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Search the School of Mathematical SciencesPeople matching "Higher geometric structures: stacks and gerbes"Events matching "Higher geometric structures: stacks and gerbes" 
Inconsistent Mathematics 15:10 Fri 28 Apr, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Chris Mortensen
The Theory of Inconsistency arose historically from a
number of sources, such as the semantic paradoxes including The Liar
and the settheoretic paradoxes including Russell's. But these sources
are rather too closely connected with Foundationalism: the view that
mathematics has a foundation such as logic or set theory or category
theory etc. It soon became apparent that inconsistent mathematical
structures are of interest in their own right and do not depend on the
existence of foundations. This paper will survey some of the results
in inconsistent mathematics and discuss the bearing on various
philosophical positions including Platonism, Logicism, Hilbert's
Formalism, and Brouwer's Intuitionism. 

Mathematics of underground mining. 15:10 Fri 12 May, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Hyam Rubinstein
Underground mining infrastructure involves an
interesting range of optimisation problems with geometric
constraints. In particular, ramps, drives and tunnels have gradient
within a certain prescribed range and turning circles (curvature) are
also bounded. Finally obstacles have to be avoided, such as faults,
ore bodies themselves and old workings. A group of mathematicians and
engineers at Uni of Melb and Uni of SA have been working on this
problem for a number of years. I will summarise what we have found and
the challenges of working in the mining industry. 

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. 

Likelihood inference for a problem in particle physics 15:10 Fri 27 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Anthony Davison
The Large Hadron Collider (LHC), a particle accelerator located at CERN, near Geneva, is (currently!) expected to start operation in early 2008. It is located in an underground tunnel 27km in circumference, and when fully operational, will be the world's largest and highest energy particle accelerator. It is hoped that it will provide evidence for the existence of the Higgs boson, the last remaining particle of the socalled Standard Model of particle physics. The quantity of data that will be generated by the LHC is roughly equivalent to that of the European telecommunications network, but this will be boiled down to just a few numbers. After a brief introduction, this talk will outline elements of the statistical problem of detecting the presence of a particle, and then sketch how higher order likelihood asymptotics may be used for signal detection in this context. The work is joint with Nicola Sartori, of the Università Ca' Foscari, in Venice. 

Betti's Reciprocal Theorem for Inclusion and Contact Problems 15:10 Fri 1 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University
Enrico Betti (18231892) is recognized in the mathematics community for his pioneering contributions to topology. An equally important contribution is his formulation of the reciprocity theorem applicable to elastic bodies that satisfy the classical equations of linear elasticity. Although James Clerk Maxwell (18311879) proposed a law of reciprocal displacements and rotations in 1864, the contribution of Betti is acknowledged for its underlying formal mathematical basis and generality. The purpose of this lecture is to illustrate how Betti's reciprocal theorem can be used to full advantage to develop compact analytical results for certain contact and inclusion problems in the classical theory of elasticity. Inclusion problems are encountered in number of areas in applied mechanics ranging from composite materials to geomechanics. In composite materials, the inclusion represents an inhomogeneity that is introduced to increase either the strength or the deformability characteristics of resulting material. In geomechanics, the inclusion represents a constructed material region, such as a ground anchor, that is introduced to provide load transfer from structural systems. Similarly, contact problems have applications to the modelling of the behaviour of indentors used in materials testing to the study of foundations used to distribute loads transmitted from structures. In the study of conventional problems the inclusions and the contact regions are directly loaded and this makes their analysis quite straightforward. When the interaction is induced by loads that are placed exterior to the indentor or inclusion, the direct analysis of the problem becomes inordinately complicated both in terns of formulation of the integral equations and their numerical solution. It is shown by a set of selected examples that the application of Betti's reciprocal theorem leads to the development of exact closed form solutions to what would otherwise be approximate solutions achievable only through the numerical solution of a set of coupled integral equations. 

Key Predistribution in GridBased Wireless Sensor Networks 15:10 Fri 12 Dec, 2008 :: Napier G03 :: Dr Maura Paterson :: Information Security Group at Royal Holloway, University of London.
Wireless sensors are small, batterypowered devices that are deployed to
measure quantities such as temperature within a given region, then form
a wireless network to transmit and process the data they collect.
We discuss the problem of distributing symmetric cryptographic keys to
the nodes of a wireless sensor network in the case where the sensors are
arranged in a square or hexagonal grid, and we propose a key
predistribution scheme for such networks that is based on Costas arrays.
We introduce more general structures known as distinctdifference
configurations, and show that they provide a flexible choice of
parameters in our scheme, leading to more efficient performance than
that achieved by prior schemes from the literature. 

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). 

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. 

How to see in higher dimensions 12:10 Thu 7 May, 2009 :: Napier 210 :: Prof Michael Murray
Media...The human brain has evolved to be able to
think intuitively in three dimensions. Unfortunately the
real world is at least four and maybe 10, 11 or 26 dimensional.
In this talk I will discuss some of the tricks mathematicians
have devised to think about higher dimensional objects.


