaumConnes conjecture. (This is joint work with Hang Wang.) 

Conformal geometry in four variables and a special geometry in five 12:10 Fri 20 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Dennis The :: Australian National University
Starting with a split signature 4dimensional conformal manifold, one can build a 5dimensional bundle over it equipped with a 2plane distribution. Generically, this is a (2,3,5)distribution in the sense of Cartan's five variables paper, an aspect that was recently pursued by Daniel An and Pawel Nurowski (finding new examples concerning the geometry of rolling bodies where the (2,3,5)distribution has G2symmetry). I shall explain how to understand some elementary aspects of this "twistor construction" from the perspective of parabolic geometry. This is joint work with Michael Eastwood and Katja Sagerschnig. 

Symmetry gaps for geometric structures 15:10 Fri 20 Sep, 2013 :: B.18 Ingkarni Wardli :: Dr Dennis The :: Australian National University
Media...Klein's Erlangen program classified geometries based on their (transitive) groups of symmetries, e.g. Euclidean geometry is the quotient of the rigid motion group by the subgroup of rotations. While this perspective is homogeneous, Riemann's generalization of Euclidean geometry is in general very "lumpy"  i.e. there exist Riemannian manifolds that have no symmetries at all. A common generalization where a group still plays a dominant role is Cartan geometry, which first arose in Cartan's solution to the equivalence problem for geometric structures, and which articulates what a "curved version" of a flat (homogeneous) model means. Parabolic geometries are Cartan geometries modelled on (generalized) flag varieties (e.g. projective space, isotropic Grassmannians) which are wellknown objects from the representation theory of semisimple Lie groups. These curved versions encompass a zoo of interesting geometries, including conformal, projective, CR, systems of 2nd order ODE, etc. This interaction between differential geometry and representation theory has proved extremely fruitful in recent years. My talk will be an examplebased tour of various types of parabolic geometries, which I'll use to outline some of the main aspects of the theory (suppressing technical details). The main thread throughout the talk will be the symmetry gap problem: For a given type of Cartan geometry, the maximal symmetry dimension is realized by the flat model, but what is the next possible ("submaximal") symmetry dimension? I'll sketch a recent solution (in joint work with Boris Kruglikov) for a wide class of parabolic geometries which gives a combinatorial recipe for reading the submaximal symmetry dimension from a Dynkin diagram. 

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

Dynamics and the geometry of numbers 14:10 Fri 27 Sep, 2013 :: Horace Lamb Lecture Theatre :: Prof Akshay Venkatesh :: Stanford University
Media...It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in R^n. (A lattice is simply a grid of points.) This technique is called the "geometry of numbers." We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects. 

Exact FeffermanGraham metrics 12:10 Fri 11 Oct, 2013 :: Ingkarni Wardli B19 :: Prof Pawel Nurowski :: University of Warsaw


Geodesic completeness of compact ppwaves 12:10 Fri 18 Oct, 2013 :: Ingkarni Wardli B19 :: Dr Thomas Leistner :: University of Adelaide
A semiRiemannian 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 CliftonPohl 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 ppwaves, 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 ppwave 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^2Lefschetz 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, cocompactly and isometrically. These localised indices, generalising the L^2index of Atiyah, are obtained by taking HattoriStallings 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 BaiLing Wang. 

Group meeting 15:10 Fri 25 Oct, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Ben Binder and Mr David Wilke :: University of Adelaide
Dr Ben Binder :: 'An inverse approach for solutions to freesurface flow problems'
:: Abstract: Surface water waves are familiar to most people, for example, the wave
pattern generated at the stern of a ship. The boundary or interface
between the air and water is called the freesurface. When determining a
solution to a freesurface flow problem it is commonplace for the forcing
(eg. shape of ship or waterbed topography) that creates the surface waves
to be prescribed, with the freesurface coming as part of the solution.
Alternatively, one can choose to prescribe the shape of the freesurface
and find the forcing inversely. In this talk I will discuss my ongoing
work using an inverse approach to discover new types of solutions to
freesurface flow problems in two and three dimensions, and how the
predictions of the method might be verified with experiments. ::
Mr David Wilke:: 'A Computational Fluid Dynamic Study of Blood Flow Within the Coiled Umbilical Arteries'::
Abstract: The umbilical cord is the lifeline of the fetus throughout gestation. In a normal pregnancy it facilitates the supply of oxygen and nutrients from the placenta via a single vein, in addition to the return of deoxygenated blood from the developing embryo or fetus via two umbilical arteries. Despite the major role it plays in the growth of the fetus, pathologies of the umbilical cord are poorly understood. In particular, variations in the cord geometry, which typically forms a helical arrangement, have been correlated with adverse outcomes in pregnancy. Cords exhibiting either abnormally low or high levels of coiling have been associated with pathological results including growthrestriction and fetal demise. Despite this, the methodology currently employed by clinicians to characterise umbilical pathologies can misdiagnose cords and is prone to error. In this talk a computational model of blood flow within rigid threedimensional structures representative of the umbilical arteries will be presented. This study determined that the current characterization was unable to differentiate between cords which exhibited clinically distinguishable flow properties, including the cord pressure drop, which provides a measure of the loading on the fetal heart.


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 byproduct of research into Finsler geometry. If time permits, I will also discuss some of the open problems in the subject. 

The geometry of rolling surfaces and nonholonomic mechanics 15:10 Fri 1 Nov, 2013 :: B.18 Ingkarni Wardli :: Prof Robert Bryant :: Duke University
Media...In mechanics, the system of a sphere rolling over a plane without slipping or twisting is a fundamental example of what is called a nonholonomic mechanical system, the study of which belongs to the subject of control theory. The more general case of one surface rolling over another without slipping or twisting is, similarly, of great interest for both practical and theoretical reasons. In this talk, which is intended for a general mathematical audience (i.e., no familiarity with control theory or differential geometry will be assumed), I will describe some of the basic features of this problem, a bit of its history, and some of the surprising developments that its study reveals, such as the unexpected appearance of the exceptional group G_2. 

Braids and entropy 10:10 Fri 8 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Burglind Joricke :: Australian National University
This talk will be a brief introduction to some aspects of braid theory and to entropy, to provide background for the speaker's talk at 12:10 pm the same day.


Braids, conformal module and entropy 12:10 Fri 8 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Burglind Joricke :: Australian National University
I will discuss two invariants of conjugacy classes of braids.
The first invariant is the conformal module which implicitly occurred
already in a paper of Gorin and Lin in connection with their
interest in Hilbert's 13th problem. The second is a popular
dynamical invariant, the entropy. It appeared in connection
with Thurston's theory of surface homeomorphisms.
It turns out that these invariants are related: They are inversely
proportional.
In a preparatory talk (at 10:10 am) I will give a brief introduction to some aspects of braid theory and to entropy.


Euler and Lagrange solutions of the threebody problem and beyond 12:10 Fri 15 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Pawel Nurowski :: Centre for Theoretical Physics, Polish Academy of Sciences


Weak Stochastic Maximum Principle (SMP) and Applications 15:10 Thu 12 Dec, 2013 :: B.21 Ingkarni Wardli :: Dr Harry Zheng :: Imperial College, London
Media...In this talk we discuss a weak necessary and sufficient SMP for Markov modulated optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke's generalized gradient of the Hamiltonian and Clarke's normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian the necessary condition becomes sufficient. We give examples to demonstrate the weak SMP and its applications in quadratic loss minimization. 

Reductive group actions and some problems concerning their quotients 12:10 Fri 17 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Gerald Schwarz :: Brandeis University
Media...We will gently introduce the concept of a complex reductive group and the notion of the quotient Z of a complex vector space V on which our complex reductive group G acts linearly. There is the quotient mapping p from V to Z. The quotient is an affine variety with a stratification coming from the group action. Let f be an automorphism of Z. We consider the following questions (and give some answers).
1) Does f preserve the stratification of Z, i.e., does it permute the strata?
2) Is there a lift F of f? This means that F maps V to V and p(F(v))=f(p(v)) for all v in V.
3) Can we arrange that F is equivariant?
We show that 1) is almost always true, that 2) is true in a lot of cases and that a twisted version of 3) then holds. 

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


Holomorphic null curves and the conformal CalabiYau problem 12:10 Tue 28 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Franc Forstneric :: University of Ljubljana
Media...I shall describe how methods of complex analysis can be used to give new results on the conformal CalabiYau problem concerning the existence of bounded metrically complete minimal surfaces in real Euclidean 3space R^3. We shall see in particular that every bordered Riemann surface admits a proper complete holomorphic immersion into the ball of C^2, and a proper complete embedding as a
holomorphic null curve into the ball of C^3. Since the real and the imaginary parts of a holomorphic null curve in C^3 are conformally immersed minimal surfaces in R^3, we obtain a bounded complete conformal minimal immersion of any bordered Riemann surface into R^3. The main advantage of our methods, when compared to the existing ones in the literature, is that we do not need to change the conformal type of the Riemann surface. (Joint work with A. Alarcon, University of Granada.)


Integrability of infinitedimensional 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 finitedimensional Lie algebra is the Lie algebra of a Lie group (we also say "integrates to a Lie group"). The corresponding statement for infinitedimensional 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 nonintegrability 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 dbar 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 OhsawaTakegoshi extension theorem with optimal constant, the onedimensional Suita Conjecture, and Nazarov's approach to the BourgainMilman 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 10100 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. 

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

Dynamical systems approach to fluidplasma turbulence 15:10 Fri 14 Mar, 2014 :: 5.58 Ingkarni Wardli :: Professor Abraham Chian
SunEarth system is a complex, electrodynamically coupled system dominated by multiscale interactions. The complex behavior of the space environment is indicative of a state driven far from equilibrium whereby instabilities, nonlinear waves, and turbulence play key roles in the system dynamics. First, we review the fundamental concepts of nonlinear dynamics in fluids and plasmas and discuss their relevance to the study of the SunEarth relation. Next, we show how Lagrangian coherent structures identify the transport barriers of plasma turbulence modeled by 3D solar convective dynamo. Finally, we show how Lagrangian coherent structures can be detected in the solar photospheric turbulence using satellite observations. 

Embed to homogenise heterogeneous wave equation. 12:35 Mon 17 Mar, 2014 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide
Media...Consider materials with complicated microstructure: we want to model their large scale dynamics by equations with effective, `average' coefficients. I will show an example of heterogeneous wave equation in 1D. If Centre manifold theory is applied to model the original heterogeneous wave equation directly, we will get a trivial model. I embed the wave equation into a family of more complex wave problems and I show the equivalence of the two sets of solutions. 

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 YangMills instantons. This talk concerns one such case, contact instantons, defined for 5dimensional 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. 

Scattering theory and noncommutative geometry 01:10 Mon 31 Mar, 2014 :: Ingkarni Wardli B20 :: Alan Carey :: Australian National University


Semiclassical restriction estimates 12:10 Fri 4 Apr, 2014 :: Ingkarni Wardli B20 :: Melissa Tacy :: University of Adelaide
Eigenfunctions of Hamiltonians arise naturally in the theory of quantum mechanics as stationary states of quantum systems. Their eigenvalues have an interpretation as the square root of E, where E is the energy of the system. We wish to better understand the high energy limit which defines the boundary between quantum and classical mechanics. In this talk I will focus on results regarding the restriction of eigenfunctions to lower dimensional subspaces, in particular to hypersurfaces. A convenient way to study such problems is to reframe them as problems in semiclassical analysis. 

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

TDuality 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 3cocycle H, Tduality yields another manifold with a torus action and integral 3cocyle. It induces a number of surprising automorphisms between structures on these manifolds. In this talk I will review Tduality and describe some work on two generalizations which are realized in string theory: NS5branes and heterotic strings. These respectively correspond to nonclosed 3classes H and to principal bundles fibered over M. 

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

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 Diracdual Dirac method to derive the Lefschetz number on Ktheory 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. 

Networkbased approaches to classification and biomarker identification in metastatic melanoma 15:10 Fri 2 May, 2014 :: B.21 Ingkarni Wardli :: Associate Professor Jean Yee Hwa Yang :: The University of Sydney
Media...Finding prognostic markers has been a central question in much of current research in medicine and biology. In the last decade, approaches to prognostic prediction within a genomics setting are primarily based on changes in individual genes / protein. Very recently, however, network based approaches to prognostic prediction have begun to emerge which utilize interaction information between genes. This is based on the believe that largescale molecular interaction networks are dynamic in nature and changes in these networks, rather than changes in individual genes/proteins, are often drivers of complex diseases such as cancer.
In this talk, I use data from stage III melanoma patients provided by Prof. Mann from Melanoma Institute of Australia to discuss how network information can be utilize in the analysis of gene expression analysis to aid in biological interpretation. Here, we explore a number of novel and previously published networkbased prediction methods, which we will then compare to the common singlegene and geneset methods with the aim of identifying more biologically interpretable biomarkers in the form of networks. 

The Mandelbrot Set 12:10 Mon 5 May, 2014 :: B.19 Ingkarni Wardli :: David Bowman :: University of Adelaide
Media...The Mandelbrot set is an icon of modern mathematics, an image which fires the popular imagination when accompanied by the words 'chaos' and 'fractal'. However, few could give even a vague definition of this mysterious set and fewer still know the mathematical meaning behind it. In this talk we will be looking at the role that the Mandelbrot set plays in complex dynamics, the study of iterated complex valued functions. We shall discuss attracting and repelling cycles and how they are related to the different components of the Mandelbrot set. 

A geometric model for odd differential Ktheory 12:10 Fri 9 May, 2014 :: Ingkarni Wardli B20 :: Raymond Vozzo :: University of Adelaide
Odd Ktheory has the interesting property thatunlike even Ktheoryit admits an infinite number of inequivalent differential refinements. In this talk I will give a description of odd differential Ktheory using infinite rank bundles and explain why it is the correct differential refinement. This is joint work with Michael Murray, Pedram Hekmati and Vincent Schlegel. 

Oka properties of groups of holomorphic and algebraic automorphisms of complex affine space 12:10 Fri 6 Jun, 2014 :: Ingkarni Wardli B20 :: Finnur Larusson :: University of Adelaide
I will discuss new joint work with Franc Forstneric. The group of holomorphic automorphisms of complex affine space C^n, n>1, is huge. It is not an infinitedimensional manifold in any recognised sense. Still, our work shows that in some ways it behaves like a finitedimensional Oka manifold. 

The pMinkowski problem 12:10 Fri 13 Jun, 2014 :: Ingkarni Wardli B20 :: XuJia Wang :: Australian National University
The pMinkowski problem is an extension of the classical Minkowski problem. It concerns the existence, uniqueness, and regularity of closed convex hypersurfaces with prescribed Gauss curvature. The Minkowski problem has been studied by many people in the last century and has been completely resolved. The pMinkowski problem involves more applications. In this talk we will review the development of the study of the pMinkowski problem and discuss some recent works on the problem.â 

Complexifications, Realifications, Real forms and Complex Structures 12:10 Mon 23 Jun, 2014 :: B.19 Ingkarni Wardli :: Kelli FrancisStaite :: University of Adelaide
Media...Italian mathematicians NiccolÃ² Fontana Tartaglia and Gerolamo Cardano introduced complex numbers to solve polynomial equations such as x^2+1=0. Solving a standard real differential equation often uses complex eigenvalues and eigenfunctions. In both cases, the solution space is expanded to include the complex numbers, solved, and then translated back to the real case.
My talk aims to explain the process of complexification and related concepts. It will give vocabulary and some basic results about this important process. And it will contain cute cat pictures.


The BismutChern character as dimension reduction functor and its twisting 12:10 Fri 4 Jul, 2014 :: Ingkarni Wardli B20 :: Fei Han :: National University of Singapore
The BismutChern character is a loop space refinement of the Chern character. It plays an essential role in the interpretation of the AtiyahSinger index theorem from the point of view of loop space. In this talk, I will first briefly review the construction of the BismutChern character and show how it can be viewed as a dimension reduction functor in the StolzTeichner program on supersymmetric quantum field theories. I will then introduce the construction of the twisted BismutChern character, which represents our joint work with Varghese Mathai. 

HigherDimensional Geometry 12:10 Mon 28 Jul, 2014 :: B.19 Ingkarni Wardli :: Ashley Gibson :: University of Adelaide
Media...Since the first millennium BC, geometers have been fascinated by convex regular polytopes. The two and threedimensional cases are wellknown, with the latter being named after the Greek philosopher Plato. Much less attention has been paid to the higherdimensional cases, so this seminar will investigate the existence of convex regular polytopes in four or more dimensions. It will also cover the existence of higherdimensional versions of the cross product, which most people are only familiar with in three dimensions. 

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 higheigenvalue 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 higheigenvalue estimates, geometry, and the dynamics of geodesic flow will be emphasized. 

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


The Dirichlet problem for the prescribed Ricci curvature equation 12:10 Fri 15 Aug, 2014 :: Ingkarni Wardli B20 :: Artem Pulemotov :: University of Queensland
We will discuss the following question: is it possible to find a Riemannian metric whose Ricci curvature
is equal to a given tensor on a manifold M? To answer this question, one must analyze a weakly elliptic
secondorder geometric PDE. In the first part of the talk, we will review the history of the subject and state
several classical theorems. After that, our focus will be on new results concerning the case where M has
nonempty boundary. 

Quasimodes that do not Equidistribute 13:10 Tue 19 Aug, 2014 :: Ingkarni Wardli B17 :: Shimon Brooks :: BarIlan University
The QUE Conjecture of RudnickSarnak 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 highlydegenerate 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. 

Tduality and the chiral de Rham complex 12:10 Fri 22 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Linshaw :: University of Denver
The chiral de Rham complex of Malikov, Schechtman, and Vaintrob is a sheaf of vertex algebras that exists on any smooth manifold M. It has a squarezero differential D, and contains the algebra of differential forms on M as a subcomplex. In this talk, I'll give an introduction to vertex algebras and sketch this construction. Finally, I'll discuss a notion of Tduality in this setting. This is based on joint work in progress with V. Mathai. 

Spherical Tduality 01:10 Mon 25 Aug, 2014 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide
I will talk on a new variant of Tduality, called spherical Tduality, which relates pairs of the form (P,H) consisting of a principal SU(2)bundle P > M and a 7cocycle H on P. Intuitively spherical Tduality exchanges H with the second Chern class c_2(P). This is precisely true when M is compact oriented and dim(M) is at most 4. When M is higher dimensional, not all pairs (P,H) admit spherical Tduals and even when they exist, the spherical Tduals are not always unique. We will try and explain this phenomenon. Nonetheless, we prove that all spherical Tdualities induce a degreeshifting isomorphism on the 7twisted cohomologies of the bundles and, when dim(M) is at most 7, also their integral twisted cohomologies and, when dim(M) is at most 4, even their 7twisted Ktheories. While the complete physical relevance of spherical Tduality is still being explored, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.
This is joint work with Peter Bouwknegt and Jarah Evslin. 

Ideal membership on singular varieties by means of residue currents 12:10 Fri 29 Aug, 2014 :: Ingkarni Wardli B20 :: Richard Larkang :: University of Adelaide
On a complex manifold X, one can consider the following ideal membership problem: Does a holomorphic function on X belong to a given ideal of holomorphic functions on X? Residue currents give a way of expressing analytically this essentially algebraic problem. I will discuss some basic cases of this, why such an analytic description might be useful, and finish by discussing a generalization of this to singular varieties. 

Modelling biological gel mechanics 12:10 Mon 8 Sep, 2014 :: B.19 Ingkarni Wardli :: James Reoch :: University of Adelaide
Media...The behaviour of gels such as collagen is the result of complex interactions between mechanical and chemical forces. In this talk, I will outline the modelling approaches we are looking at in order to incorporate the influence of cell behaviour alongside chemical potentials, and the various circumstances which lead to gel swelling and contraction. 

The FKMM invariant in low dimension 12:10 Fri 12 Sep, 2014 :: Ingkarni Wardli B20 :: Kiyonori Gomi (Shinshu University)
On a space with involutive action, the natural notion of
vector bundles is equivariant vector bundles. But, there is an
important variant called `Real' vector bundles in the sense of Atiyah,
and, its cousin, `symplectic' or `Quaternionic' vector bundles in the
sense of Dupont. The FKMM invariant is an invariant of `symplectic'
vector bundles originally introduced by Furuta, Kametani, Matsue and
Minami. The subject of my talk is recent development of this invariant
in my joint work with Giuseppe De Nittis: The classifications of
`symplectic' vector bundles in low dimension and the descriptions of
some Z/2invariants by using the FKMM invariant. 

Translating solitons for mean curvature flow 12:10 Fri 19 Sep, 2014 :: Ingkarni Wardli B20 :: Julie Clutterbuck :: Monash University
Mean curvature flow gives a deformation of a submanifold in the direction of its mean curvature vector. Singularities may arise, and can be modelled by special solutions of the flow. I will describe the special solutions that move by only a translation under the flow, and give some explicit constructions of such surfaces. This is based on joint work with Oliver Schnuerer and Felix Schulze. 

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

Spectral asymptotics on random Sierpinski gaskets 12:10 Fri 26 Sep, 2014 :: Ingkarni Wardli B20 :: Uta Freiberg :: Universitaet Stuttgart
Self similar fractals are often used in modeling porous media. Hence, defining a Laplacian and a Brownian motion on such sets describes transport through such materials. However, the assumption of strict self similarity could be too restricting. So, we present several models of random fractals which could be used instead. After recalling the classical approaches of random homogenous and recursive random fractals, we show how to interpolate between these two model classes with the help of so called Vvariable fractals. This concept (developed by Barnsley, Hutchinson & Stenflo) allows the definition of new families of random fractals, hereby the parameter V describes the degree of `variability' of the realizations. We discuss how the degree of variability influences the geometric, analytic and stochastic properties of these sets.  These results have been obtained with Ben Hambly (University of Oxford) and John Hutchinson (ANU Canberra). 