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. 

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.


From linear algebra to knot theory 15:10 Fri 21 Aug, 2009 :: Badger Labs G13
Macbeth Lecture Theatre :: Prof Ross Street :: Macquarie University, Sydney
Vector spaces and linear functions form our paradigmatic monoidal category. The concepts underpinning linear algebra admit definitions, operations and constructions with analogues in many other parts of mathematics. We shall see how to generalize much of linear algebra to the context of monoidal categories. Traditional examples of such categories are obtained by replacing vector spaces by linear representations of a given compact group or by sheaves of vector spaces. More recent examples come from lowdimensional topology, in particular, from knot theory where the linear functions are replaced by braids or tangles. These geometric monoidal categories are often free in an appropriate sense, a fact that can be used to obtain algebraic invariants for manifolds. 

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

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.


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

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.


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. 

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. 

Estimation of sparse Bayesian networks using a scorebased approach 15:10 Fri 30 Apr, 2010 :: School Board Room :: Dr Jessica Kasza :: University of Copenhagen
The estimation of Bayesian networks given highdimensional data sets, with more variables than there are observations, has been the focus of much recent research. These structures provide a flexible framework for the representation of the conditional independence relationships of a set of variables, and can be particularly useful in the estimation of genetic regulatory networks given gene expression data.
In this talk, I will discuss some new research on learning sparse networks, that is, networks with many conditional independence restrictions, using a scorebased approach. In the case of genetic regulatory networks, such sparsity reflects the view that each gene is regulated by relatively few other genes. The presented approach allows prior information about the overall sparsity of the underlying structure to be included in the analysis, as well as the incorporation of prior knowledge about the connectivity of individual nodes within the network.


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.


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. 

Spot the difference: how to tell when two things are the same (and when they're not!) 13:10 Wed 19 May, 2010 :: Napier 210 :: Dr Raymond Vozzo :: University of Adelaide
Media...High on a mathematician's todo list is classifying objects and structures that arise in mathematics. We see patterns in things and want to know what other sorts of things behave similarly. This poses several problems. How can you tell when two seemingly different mathematical objects are the same? Can you even tell when two seemingly similar mathematical objects are the same? In fact, what does "the same" even mean? How can you tell if two things are the same when you can't even see them! In this talk, we will take a walk through some areas of maths known as algebraic topology and category theory and I will show you some of the ways mathematicians have devised to tell when two things are "the same". 

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.


Meteorological drivers of extreme bushfire events in southern Australia 15:10 Fri 2 Jul, 2010 :: Benham Lecture Theatre :: Prof Graham Mills :: Centre for Australian Weather and Climate Research, Melbourne
Bushfires occur regularly during summer in southern Australia, but only a few of these fires become iconic due to their effects, either in terms of loss of life or economic and social cost. Such events include Black Friday (1939), the Hobart fires (1967), Ash Wednesday (1983), the Canberra bushfires (2003), and most recently Black Saturday in February 2009. In most of these events the weather of the day was statistically extreme in terms of heat, (low) humidity, and wind speed, and in terms of antecedent drought. There are a number of reasons for conducting postevent analyses of the meteorology of these events. One is to identify any meteorological circulation systems or dynamic processes occurring on those days that might not be widely or hitherto recognised, to document these, and to develop new forecast or guidance products. The understanding and prediction of such features can be used in the short term to assist in effective management of fires and the safety of firefighters and in the medium range to assist preparedness for the onset of extreme conditions. The results of such studies can also be applied to simulations of future climates to assess the likely changes in frequency of the most extreme fire weather events, and their documentary records provide a resource that can be used for advanced training purposes. In addition, particularly for events further in the past, revisiting these events using reanalysis data sets and contemporary NWP models can also provide insights unavailable at the time of the events.
Over the past few years the Bushfire CRC's Fire Weather and Fire Danger project in CAWCR has studied the mesoscale meteorology of a number of major fire events, including the days of Ash Wednesday 1983, the Dandenong Ranges fire in January 1997, the Canberra fires and the Alpine breakout fires in January 2003, the Lower Eyre Peninsula fires in January 2005 and the Boorabbin fire in December 2007January 2008. Various aspects of these studies are described below, including the structures of dry cold frontal wind changes, the particular character of the cold fronts associated with the most damaging fires in southeastern Australia, and some aspects of how the vertical temperature and humidity structure of the atmosphere may affect the fire weather at the surface.
These studies reveal much about these major events, but also suggest future research directions, and some of these will be discussed.


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. 

Compound and constrained regression analyses for EIV models 15:05 Fri 27 Aug, 2010 :: Napier LG28 :: Prof Wei Zhu :: State University of New York at Stony Brook
In linear regression analysis, randomness often exists in the independent variables and the resulting models are referred to errorsinvariables (EIV) models. The existing general EIV modeling framework, the structural model approach, is parametric and dependent on the usually unknown underlying distributions. In this work, we introduce a general nonparametric EIV modeling framework, the compound regression analysis, featuring an intuitive geometric representation and a 11 correspondence to the structural model. Properties, examples and further generalizations of this new modeling approach are discussed in this talk. 