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 noncompact Riemann surfaces are Stein; which loosely speaking means that their function theory is similar to that of C. 

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

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

The SerreGrothendieck theorem by geometric means 12:10 Fri 24 Oct, 2014 :: Ingkarni Wardli B20 :: David Roberts :: University of Adelaide
The SerreGrothendieck theorem implies that every torsion
integral 3rd cohomology class on a finite CWcomplex 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 Ktheory. 

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 socalled 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. 

Modelling segregation distortion in multiparent crosses 15:00 Mon 17 Nov, 2014 :: 5.57 Ingkarni Wardli :: Rohan Shah (joint work with B. Emma Huang and Colin R. Cavanagh) :: The University of Queensland
Construction of highdensity genetic maps has been made feasible by lowcost highthroughput genotyping technology; however, the process is still complicated by biological, statistical and computational issues. A major challenge is the presence of segregation distortion, which can be caused by selection, difference in fitness, or suppression of recombination due to introgressed segments from other species. Alien introgressions are common in major crop species, where they have often been used to introduce beneficial genes from wild relatives.
Segregation distortion causes problems at many stages of the map construction process, including assignment to linkage groups and estimation of recombination fractions. This can result in incorrect ordering and estimation of map distances. While discarding markers will improve the resulting map, it may result in the loss of genomic regions under selection or containing beneficial genes (in the case of introgression).
To correct for segregation distortion we model it explicitly in the estimation of recombination fractions. Previously proposed methods introduce additional parameters to model the distortion, with a corresponding increase in computing requirements. This poses difficulties for large, densely genotyped experimental populations. We propose a method imposing minimal additional computational burden which is suitable for highdensity map construction in large multiparent crosses. We demonstrate its use modelling the known Sr36 introgression in wheat for an eightparent complex cross.


Fractal substitution tilings 11:10 Wed 17 Dec, 2014 :: Ingkarni Wardli B17 :: Mike Whittaker :: University of Wollongong
Starting with a substitution tiling, I will demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles typically have fractal boundary. As an application, we construct an odd spectral triple on a C*algebra associated with an aperiodic substitution tiling. No knowledge of tilings, C*algebras, or spectral triples will be assumed. This is joint work with Natalie Frank, Michael Mampusti, and Sam Webster. 

Factorisations of Distributive Laws 12:10 Fri 19 Dec, 2014 :: Ingkarni Wardli B20 :: Paul Slevin :: University of Glasgow
Recently, distributive laws have been used by Boehm and Stefan to construct new examples of duplicial (paracyclic) objects, and hence cyclic homology theories. The paradigmatic example of such a theory is the cyclic homology HC(A) of an associative algebra A. It was observed by Kustermans, Murphy, and Tuset that the functor HC can be twisted by automorphisms of A. It turns out that this twisting procedure can be applied to any duplicial object defined by a distributive law.
I will begin by defining duplicial objects and cyclic homology, as well as discussing some categorical concepts, then describe the construction of Boehm and Stefan. I will then define the category of factorisations of a distributive law and explain how this acts on their construction, and give some examples, making explicit how the action of this category generalises the twisting of an associative algebra. 

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 leftinvariant 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
Ricciflat Riemannian mertrics of special holonomy in dimensions 6, 7 and 8.
Assuming that the initial geometric structure is leftinvariant, we study whether the resulting Ricciflat manifolds can be extended in a natural way to complete Ricciflat manifolds. This talk is based on joint work with Florin Belgun, Marco Freibert and Oliver Goertsches, see arXiv:1405.1866 (math.DG). 

Tannaka duality for stacks 12:10 Fri 6 Mar, 2015 :: Ingkarni Wardli B20 :: Jack Hall :: Australian National University
Traditionally, Tannaka duality is used to reconstruct a
group from its representations. I will describe a reformulation of
this duality for stacks, which is due to Lurie, and briefly touch on
some applications. 

On the analyticity of CRdiffeomorphisms 12:10 Fri 13 Mar, 2015 :: Engineering North N132 :: Ilya Kossivskiy :: University of Vienna
One of the fundamental objects in several complex variables is CRmappings. CRmappings naturally occur in complex analysis as boundary values of mappings between domains, and as restrictions of holomorphic mappings onto real submanifolds. It was already observed by Cartan that smooth CRdiffeomorphisms between CRsubmanifolds in C^N tend to be very regular, i.e., they are restrictions of holomorphic maps. However, in general smooth CRmappings form a more restrictive class of mappings. Thus, since the inception of CRgeometry, the following general question has been of fundamental importance for the field: Are CRequivalent realanalytic CRstructures also equivalent holomorphically? In joint work with Lamel, we answer this question in the negative, in any positive CRdimension and CRcodimension. Our construction is based on a recent dynamical technique in CRgeometry, developed in my earlier work with Shafikov. 

Singular Pfaffian systems in dimension 6 12:10 Fri 20 Mar, 2015 :: Napier 144 :: Pawel Nurowski :: Center for Theoretical Physics, Polish Academy of Sciences
We consider a pair of rank 3 distributions in dimension 6 with some remarkable properties.
They define an analog of the celebrated nearlyKahler structure on the 6 sphere, with the exceptional simple Lie group G2 as a group of symmetries. In our case the metric associated with the structure is pseudoRiemannian, of split signature. The 6 manifold has a 5dimensional boundary with interesting induced geometry. This structure on the boundary has no analog in the Riemannian case.


Higher homogeneous bundles 12:10 Fri 27 Mar, 2015 :: Napier 144 :: David Roberts :: University of Adelaide
Historically, homogeneous bundles were among the first
examples of principal bundles. This talk will cover a general method
that gives rise to many homogeneous principal 2bundles. 

Topological matter and its Ktheory 11:10 Thu 2 Apr, 2015 :: Ingkarni Wardli B18 :: Guo Chuan Thiang :: University of Adelaide
The notion of fundamental particles, as well as phases of condensed matter, evolves as new mathematical tools become available to the physicist. I will explain how Ktheory provides a powerful language for describing quantum mechanical symmetries, homotopies of their realisations, and topological insulators. Real Ktheory is crucial in this framework, and its rich structure is still being explored both physically and mathematically. 

Higher rank discrete Nahm equations for SU(N) monopoles in hyperbolic space 11:10 Wed 8 Apr, 2015 :: Engineering & Maths EM213 :: Joseph Chan :: University of Melbourne
Braam and Austin in 1990, proved that SU(2) magnetic monopoles in hyperbolic space H^3 are the same as solutions of the discrete Nahm equations. I apply equivariant Ktheory to the ADHM construction of instantons/holomorphic bundles to extend the BraamAustin result from SU(2) to SU(N). During its evolution, the matrices of the higher rank discrete Nahm equations jump in dimensions and this behaviour has not been observed in discrete evolution equations before. A secondary result is that the monopole field at the boundary of H^3 determines the monopole. 

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 GuptaSidki pgroups. 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 GrigorchukGuptaSidki groups,
and we examine the restricted occurrence of their maximal subgroups. 

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

Spherical Tduality: the nonprincipal case 12:10 Fri 1 May, 2015 :: Napier 144 :: Mathai Varghese :: University of Adelaide
Spherical Tduality is related to Mtheory and was introduced in recent joint work with Bouwknegt and Evslin. I will begin by briefly reviewing the case of principal SU(2)bundles with degree 7 flux, and then focus on the nonprincipal case for most of the talk, ending with the relation to SUGRA/Mtheory. 

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

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

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. 

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

Some approaches toward a stronger Jacobian conjecture 12:10 Fri 5 Jun, 2015 :: Napier 144 :: Tuyen Truong :: University of Adelaide
The Jacobian conjecture states that if a polynomial selfmap of C^n has invertible Jacobian, then the map has a polynomial inverse. Is it true, false or simply undecidable? In this talk I will propose a conjecture concerning general square matrices with complex coefficients, whose validity implies the Jacobian conjecture. The conjecture is checked in various cases, in particular it is true for generic matrices. Also, a heuristic argument is provided explaining why the conjecture (and thus, also the Jacobian conjecture) should be true. 

Complex Systems, Chaotic Dynamics and Infectious Diseases 15:10 Fri 5 Jun, 2015 :: Engineering North N132 :: Prof Michael Small :: UWA
Media...In complex systems, the interconnection between the components of the system determine the dynamics. The system is described by a very large and random mathematical graph and it is the topological structure of that graph which is important for understanding of the dynamical behaviour of the system. I will talk about two specific examples  (1) spread of infectious disease (where the connection between the agents in a population, rather than epidemic parameters, determine the endemic state); and, (2) a transformation to represent a dynamical system as a graph (such that the "statistical mechanics" of the graph characterise the dynamics). 

Instantons and Geometric Representation Theory 12:10 Thu 23 Jul, 2015 :: Engineering and Maths EM212 :: Professor Richard Szabo :: HeriotWatt University
We give an overview of the various approaches to studying
supersymmetric quiver gauge theories on ALE spaces, and their conjectural
connections to twodimensional conformal field theory via AGTtype
dualities. From a mathematical perspective, this is formulated as a
relationship between the equivariant cohomology of certain moduli spaces
of sheaves on stacks and the representation theory of infinitedimensional
Lie algebras. We introduce an orbifold compactification of the minimal
resolution of the Atype toric singularity in four dimensions, and then
construct a moduli space of framed sheaves which is conjecturally
isomorphic to a Nakajima quiver variety. We apply this construction to
derive relations between the equivariant cohomology of these moduli spaces
and the representation theory of the affine Lie algebra of type A.


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

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

Quantising proper actions on Spinc 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 Spinc manifold (both of which may be noncompact), we study an index of deformations of the Spinc 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 finitedimensional, 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 ParadanVergne in the compact Spinc case), for sufficiently large powers of the determinant line bundle. Furthermore, this result extends to Spinc 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. 

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

Mathematical Modeling and Analysis of Active Suspensions 14:10 Mon 3 Aug, 2015 :: Napier 209 :: Professor Michael Shelley :: Courant Institute of Mathematical Sciences, New York University
Complex fluids that have a 'bioactive' microstructure, like
suspensions of swimming bacteria or assemblies of immersed biopolymers
and motorproteins, are important examples of socalled active matter.
These internally driven fluids can have strange mechanical properties,
and show persistent activitydriven flows and selforganization. I will
show how firstprinciples PDE models are derived through reciprocal
coupling of the 'active stresses' generated by collective microscopic
activity to the fluid's macroscopic flows. These PDEs have an
interesting analytic structures and dynamics that agree qualitatively
with experimental observations: they predict the transitions to flow
instability and persistent mixing observed in bacterial suspensions, and
for microtubule assemblies show the generation, propagation, and
annihilation of disclination defects. I'll discuss how these models
might be used to study yet more complex biophysical systems.


Gromov's method of convex integration and applications to minimal surfaces 12:10 Fri 7 Aug, 2015 :: Ingkarni Wardli B17 :: Finnur Larusson :: The University of Adelaide
Media...We start by considering an applied problem. You are interested in buying a used car. The price is tempting, but the car has a curious defect, so it is not clear whether you can even take it for a test drive. This problem illustrates the key idea of Gromov's method of convex integration. We introduce the method and some of its many applications, including new applications in the theory of minimal surfaces, and end with a sketch of ongoing joint work with Franc Forstneric. 

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

Bilinear L^p estimates for quasimodes 12:10 Fri 14 Aug, 2015 :: Ingkarni Wardli B17 :: Melissa Tacy :: The University of Adelaide
Media...Understanding the growth of the product of eigenfunctions
$$u\cdot{}v$$
$$\Delta{}u=\lambda^{2}u\quad{}\Delta{}v=\mu^{2}v$$
is vital to understanding the regularity properties of nonlinear PDE such as the nonlinear Schr\"{o}dinger equation. In this talk I will discuss some recent results that I have obtain in collaboration with Zihua Guo and Xiaolong Han which provide a full range of estimates of the form
$$uv_{L^{p}}\leq{}G(\lambda,\mu)u_{L^{2}}v_{L^{2}}$$
where $u$ and $v$ are approximate eigenfunctions of the Laplacian. We obtain these results by recasting the problem to a more general related semiclassical problem.


Deformation retractions from the space of continuous maps between domains in C onto the space of holomorphic maps 12:10 Mon 17 Aug, 2015 :: Benham Labs G10 :: Brett Chenoweth :: University of Adelaide
Media...Mikhail Gromov proved in 1989 that every continuous map from a Stein manifold S to an elliptic manifold X could be deformed to a holomorphic map. More generally, it is true that if X is an Oka manifold then a continuous map from a Stein source into X can always be deformed to a holomorphic map. The question is whether we can do this for all continuous maps at once, in a `nice' way that does not change a map f if f is already holomorphic. In a recent paper by Larusson, we see that ANRs play an important in producing a partial answer to this question. In this talk we will explore the question in the relatively simple situation where the source and target are domains in the complex plane. 

Equivariant bundle gerbes 12:10 Fri 21 Aug, 2015 :: Ingkarni Wardli B17 :: Michael Murray :: The University of Adelaide
Media...I will present the definitions of strong and weak group actions on a bundle gerbe and calculate the strongly equivariant
class of the basic bundle gerbe on a unitary group. This is joint work with David Roberts, Danny Stevenson and
Raymond Vozzo and forms part of arXiv:1506.07931. 

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

Integrability conditions for the Grushin operators 12:10 Fri 4 Sep, 2015 :: Ingkarni Wardli B17 :: Michael Eastwood :: The University of Adelaide
Fix a nonnegative integer k and consider the vector fields in the plane X=d/dx and Y=x^kd/dy. A smooth function f(x,y) is locally constant if and only if it is annihilated by the k^th Grushin operator f\mapsto(Xf,Yf). What about the range of this operator?


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

The Calderon Problem: From the Past to the Present 15:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B21 :: Dr Leo Tzou :: University of Sydney
The problem of determining the electrical conductivity of a body by making voltage and current measurements on the object's surface has various applications in fields such as oil exploration and early detection of malignant breast tumour. This classical problem posed by Calderon remained open until the late '80s when it was finally solved in a breakthrough paper by SylvesterUhlmann.
In the recent years, geometry has played an important role in this problem. The unexpected connection of this subject to fields such as dynamical systems, symplectic geometry, and Riemannian geometry has led to some interesting progress. This talk will be an overview of some of the recent results and an outline of the techniques used to treat this problem. 

Base change and Ktheory 12:10 Fri 18 Sep, 2015 :: Ingkarni Wardli B17 :: Hang Wang :: The University of Adelaide
Media...Tempered representations of an algebraic group can be classified by Ktheory of the corresponding group C^*algebra. We use Archimedean base change between Langlands parameters of real and complex algebraic groups to compare Ktheory of the corresponding C^*algebras of groups over different number fields. This is work in progress with K.F. Chao.


Tdual noncommutative principal torus bundles 12:10 Fri 25 Sep, 2015 :: Engineering Maths Building EMG07 :: Keith Hannabuss :: University of Oxford
Media...Since the work of Mathai and Rosenberg it is known that the Tdual of a principal torus bundle
can be described as a noncommutative torus bundle. This talk will look at a simple example of
two Tdual bundles both of which are noncommutative. Then it will discuss a strategy for extending
this to more general noncommutative bundles. 

Analytic complexity of bivariate holomorphic functions and cluster trees 12:10 Fri 2 Oct, 2015 :: Ingkarni Wardli B17 :: Timur Sadykov :: Plekhanov University, Moscow
The KolmogorovArnold theorem yields a representation of a multivariate continuous function in terms of a composition of functions which depend on at most two variables. In the analytic case, understanding the complexity of such a representation naturally leads to the notion of the analytic complexity of (a germ of) a bivariate multivalued analytic function. According to Beloshapka's local definition, the order of complexity of any univariate function is equal to zero while the nth complexity class is defined recursively to consist of functions of the form a(b(x,y)+c(x,y)), where a is a univariate analytic function and b and c belong to the (n1)th complexity class. Such a represenation is meant to be valid for suitable germs of multivalued holomorphic functions.
A randomly chosen bivariate analytic functions will most likely have infinite analytic complexity. However, for a number of important families of special functions of mathematical physics their complexity is finite and can be computed or estimated. Using this, we introduce the notion of the analytic complexity of a binary tree, in particular, a cluster tree, and investigate its properties.


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


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


IGA/AMSI Workshop  AustraliaJapan Geometry, Analysis and their Applications 09:00 Mon 19 Oct, 2015 :: Ingkarni Wardli Conference Room 7.15 (Level 7)
Media...Interdisciplinary workshop between Australia and Japan on Geometry, Analysis and their Applications. 

Quasiisometry 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 rightangled 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 quasiisometry 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 quasiisometric if and only if their JSJ trees are the same. This is joint work with Pallavi Dani (Louisiana State University). 

Covariant model structures and simplicial localization 12:10 Fri 30 Oct, 2015 :: Ingkarni Wardli B17 :: Danny Stevenson :: The University of Adelaide
Media...This talk will describe some aspects of the theory of quasicategories, in particular the notion of left fbration and the allied covariant model structure. If B is a simplicial set, then I will describe some Quillen equivalences relating the covariant model structure on simplicial sets over B to a certain localization of simplicial presheaves on the simplex category of B. I will show how this leads to a new description of Lurie's simplicial rigidification functor as a hammock localization and describe some applications to Lurie's theory of straightening and unstraightening functors. 

Locally homogeneous ppwaves 12:10 Fri 6 Nov, 2015 :: Ingkarni Wardli B17 :: Thomas Leistner :: The University of Adelaide
Media...For a certain type of Lorentzian manifolds, the socalled ppwaves, 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 ppwave to be a plane wave, and yielding a classification of homogeneous ppwaves. This also leads to a generalisation of a classical
result by Jordan, Ehlers and Kundt about vacuum ppwaves in dimension 4 to arbitrary dimensions. Several examples show that our genericity assumptions are essential.
This is joint work with W. Globke.


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

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 Gbundles 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 Gorbits 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" Gactions.
This is joint work with F. Kutzschebauch and F. Larusson.


A fibered density property and the automorphism group of the spectral ball 12:10 Fri 15 Jan, 2016 :: Engineering North N132 :: Frank Kutzschebauch :: University of Bern
Media...The spectral ball is defined as the set of complex n by n matrices whose eigenvalues are all less than 1 in absolute value. Its group of holomorphic automorphisms has been studied over many decades in several papers and a precise conjecture about its structure has been formulated. In dimension 2 this conjecture was recently disproved by Kosinski. We not only disprove the conjecture in all dimensions but also give the best possible description of the automorphism group.
Namely we explain how the invariant theoretic quotient map divides the automorphism group of the spectral ball into a finite dimensional part of symmetries which lift from the quotient and an infinite dimensional part which leaves the fibration invariant. We prove a precise statement as to how hopelessly huge this latter part is. This is joint work with R. Andrist. 

Quantisation of Hitchin's moduli space 12:10 Fri 22 Jan, 2016 :: Engineering North N132 :: Siye Wu :: National Tsing Hua Univeristy
In this talk, I construct prequantum line bundles on Hitchin's
moduli spaces of orientable and nonorientable surfaces and study the
geometric quantisation and quantisation via branes by complexification
of the moduli spaces. 

A long C^2 without holomorphic functions 12:10 Fri 29 Jan, 2016 :: Engineering North N132 :: Franc Forstneric :: University of Ljubljana
Media...For every integer n>1 we construct a complex manifold of dimension n which is exhausted by an increasing sequence of biholomorphic images of C^n (i.e., a long C^n), but it does not admit any nonconstant holomorphic functions. We also introduce new biholomorphic invariants of a complex manifold, the stable core and the strongly stable core, and we prove that every compact strongly pseudoconvex and polynomially convex domain B in C^n is the strongly stable core of a long C^n; in particular, nonequivalent domains give rise to nonequivalent long C^n's. Thus, for any n>1 there exist uncountably many pairwise nonequivalent long C^n's. These results answer several long standing open questions. (Joint work with Luka Boc Thaler.) 

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 AtiyahSegalSinger 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 Weylâs character formula. We extend the definition of the equivariant index to noncompact manifolds, and prove a generalisation of the AtiyahSegalSinger 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.) 

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

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

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


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

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


Sard Theorem for the endpoint map in subRiemannian manifolds 12:10 Fri 29 Apr, 2016 :: Eng & Maths EM205 :: Alessandro Ottazzi :: University of New South Wales
Media...SubRiemannian 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 subRiemannian manifolds and give some examples. Therefore we discuss some of the open problems, and in particular we focus on the Sard Theorem for the endpoint map, which is related to the study of length minimizers. Finally, we consider some recent results obtained in collaboration with E. Le Donne, R. Montgomery, P. Pansu and D. Vittone. 

Extreme eigenvalues 15:10 Fri 29 Apr, 2016 :: Engineering South S112 :: Dr Julie Clutterbuck :: Monash University
Media...Each bounded domain has a sequence of eigenvalues attached to it. These are determined by the geometry of the domain, but do not completely encode the geometry. A natural question is to ask: which domains optimise the eigenvalues? For example, which domains have the smallest or largest first eigenvalue, or have the largest gap between eigenvalues? This is a rather old problem, with connections to the isoperimetric problem. I will describe some old and new results. 

How to count Betti numbers 12:10 Fri 6 May, 2016 :: Eng & Maths EM205 :: David Baraglia :: University of Adelaide
Media...I will begin this talk by showing how to obtain the Betti numbers of certain smooth complex projective varieties by counting points over a finite field. For singular or noncompact varieties this motivates us to consider the "virtual Hodge numbers" encoded by the "HodgeDeligne polynomial", a refinement of the topological Euler characteristic. I will then discuss the computation of HodgeDeligne polynomials for certain singular character varieties (i.e. moduli spaces of flat connections). 

Harmonic analysis of HodgeDirac operators 12:10 Fri 13 May, 2016 :: Eng & Maths EM205 :: Pierre Portal :: Australian National University
Media...When the metric on a Riemannian manifold is perturbed in a rough (merely bounded and measurable) manner, do basic estimates involving the Hodge Dirac operator $D = d+d^*$ remain valid? Even in the model case of a perturbation of the euclidean metric on $\mathbb{R}^n$, this is a difficult question. For instance, the fact that the $L^2$ estimate $\Du\_2 \sim \\sqrt{D^{2}}u\_2$ remains valid for perturbed versions of $D$ was a famous conjecture made by Kato in 1961 and solved, positively, in a ground breaking paper of Auscher, Hofmann, Lacey, McIntosh and Tchamitchian in 2002. In the past fifteen years, a theory has emerged from the solution of this conjecture, making rough perturbation problems much more tractable. In this talk, I will give a general introduction to this theory, and present one of its latest results: a flexible approach to $L^p$ estimates for the holomorphic functional calculus of $D$. This is joint work with D. Frey (Delft) and A. McIntosh (ANU).


Smooth mapping orbifolds 12:10 Fri 20 May, 2016 :: Eng & Maths EM205 :: David Roberts :: University of Adelaide
It is wellknown that orbifolds can be represented by a special kind of Lie groupoid, namely those that are Ã©tale and proper. Lie groupoids themselves are one way of presenting certain nice differentiable stacks.
In joint work with Ray Vozzo we have constructed a presentation of the mapping stack Hom(disc(M),X), for M a compact manifold and X a differentiable stack, by a FrÃ©chetLie groupoid. This uses an apparently new result in global analysis about the map C^\infty(K_1,Y) \to C^\infty(K_2,Y) induced by restriction along the inclusion K_2 \to K_1, for certain compact K_1,K_2. We apply this to the case of X being an orbifold to show that the mapping stack is an infinitedimensional orbifold groupoid. We also present results about mapping groupoids for bundle gerbes. 

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 ninetydegree 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 selfsimilar solution. We also discuss the possibility of a curvature singularity appearing on the free boundary contained in the contact hypersurface. We extend some of these results to the setting of a hypersurface evolving in its normal direction with speed given by a fully nonlinear functional of the principal curvatures.


Time series analysis of paleoclimate proxies (a mathematical perspective) 15:10 Fri 27 May, 2016 :: Engineering South S112 :: Dr Thomas Stemler :: University of Western Australia
Media...In this talk I will present the work my colleagues from the School of
Earth and Environment (UWA), the "trans disciplinary methods" group of
the Potsdam Institute for Climate Impact Research, Germany, and I did to
explain the dynamics of the AustralianSouth East Asian monsoon system
during the last couple of thousand years.
From a time series perspective paleoclimate proxy series are more or
less the monsters moving under your bed that wake you up in the middle
of the night. The data is clearly nonstationary, nonuniform sampled in
time and the influence of stochastic forcing or the level of measurement
noise are more or less unknown. Given these undesirable properties
almost all traditional time series analysis methods fail.
I will highlight two methods that allow us to draw useful conclusions
from the data sets. The first one uses Gaussian kernel methods to
reconstruct climate networks from multiple proxies. The coupling
relationships in these networks change over time and therefore can be
used to infer which areas of the monsoon system dominate the complex
dynamics of the whole system. Secondly I will introduce the
transformation cost time series method, which allows us to detect
changes in the dynamics of a nonuniform sampled time series. Unlike the
frequently used interpolation approach, our new method does not corrupt
the data and therefore avoids biases in any subsequence analysis. While
I will again focus on paleoclimate proxies, the method can be used in
other applied areas, where regular sampling is not possible.


On the Strong Novikov Conjecture for Locally Compact Groups in Low Degree Cohomology Classes 12:10 Fri 3 Jun, 2016 :: Eng & Maths EM205 :: Yoshiyasu Fukumoto :: Kyoto University
Media...The main result I will discuss is nonvanishing of the image of the index map from the Gequivariant Khomology of a Gmanifold X to the Ktheory of the C*algebra of the group G. The action of G on X is assumed to be proper and cocompact. Under the assumption that the Kronecker pairing of a Khomology class with a lowdimensional cohomology class is nonzero, we prove that the image of this class under the index map is nonzero. Neither discreteness of the locally compact group G nor freeness of the action of G on X are required. The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.


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

ChernSimons 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 ChernSimons functional for connections on Gbundles over threemanfolds has lead to a deep understanding of the geometry of threemanfiolds, as well as knot invariants such as the Jones polynomial. Here we study this functional for threemanfolds 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 ChernSimons functional reduces to a particular gaugetheoretic 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 levelk affine central extension of the loop group LG. We show that this formulation gives a new understanding of results of BeasleyWitten on the computability of quantum ChernSimons 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 MurrayStevensonVozzo.


Twists over etale groupoids and twisted vector bundles 12:10 Fri 22 Jul, 2016 :: Ingkarni Wardli B18 :: Elizabeth Gillaspy :: University of Colorado, Boulder
Media...Given a twist over an etale groupoid, one can construct an associated C*algebra which carries a good deal of geometric and physical meaning; for example, the Ktheory group of this C*algebra classifies Dbrane charges in string theory. Twisted vector bundles, when they exist, give rise to particularly important elements in this Ktheory group. In this talk, we will explain how to use the classifying space of the etale groupoid to construct twisted vector bundles, under some mild hypotheses on the twist and the classifying space.
My hope is that this talk will be accessible to a broad audience; in particular, no prior familiarity with groupoids, their twists, or the associated C*algebras will be assumed. This is joint work with Carla Farsi.


Holomorphic Flexibility Properties of Spaces of Elliptic Functions 12:10 Fri 29 Jul, 2016 :: Ingkarni Wardli B18 :: David Bowman :: University of Adelaide
The set of meromorphic functions on an elliptic curve naturally possesses the structure of a complex manifold. The component of degree 3 functions is 6dimensional and enjoys several interesting complexanalytic properties that make it, loosely speaking, the opposite of a hyperbolic manifold. Our main result is that this component has a 54sheeted branched covering space that is an Oka manifold. 

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


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

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 FubiniStudy metric and its Xray transform. This talk, which will start from scratch, is based on the work of many authors but, especially, current joint work with Jan Slovak. 

Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type 12:10 Fri 19 Aug, 2016 :: Ingkarni Wardli B18 :: Lesley Ward :: University of South Australia
Media...Much effort has been devoted to generalizing the
Calder'onZygmund theory in harmonic analysis from Euclidean
spaces to metric measure spaces, or spaces of homogeneous type.
Here the underlying space R^n with Euclidean metric
and Lebesgue measure is replaced by a set X with general
metric or quasimetric and a doubling measure. Further, one can
replace the Laplacian operator that underpins the
CalderonZygmund theory by more general operators L
satisfying heat kernel estimates.
I will present recent joint work with P. Chen, X.T. Duong,
J. Li and L.X. Yan along these lines. We develop the theory of
product Hardy spaces H^p_{L_1,L_2}(X_1 x X_2), for 1 

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

Geometry of pseudodifferential algebra bundles 12:10 Fri 16 Sep, 2016 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide
Media...I will motivate the construction of pseudodifferential algebra bundles arising in index theory, and also outline the construction of general pseudodifferential algebra bundles (and the associated sphere bundles), showing that there are many that are purely infinite dimensional that do not come from usual constructions in index theory. I will also discuss characteristic classes of such bundles. This is joint work with Richard Melrose. 

Hilbert schemes of points of some surfaces and quiver representations 12:10 Fri 23 Sep, 2016 :: Ingkarni Wardli B17 :: Ugo Bruzzo :: International School for Advanced Studies, Trieste
Media...Hilbert schemes of points on the total spaces of the line bundles
O(n) on P1 (desingularizations of toric singularities of type (1/n)(1,1)) can be given
an ADHM description, and as a result, they can be realized as varieties
of quiver representations.


Energy quantisation for the Willmore functional 11:10 Fri 7 Oct, 2016 :: Ligertwood 314 Flinders Room :: Yann Bernard :: Monash University
Media...We prove a bubbleneck decomposition and an energy quantisation result for sequences of Willmore surfaces immersed into R^(m>=3) with uniformly bounded energy and nondegenerating conformal structure. We deduce the strong compactness (modulo the action of the Moebius group) of closed Willmore surfaces of a given genus below some energy threshold.
This is jointwork with Tristan Riviere (ETH Zuerich).


On the Willmore energy 15:10 Fri 7 Oct, 2016 :: Napier G03 :: Dr Yann Bernard :: Monash University
Media...The Willmore energy of a surface captures its bending. Originally discovered 200 years ago by Sophie Germain in the context of elasticity theory, it has since then been rediscovered numerous times in several areas of science: general relativity, optics, string theory, conformal geometry, and cell biology. For example, our red blood cells assume a peculiar shape that minimises the Willmore energy.
In this talk, I will present the thrilling history of the Willmore energy, its applications, and its main properties. The presentation will be accessible to all mathematicians as well as to advanced undergraduate students. 

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 AtiyahBott fixed point theorem or the AtiyahSegalSinger index theorem. HarishChandra 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 Ktheory of HarishChandra Schwartz algebra of a semisimple Lie group G, and then use geometric method to deduce HarishChandra character formulas for discrete series representations of G. This is work in progress with Peter Hochs.


Parahoric bundles, invariant theory and the KazhdanLusztig map 12:10 Fri 21 Oct, 2016 :: Ingkarni Wardli B18 :: David Baraglia :: University of Adelaide
Media...In this talk I will introduce the notion of parahoric groups, a loop group analogue of parabolic subgroups. I will also discuss a global version of this, namely parahoric bundles on a complex curve. This leads us to a problem concerning the behaviour of invariant polynomials on the dual of the Lie algebra, a kind of "parahoric invariant theory". The key to solving this problem turns out to be the KazhdanLusztig map, which assigns to each nilpotent orbit in a semisimple Lie algebra a conjugacy class in the Weyl group. Based on joint work with Masoud Kamgarpour and Rohith Varma. 

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 modulispace 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.


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


Leavitt path algebras 12:10 Fri 2 Dec, 2016 :: Engineering & Math EM213 :: Roozbeh Hazrat :: Western Sydney University
Media...From a directed graph one can generate an algebra which captures the movements along the graph. One such algebras are Leavitt path algebras.
Despite being introduced only 10 years ago, Leavitt path algebras have arisen in a variety of different contexts as diverse as analysis, symbolic dynamics, noncommutative geometry and representation theory. In fact, Leavitt path algebras are algebraic counterpart to graph C*algebras, a theory which has become an area of intensive research globally. There are strikingly parallel similarities between these two theories. Even more surprisingly, one cannot (yet) obtain the results in one theory as a consequence of the other; the statements look the same, however the techniques to prove them are quite different (as the names suggest, one uses Algebra and other Analysis). These all suggest that there might be a bridge between Algebra and Analysis yet to be uncovered.
In this talk, we introduce Leavitt path algebras and try to classify them by means of (graded) Grothendieck groups. We will ask nice questions!


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

Collective and aneural foraging in biological systems 15:10 Fri 3 Mar, 2017 :: Lower Napier LG14 :: Dr Jerome Buhl and Dr David Vogel :: The University of Adelaide
The field of collective behaviour uses concepts originally adapted from statistical physics to study how complex collective phenomena such as mass movement or swarm intelligence emerge from relatively simple interactions between individuals. Here we will focus on two applications of this framework. First we will have look at new insights into the evolution of sociality brought by combining models of nutrition and social interactions to explore phenomena such as collective foraging decisions, emergence of social organisation and social immunity. Second, we will look at the networks built by slime molds under exploration and foraging context. 

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 kdisc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have nonzero 8periodic 2torsion detected in real Ktheory. 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 nonempty, space of positive scalar curvature metrics on M has nonzero 8periodic 2torsion in its homotopy groups which is detected in real Ktheory. 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 areaminimizing, meaning that every point in the surface admits a compact neighborhood with the least area among all the surfaces with the same boundary. Although the origin of minimal surfaces is in physics, since they can be realized locally as soap films, this family of surfaces lies in the intersection of many fields of mathematics. In particular, complex analysis in one and several variables plays a fundamental role in the theory. In this lecture we will discuss the influence of complex analysis in the study of minimal surfaces. 

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

Ktypes 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 Spinc analogues of reduced spaces in symplectic geometry, defined in terms of moment maps that represent conserved quantities. This result involves a Spinc version of the quantisation commutes with reduction principle for noncompact manifolds. For discrete series representations, this was done by Paradan in 2003. 

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

Geometric limits of knot complements 12:10 Fri 28 Apr, 2017 :: Napier 209 :: Jessica Purcell :: Monash University
Media...The complement of a knot often admits a hyperbolic metric: a metric with constant curvature 1. In this talk, we will investigate sequences of hyperbolic knots, and the possible spaces they converge to as a geometric limit. In particular, we show that there exist hyperbolic knots in the 3sphere such that the set of points of large injectivity radius in the complement take up the bulk of the volume. This is joint work with Autumn Kent. 

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

Algae meet the mathematics of multiplicative multifractals 12:10 Tue 2 May, 2017 :: Inkgarni Wardli Conference Room 715 :: Professor Tony Roberts :: School of Mathematical Sciences
Media...There is much that is fragmented and rough in the world around us: clouds and landscapes are examples, as is algae.
We need fractal geometry to encompass these.
In practice we need multifractals: a composite of interwoven sets, each with their own fractal structure.
Multiplicative multifractals have known properties.
Optimising a fit between them and the data then empowers us to quantify subtle details of fractal geometry in applications, such as in algae distribution. 

Hodge theory on the moduli space of Riemann surfaces 12:10 Fri 5 May, 2017 :: Napier 209 :: Jesse GellRedman :: 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 noncompact 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 noncompact 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 WeilPetersson metric on the compactified Riemann moduli space near the interior of a divisor. Joint with J. Swoboda and R. Melrose. 

Graded Ktheory and C*algebras 11:10 Fri 12 May, 2017 :: Engineering North 218 :: Aidan Sims :: University of Wollongong
Media...C*algebras can be regarded, in a very natural way, as noncommutative algebras of continuous functions on topological spaces. The analogy is strong enough that topological Ktheory in terms of formal differences of vector bundles has a direct analogue for C*algebras. There is by now a substantial array of tools out there for computing C*algebraic Ktheory. However, when we want to model physical phenomena, like topological phases of matter, we need to take into account various physical symmetries, some of which are encoded by gradings of C*algebras by the twoelement group. Even the definition of graded C*algebraic Ktheory is not entirely settled, and there are relatively few computational tools out there. I will try to outline what a C*algebra (and a graded C*algebra is), indicate what graded Ktheory ought to look like, and discuss recent work with Alex Kumjian and David Pask linking this with the deep and powerful work of Kasparov, and using this to develop computational tools. 

Real bundle gerbes 12:10 Fri 19 May, 2017 :: Napier 209 :: Michael Murray :: University of Adelaide
Media...Bundle gerbe modules, via the notion of bundle gerbe Ktheory provide a realisation of twisted Ktheory. I will discuss the existence or Real bundle gerbes which are the corresponding objects required to construct Real twisted Ktheory in the sense of Atiyah. This is joint work with Richard Szabo (HeriotWatt), Pedram Hekmati (Auckland) and Raymond Vozzo which appeared in arXiv:1608.06466. 

Schubert Calculus on Lagrangian Grassmannians 12:10 Tue 23 May, 2017 :: EM 213 :: Hiep Tuan Dang :: National centre for theoretical sciences, Taiwan
Media...The Lagrangian Grassmannian $LG = LG(n,2n)$ is the projective complex manifold which parametrizes Lagrangian (i.e. maximal isotropic) subspaces in a symplective vector space of dimension $2n$. This talk is mainly devoted to Schubert calculus on $LG$. We first recall the definition of Schubert classes in this context. Then we present basic results which are similar to the classical formulas due to Pieri and Giambelli. These lead to a presentation of the cohomology ring of $LG$. Finally, we will discuss recent results related to the Schubert structure constants and GromovWitten invariants of $LG$. 

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. 

Constructing differential string structures 14:10 Wed 7 Jun, 2017 :: EM213 :: David Roberts :: University of Adelaide
Media...String structures on a manifold are analogous to spin structures, except instead of lifting the structure group through the extension Spin(n)\to SO(n) of Lie groups, we need to lift through the extension String(n)\to Spin(n) of Lie *2groups*. Such a thing exists if the first fractional Pontryagin class (1/2)p_1 vanishes in cohomology. A differential string structure also lifts connection data, but this is rather complicated, involving a number of locally defined differential forms satisfying cocyclelike conditions. This is an expansion of the geometric string structures of Stolz and Redden, which is, for a given connection A, merely a 3form R on the frame bundle such that dR = tr(F^2) for F the curvature of A; in other words a trivialisation of the de Rham class of (1/2)p_1. I will present work in progress on a framework (and specific results) that allows explicit calculation of the differential string structure for a large class of homogeneous spaces, which also yields formulas for the StolzRedden form. I will comment on the application to verifying the refined Stolz conjecture for our particular class of homogeneous spaces. Joint work with Ray Vozzo. 

Quaternionic Kaehler manifolds of cohomogeneity 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 nonzero 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 cohomogeneity one, based on arXiv:1701.07882. 

Complex methods in real integral geometry 12:10 Fri 28 Jul, 2017 :: Engineering Sth S111 :: Mike Eastwood :: University of Adelaide
There are wellknown analogies between holomorphic integral transforms such as the Penrose transform and real integral transforms such as the Radon, Funk, and John transforms. In fact, one can make a precise connection between them and hence use complex methods to establish results in the real setting. This talk will introduce some simple integral transforms and indicate how complex analysis may be applied. 

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

Weil's Riemann hypothesis (RH) and dynamical systems 12:10 Fri 11 Aug, 2017 :: Engineering Sth S111 :: Tuyen Truong :: University of Adelaide
Media...Weil proposed an analogue of the RH in finite fields, aiming at counting asymptotically the number of solutions to a given system of polynomial equations (with coefficients in a finite field) in finite field extensions of the base field. This conjecture influenced the development of Algebraic Geometry since the 1950Ã¢ÂÂs, most important achievements include: Grothendieck et al.Ã¢ÂÂs etale cohomology, and Bombieri and GrothendieckÃ¢ÂÂs standard conjectures on algebraic cycles (inspired by a Kahlerian analogue of a generalisation of WeilÃ¢ÂÂs RH by Serre). WeilÃ¢ÂÂs RH was solved by Deligne in the 70Ã¢ÂÂs, but the finite field analogue of SerreÃ¢ÂÂs result is still open (even in dimension 2). This talk presents my recent work proposing a generalisation of WeilÃ¢ÂÂs RH by relating it to standard conjectures and a relatively new notion in complex dynamical systems called dynamical degrees. In the course of the talk, I will present the proof of a question proposed by Esnault and Srinivas (which is related to a result by Gromov and Yomdin on entropy of complex dynamical systems), which gives support to the finite field analogue of SerreÃ¢ÂÂs result. 

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

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

Compact pseudoRiemannian homogeneous spaces 12:10 Fri 18 Aug, 2017 :: Engineering Sth S111 :: Wolfgang Globke :: University of Adelaide
Media...A pseudoRiemannian homogeneous space $M$ of finite volume can be presented as $M=G/H$, where $G$ is a Lie group acting transitively and isometrically on $M$, and $H$ is a closed subgroup of $G$.
The condition that $G$ acts isometrically and thus preserves a finite measure on $M$ leads to strong algebraic restrictions on $G$. In the special case where $G$ has no compact semisimple normal subgroups, it turns out that the isotropy subgroup $H$ is a lattice, and that the metric on $M$ comes from a biinvariant metric on $G$.
This result allows us to recover Zeghibâs classification of Lorentzian compact homogeneous spaces, and to move towards a classification for metric index 2.
As an application we can investigate which pseudoRiemannian homogeneous spaces of finite volume are Einstein spaces. Through the existence questions for lattice subgroups, this leads to an interesting connection with the theory of transcendental numbers, which allows us to characterize the Einstein cases in low dimensions.
This talk is based on joint works with Oliver Baues, Yuri Nikolayevsky and Abdelghani Zeghib. 

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

In space there is noone 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 twodimensional 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. 

Dynamics of transcendental Hanon maps 11:10 Wed 20 Sep, 2017 :: Engineering & Math EM212 :: Leandro Arosio :: University of Rome
The dynamics of a polynomial in the complex plane is a classical topic studied already at the beginning of the 20th century by Fatou and Julia. The complex plane is partitioned in two natural invariant sets: a compact set called the Julia set, with (usually) fractal structure and chaotic behaviour, and the Fatou set, where dynamics has no sensitive dependence on initial conditions. The dynamics of a transcendental map was first studied by Baker fifty years ago, and shows striking differences with the polynomial case: for example, there are wandering Fatou components. Moving to C^2, an analogue of polynomial dynamics is given by Hanon maps, polynomial automorphisms with interesting dynamics. In this talk I will introduce a natural generalisation of transcendental dynamics to C^2, and show how to construct wandering domains for such maps. 

An action of the GrothendieckTeichmuller group on stable curves of genus zero 11:10 Fri 22 Sep, 2017 :: Engineering South S111 :: Marcy Robertson :: University of Melbourne
Media...In this talk, we show that the group of homotopy automorphisms of the profinite completion of the framed little 2discs operad is isomorphic to the (profinite) GrothendieckTeichmuller group. We deduce that the GrothendieckTeichmuller group acts nontrivially on an operadic model of the genus zero Teichmuller tower. This talk will be aimed at a general audience and will not assume previous knowledge of the GrothendieckTeichmuller group or operads. This is joint work with Pedro Boavida and Geoffroy Horel. 

On directions and operators 11:10 Wed 27 Sep, 2017 :: Engineering & Math EM213 :: Malabika Pramanik :: University of British Columbia
Media...Many fundamental operators arising in harmonic analysis are governed by sets of directions that they are naturally associated with. This talk will survey a few representative results in this area, and report on some new developments. 

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

Operator algebras in rigid C*tensor categories 12:10 Fri 6 Oct, 2017 :: Engineering Sth S111 :: Corey Jones :: Australian National University
Media...In noncommutative geometry, operator algebras are often regarded as the algebras of functions on noncommutative spaces. Rigid C*tensor categories are algebraic structures that appear in the study of quantum field theories, subfactors, and compact quantum groups. We will explain how they can be thought of as ``noncommutative'' versions of the tensor category of Hilbert spaces. Combining these two viewpoints, we describe a notion of operator algebras internal to a rigid C*tensor category, and discuss applications to the theory of subfactors. 

Endperiodic Khomology and spin bordism 12:10 Fri 20 Oct, 2017 :: Engineering Sth S111 :: Michael Hallam :: University of Adelaide
This talk introduces new "endperiodic" variants of geometric Khomology and spin bordism theories that are tailored to a recent index theorem for evendimensional manifolds with periodic ends. This index theorem, due to Mrowka, Ruberman and Saveliev, is a generalisation of the AtiyahPatodiSinger index theorem for manifolds with odddimensional boundary. As in the APS index theorem, there is an (endperiodic) eta invariant that appears as a correction term for the periodic end. Invariance properties of the standard relative eta invariants are elegantly expressed using Khomology and spin bordism, and this continues to hold in the endperiodic case. In fact, there are natural isomorphisms between the standard Khomology/bordism theories and their endperiodic 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 odddimensional case to the evendimensional case. This work is joint with Mathai Varghese. 

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

Stochastic Modelling of Urban Structure 11:10 Mon 20 Nov, 2017 :: Engineering Nth N132 :: Mark Girolami :: Imperial College London, and The Alan Turing Institute
Media...Urban systems are complex in nature and comprise of a large number of individuals that act according to utility, a measure of net benefit pertaining to preferences. The actions of individuals give rise to an emergent behaviour, creating the socalled urban structure that we observe. In this talk, I develop a stochastic model of urban structure to formally account for uncertainty arising from the complex behaviour. We further use this stochastic model to infer the components of a utility function from observed urban structure. This is a more powerful modelling framework in comparison to the ubiquitous discrete choice models that are of limited use for complex systems, in which the overall preferences of individuals are difficult to ascertain. We model urban structure as a realization of a Boltzmann distribution that is the invariant distribution of a related stochastic differential equation (SDE) that describes the dynamics of the urban system. Our specification of Boltzmann distribution assigns higher probability to stable configurations, in the sense that consumer surplus (demand) is balanced with running costs (supply), as characterized by a potential function. We specify a Bayesian hierarchical model to infer the components of a utility function from observed structure. Our model is doublyintractable and poses significant computational challenges that we overcome using recent advances in Markov chain Monte Carlo (MCMC) methods. We demonstrate our methodology with case studies on the London retail system and airports in England. 

A Hecke module structure on the KKtheory 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 BorelSerre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the BruhatTits tree of $SL(2,\mathbb{Z})$. This is joint work with M.H. Sengun (Sheffield). 

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

Quantum Airy structures and topological recursion 13:10 Wed 14 Mar, 2018 :: Ingkarni Wardli B17 :: Gaetan Borot :: MPI Bonn
Media...Quantum Airy structures are Lie algebras of quadratic differential operators  their classical limit describes Lagrangian subvarieties in symplectic vector spaces which are tangent to the zero section and cut out by quadratic equations. Their partition function  which is the function annihilated by the collection of differential operators  can be computed by the topological recursion. I will explain how to obtain quantum Airy structures from spectral curves, and explain how we can retrieve from them correlation functions of semisimple cohomological field theories, by exploiting the symmetries. This is based on joint work with Andersen, Chekhov and Orantin. 

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

Computing trisections of 4manifolds 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 3manifolds to
trisections of 4manifolds. A trisection describes a 4Ã¢ÂÂdimensional manifold
as a union of three 4Ã¢ÂÂdimensional handlebodies. The complexity of the
4Ã¢ÂÂmanifold 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 4manifold.
After defining trisections and giving key examples and applications, I will
describe an algorithm to compute trisections of 4Ã¢ÂÂmanifolds using arbitrary
triangulations as input. This results in the first explicit complexity
bounds for the trisection genus of a 4Ã¢ÂÂmanifold in terms of the number of
pentachora (4Ã¢ÂÂsimplices) 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 4manifolds. 

Complexity of 3Manifolds 15:10 Fri 23 Mar, 2018 :: Horace Lamb 1022 :: A/Prof Stephan Tillmann :: University of Sydney
In this talk, I will give a general introduction to complexity of
3manifolds and explain the connections between combinatorics, algebra,
geometry, and topology that arise in its study.
The complexity of a 3manifold is the minimum number of tetrahedra in a
triangulation of the manifold. It was defined and first studied by Matveev
in 1990. The complexity is generally difficult to compute, and various
upper and lower bounds have been derived during the last decades using
fundamental group, homology or hyperbolic volume.
Effective bounds have only been found in joint work with Jaco, Rubinstein
and, more recently, Spreer. Our bounds not only allowed us to determine the
first infinite classes of minimal triangulations of closed 3manifolds, but
they also lead to a structure theory of minimal triangulations of
3manifolds. 

Chaos in higherdimensional 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, Kobayashihyperbolic manifolds have at most a finitedimensional 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 Kobayashihyperbolic manifold is nonexpansive 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 antihyperbolicity 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 rightinvariant Haar form. For $G=\mathbb C^n$, this result was proved (although not explicitly stated) some 20 years ago by Fornaess and Sibony. Our generalisation follows their approach. I will give plenty of context and background, as well as some details of the proof of the main result. 

Index of Equivariant CalliasType Operators 13:10 Fri 27 Apr, 2018 :: Barr Smith South Polygon Lecture theatre :: Hao Guo :: University of Adelaide
Media...Suppose M is a smooth Riemannian manifold on which a Lie group G acts properly and isometrically. In this talk I will explore properties of a particular class of Ginvariant operators on M, called GCalliastype operators. These are Dirac operators that have been given an additional Z_2grading and a perturbation so as to be "invertible outside of a cocompact set in M". It turns out that GCalliastype operators are equivariantly Fredholm and so have an index in the Ktheory of the maximal group C*algebra of G. This index can be expressed as a KKproduct of a class in Khomology and a class in the Ktheory of the Higson Gcorona. In fact, one can show that the Ktheory of the Higson Gcorona is highly nontrivial, and thus the index theory of GCalliastype operators is not obviously trivial. As an application of the index theory of GCalliastype operators, I will mention an obstruction to the existence of Ginvariant metrics of positive scalar curvature on M. 

Braid groups and higher representation theory 13:10 Fri 4 May, 2018 :: Barr Smith South Polygon Lecture theatre :: Tony Licata :: Australian National University
Media...The Artin braid group arise in a number of different parts of mathematics. The goal of this talk will be to explain how basic grouptheoretic questions about the Artin braid group can be answered using some modern tools of linear and homological algebra, with an eye toward proving some open conjectures about other groups. 

Cobordism maps on PFH induced by Lefschetz fibration over higher genus base 13:10 Fri 11 May, 2018 :: Barr Smith South Polygon Lecture theatre :: Guan Heng Chen :: University of Adelaide
In this talk, we will discuss the cobordism maps on periodic Floer homology(PFH) induced by Lefschetz fibration. Periodic Floer homology is a Gromov types invariant for three dimensional mapping torus and it is isomorphic to a version of Seiberg Witten Floer cohomology(SWF). Our result is to define the cobordism maps on PFH induced by certain types of Lefschetz fibration via using holomorphic curves method. Also, we show that the cobordism maps is equivalent to the cobordism maps on Seiberg Witten cohomology under the isomorphism PFH=SWF. 

Obstructions to smooth group actions on 4manifolds from families SeibergWitten 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 4manifold 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 SeibergWitten theory for smooth families of 4manifolds and obtain obstructions to the existence of such lifts. For example, we construct compact simplyconnected 4manifolds 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. 

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

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

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 noncompact 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. 

Comparison Theorems under Weak Assumptions 11:10 Fri 29 Jun, 2018 :: EMG06 :: Kwok Kun Kwong :: National Cheng Kung University
TBA 

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

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 StoneWeierstrass theorem. Carlemanâs 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 Carlemanâs 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
Ktheory of C*algebras associated to a semisimple Lie group can be understood both from the geometric point of view via BaumConnes assembly map and from the representation theoretic point of view via harmonic analysis of Lie groups. A Ktheory 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 Ktheory group, we obtain the equivariant index as a fixed point formula which, for each Ktheory generators for (limit of) discrete series, recovers HarishChandraâs character formula on the representation theory side. This is a noncompact analogue of AtiyahSegalSinger fixed point theorem in relation to the Weyl character formula. This is joint work with Peter Hochs. 

TBA 11:10 Fri 17 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Jonathan Zhu :: Harvard University


TBA 11:10 Fri 24 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Siye Wu :: National Tsinghua University


TBA 11:10 Fri 31 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Vanessa Robins :: Australian National University


TBA 11:10 Fri 5 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Scott Morrison :: Australian National University

News matching "Generalized complex geometry" 
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. 

Workshop on Complex Geometry The Institute for Geometry and its Applications will host a Workshop on Complex Geometry at the University of Adelaide from Monday 16 February to Friday 20 February 2009. Click here for full details. Posted Wed 17 Sep 08. 

Mini Winter School on Geometry and Physics The Institute for Geometry and its Applications will host a Winter School on Geometry and Physics on 2022 July 2009. There will be three days of expository lectures aimed at 3rd year and honours students interested in postgraduate studies in pure mathematics or mathematical physics. Posted Wed 24 Jun 09.More information... 

Go8Germany Research Cooperation Scheme Congratulations to Thomas Leistner whose application under the Go8Germany Research Cooperation Scheme is one of 24 across Australia to be funded in 20112012. Thomas will work with Professor Helga Baum of Humbolt University in Berlin on spinor field equations in global Lorentzian geometry. Posted Thu 4 Nov 10. 

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

ARC Grant Success Congratulations to the following staff who were successful in securing funding from the Australian Research Council Discovery Projects Scheme. Associate Professor Finnur Larusson awarded $270,000 for his project Flexibility and symmetry in complex geometry; Dr Thomas Leistner, awarded $303,464 for his project Holonomy groups in Lorentzian geometry, Professor Michael Murray Murray and Dr Daniel Stevenson (Glasgow), awarded $270,000 for their project Bundle gerbes: generalisations and applications; Professor Mathai Varghese, awarded $105,000 for his project Advances in index theory and Prof Anthony Roberts and Professor Ioannis Kevrekidis (Princeton) awarded $330,000 for their project Accurate modelling of large multiscale dynamical systems for engineering and scientific
simulation and analysis Posted Tue 8 Nov 11. 

Dualities in field theories and the role of Ktheory Between Monday 19 and Friday 23 March 2012, the Institute for Geometry and its Applications will host a lecture series by Professor Jonathan Rosenberg from the University of Maryland. There
will be additional talks by other invited speakers. Posted Tue 6 Dec 11.More information... 

The mathematical implications of gaugestring dualities Between Monday 5 and Friday 9 March 2012, the Institute for Geometry and its Applications will host a lecture series by Rajesh Gopakumar from the HarishChandra Research Institute. These lectures will be supplemented by talks by other invited speakers. Posted Tue 6 Dec 11.More information... 
Publications matching "Generalized complex geometry"Publications 

A characterisation of the lines external to an oval cone in PG(3, q), q even Barwick, Susan; Butler, David, Journal of Geometry 93 (21–27) 2009  Generalized solutions to abstract stochastic problems Melnikova, I; Filinkov, Alexei, Integral Transforms and Special Functions 20 (199–206) 2009  Metric connections in projective differential geometry Eastwood, Michael; Matveev, V, Symmetries and Overdetermined Systems of Partial Differential Equations, USA 17/07/08  Notes on projective differential geometry Eastwood, Michael, Symmetries and Overdetermined Systems of Partial Differential Equations, USA 17/07/08  Equivariant and fractional index of projective elliptic operators Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 78 (465–473) 2008  The basic bundle gerbe on unitary groups Murray, Michael; Stevenson, Daniel, Journal of Geometry and Physics 58 (1571–1590) 2008  Monogenic functions in conformal geometry Eastwood, Michael; Ryan, J, Symmetry, Integrability and Geometry: Methods and Applications 84 (1–14) 2007  New models for old questions: generalized linear models for cost prediction Moran, John; Solomon, Patricia; Peisach, Aaron; Martin, J, Journal of Evaluation in Clinical Practice 13 (381–389) 2007  On the geometry of regular hyperbolic fibrations Brown, Matthew; Ebert, G; Luyckz, D, European Journal of Combinatorics 28 (1626–1636) 2007  Projective ovoids and generalized quadrangles Brown, Matthew, Advances in Geometry 7 (65–81) 2007  Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras Eastwood, Michael; Somberg, P; Soucek, V, Journal of Geometry and Physics 57 (2539–2546) 2007  Symmetries and invariant differential pairings Eastwood, Michael, Symmetry, Integrability and Geometry: Methods and Applications 113 (1–10) 2007  TDuality in type II string theory via noncommutative geometry and beyond Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007  Thermodynamics, mnemonic matrices and generalized inverses Leipnik, R; Pearce, Charles, The ANZIAM Journal 48 (493–501) 2007  Laguerre geometries and some connections to generalized quadrangles Brown, Matthew, Journal of the Australian Mathematical Society 83 (335–355) 2007  Towards the fractional quantum Hall effect: a noncummutative geometry perspective Marcolli, M; Varghese, Mathai, chapter in Noncommutative geometry and number theory (Vieweg, Springer Science+Business Media) 235–262, 2006  Conformal holonomy of Cspaces, Ricciflat, and Lorentzian manifolds Leistner, Thomas, Differential Geometry and its Applications 24 (458–478) 2006  Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q) Barwick, Susan; Brown, Matthew; Penttila, T, Journal of Combinatorial Theory Series A 113 (273–290) 2006  Formal adjoints and canonical form for linear operations Eastwood, Michael; Gover, A, Conformal Geometry and Dynamics 10 (285–287) 2006  Fractional analytic index Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 74 (265–292) 2006  Quantum Hall effect and noncommutative geometry Carey, Alan; Hannabuss, K; Varghese, Mathai, Journal of Geometry and Symmetry in Physics 6 (16–36) 2006  Screen bundles of Lorentzian manifolds and some generalisations of ppwaves Leistner, Thomas, Journal of Geometry and Physics 56 (2117–2134) 2006  Some Penrose transforms in complex differential geometry Anco, S; Bland, J; Eastwood, Michael, Science in China Series AMathematics Physics Astronomy 49 (1599–1610) 2006  Arithmetic properties of eigenvalues of generalized harper operators on graphs Dodziuk, Josef; Varghese, Mathai; Yates, Stuart, Communications in Mathematical Physics 262 (269–297) 2005  Dynamics of CP1 lumps on a cylinder Romao, Nuno, Journal of Geometry and Physics 54 (42–76) 2005  Examples of unbounded homogeneous domains in complex space Eastwood, Michael; Isaev, A, Science in China Series AMathematics Physics Astronomy 48 (248–261) 2005  Generalized quadrangles and regularity Brown, Matthew, Discrete Mathematics 294 (25–42) 2005  Smoothly parameterized ech cohomology of complex manifolds Bailey, T; Eastwood, Michael; Gindikin, S, Journal of Geometric Analysis 15 (9–23) 2005  The index of projective families of elliptic operators Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 2005  Type IIB string theory, Sduality, and generalized cohomology Kriz, I; Sati, Hicham, Nuclear Physics B 715 (639–664) 2005  Smoothly parameterized Cech cohomology of complex manifolds Bailey, T; Eastwood, Michael; Gindikin, S, Journal of Geometric Analysis 15 (9–23) 2005  A generalized Hamiltonian model for the dynamics of human motion Pearce, Charles; Ivancevic, V, chapter in Contemporary differential equations and applications (Nova Science Publishers) 15–28, 2004  A geometrical construction of the oval(s) associated with an aflock Brown, Matthew; Thas, J, Advances in Geometry 4 (9–17) 2004  Geometrical contributions to secret sharing theory Jackson, WenAi; Martin, K; O'Keefe, Christine, Journal of Geometry 79 (102–133) 2004  Gerbes, Clifford Modules and the index theorem Murray, Michael; Singer, Michael, Annals of Global Analysis and Geometry 26 (355–367) 2004  Holonomy on Dbranes Carey, Alan; Johnson, Stuart; Murray, Michael, Journal of Geometry and Physics 52 (186–216) 2004  Subquadrangles of order s of generalized quadrangles of order (s, s2), Part I Brown, Matthew; Thas, J, Journal of Combinatorial Theory Series A 106 (15–32) 2004  Subquadrangles of order s of generalized quadrangles of order (s, s2), Part II Brown, Matthew; Thas, J, Journal of Combinatorial Theory Series A 106 (33–48) 2004  The dual Yoshiara construction gives new extended generalized quadrangles Barwick, Susan; Brown, Matthew, European Journal of Combinatorics 25 (377–382) 2004  Towards a Classification of Homogeneous Tube Domains in C(4) Eastwood, Michael; Ezhov, Vladimir; Isaev, A, Journal of Differential Geometry 68 (553–569) 2004  Compact Khler surfaces with trivial canonical bundle Buchdahl, Nicholas, Annals of Global Analysis and Geometry 23 (189–204) 2003  Complex analysis and the Funk transform Bailey, T; Eastwood, Michael; Gover, A; Mason, L, Journal of the Korean Mathematical Society 40 (577–593) 2003  Hyperbolic monopoles and holomorphic spheres Murray, Michael; Norbury, Paul; Singer, Michael, Annals of Global Analysis and Geometry 23 (101–128) 2003  On a generalized form of risk measure Elliott, Robert; Siu, T; Yang, H, Actuaries Australia 9 (587–623) 2003  The geometry and physics of the SeibergWitten equations Wu, Siye, chapter in Geometric analysis and applications to quantum field theory (Birkhauser) 157–203, 2002  Automorphism groups of generalized quadrangles via an unusual action of PGL(2, 2h) O'Keefe, Christine; Penttila, T, European Journal of Combinatorics 23 (213–232) 2002  The Andr/Bruck and Bose representation of conics in Baer subplanes of PG(2, q2) Quinn, Catherine, Journal of Geometry 74 (123–138) 2002  The BorelWeil theorem for complex projective space Eastwood, Michael; Sawon, J, chapter in Invitations to geometry and topology (Oxford University Press) 126–145, 2002  Some special geometry in dimension six Eastwood, Michael; Cap, A, Czech Winter School on Geometry and Physics (22nd: 2002:, Srn'i, Czechoslovakia),  A classification of nondegenerate homogeneous equiaffine hypersurfaces in four complex dimensions Eastwood, Michael; Ezhov, Vladimir, The Asian Journal of Mathematics 5 (721–740) 2001  A proof of Atiyah's conjecture on configurations of four points in Euclidean threespace Eastwood, Michael; Norbury, Paul, Geometry & Topology 5 (885–893) 2001  Equivariant SeibergWitten Floer homology Marcolli, M; Wang, BaiLing, Communications in Analysis and Geometry 9 (451–639) 2001  Generalising a characterisation of Hermitian curves Barwick, Susan; Quinn, Catherine, Journal of Geometry 70 (1–7) 2001  On a generalized 2 + 1 dispersive water wave hierarchy Gordoa, P; Joshi, Nalini; Pickering, A, Publications of the Research Institute for Mathematical Sciences 37 (327–347) 2001  Some constructions of small generalized polygons Polster, Burkhard; Van Maldeghem, H, Journal of Combinatorial Theory Series A 96 (162–179) 2001  Subquadrangles of generalized quadrangles of order (q2, q), q Even O'Keefe, Christine; Penttila, T, Journal of Combinatorial Theory Series A 94 (218–229) 2001  Translation ovoids and spreads of the generalized hexagon H(q) Offer, Alan, Geometriae Dedicata 85 (135–145) 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  A complex from linear elasticity Eastwood, Michael, 19th Winter School Geometry and Physics, Srni, Czech Republic 09/01/99  A generalized trapezoid inequality for functions of bounded variation Cerone, Pietro; Dragomir, S; Pearce, Charles, Turkish Journal of Mathematics 24 (147–163) 2000  A note on higher cohomology groups of Khler quotients Wu, Siye, Annals of Global Analysis and Geometry 18 (569–576) 2000  Drawing with complex numbers Eastwood, Michael; Penrose, R, Mathematical Intelligencer 22 (8–13) 2000  Local Constraints on EinsteinWeyl geometries: The 3dimensional case Eastwood, Michael; Tod, K, Annals of Global Analysis and Geometry 18 (1–27) 2000  The determination of ovoids of PG(3, q) containing a pointed conic Brown, Matthew, Journal of Geometry 67 (61–72) 2000  Unitals which meet Baer subplanes in 1 modulo q points Barwick, Susan; O'Keefe, Christine; Storme, L, Journal of Geometry 68 (16–22) 2000  Weak and generalized solutions to abstract stochastic equations Melnikova, I; Filinkov, Alexei, Doklady Mathematics 62 (373–377) 2000 
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