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. 

A polyhedral model for boron nitride nanotubes 15:10 Fri 3 Sep, 2010 :: Napier G04 :: Dr Barry Cox :: University of Adelaide
The conventional rolledup model of nanotubes does not apply to the very small radii tubes, for which curvature effects become significant. In this talk an existing geometric model for carbon nanotubes proposed by the authors, which accommodates this deficiency and which is based on the exact polyhedral cylindrical structure, is extended to a nanotube structure involving two species of atoms in equal proportion, and in particular boron nitride nanotubes. This generalisation allows the principle features to be included as the fundamental assumptions of the model, such as equal bond length but distinct bond angles and radii between the two species. The polyhedral model is based on the five simple geometric assumptions: (i) all bonds are of equal length, (ii) all bond angles for the boron atoms are equal, (iii) all boron atoms lie at an equal distance from the nanotube axis, (iv) all nitrogen atoms lie at an equal distance from the nanotube axis, and (v) there exists a fixed ratio of pyramidal height H, between the boron species compared with the corresponding height in a symmetric single species nanotube.
Working from these postulates, expressions are derived for the various structural parameters such as radii and bond angles for the two species for specific values of the chiral vector numbers (n,m). The new model incorporates an additional constant of proportionality H, which we assume applies to all nanotubes comprising the same elements and is such that H = 1 for a single species nanotube. Comparison with `ab initio' studies suggest that this assumption is entirely reasonable, and in particular we determine the value H = 0.56\pm0.04 for boron nitride, based on computational results in the literature.
This talk relates to work which is a couple of years old and given time at the end we will discuss some newer results in geometric models developed with our former student Richard Lee (now also at the University of Adelaide as a post doc) and some workinprogress on carbon nanocones.
Note: pyramidal height is our own terminology and will be explained in the talk.


Totally disconnected, locally compact groups 15:10 Fri 17 Sep, 2010 :: Napier G04 :: Prof George Willis :: University of Newcastle
Locally compact groups occur in many branches of mathematics. Their study falls into two cases: connected groups, which occur as automorphisms of smooth structures such as spheres for example; and totally disconnected groups, which occur as automorphisms of discrete structures such as trees. The talk will give an overview of the currently developing structure theory of totally disconnected locally compact groups.
Techniques for analysing totally disconnected groups will be described that correspond to the familiar Lie group methods used to treat connected groups. These techniques played an essential role in the recent solution of a problem raised by R. Zimmer and G. Margulis concerning commensurated subgroups of arithmetic groups.


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). 

Mathematical modelling in nanotechnology 15:10 Fri 4 Mar, 2011 :: 7.15 Ingkarni Wardli :: Prof Jim Hill :: University of Adelaide
Media...In this talk we present an overview of the mathematical modelling contributions of the Nanomechanics Groups at the Universities of Adelaide and Wollongong. Fullerenes and carbon nanotubes have unique properties, such as low weight, high strength, flexibility, high thermal conductivity and chemical stability, and they have many potential applications in nanodevices. In this talk we first present some new results on the geometric structure of carbon nanotubes and on related nanostructures. One concept that has attracted much attention is the creation of nanooscillators, to produce frequencies in the gigahertz range, for applications such as ultrafast optical filters and nanoantennae. The sliding of an inner shell inside an outer shell of a multiwalled carbon nanotube can generate oscillatory frequencies up to several gigahertz, and the shorter the inner tube the higher the frequency. A C60nanotube oscillator generates high frequencies by oscillating a C60 fullerene inside a singlewalled carbon nanotube. Here we discuss the underlying mechanisms of nanooscillators and using the LennardJones potential together with the continuum approach, to mathematically model the C60nanotube nanooscillator. Finally, three illustrative examples of recent modelling in hydrogen storage, nanomedicine and nanocomputing are discussed. 

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. 

Permeability of heterogeneous porous media  experiments, mathematics and computations 15:10 Fri 27 May, 2011 :: B.21 Ingkarni Wardli :: Prof Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University
Permeability is a key parameter important to a variety of applications in geological engineering and in the environmental geosciences. The conventional definition of Darcy flow enables the estimation of permeability at different levels of detail. This lecture will focus on the measurement of surface permeability characteristics of a large cuboidal block of Indiana Limestone, using a surface permeameter. The paper discusses the theoretical developments, the solution of the resulting triple integral equations and associated computational treatments that enable the mapping of the near surface permeability of the cuboidal region. This data combined with a kriging procedure is used to develop results for the permeability distribution at the interior of the cuboidal region. Upon verification of the absence of dominant pathways for fluid flow through the cuboidal region, estimates are obtained for the "Effective Permeability" of the cuboid using estimates proposed by Wiener, Landau and Lifschitz, King, Matheron, Journel et al., Dagan and others. The results of these estimates are compared with the geometric mean, derived form the computational estimates. 

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

Inference and optimal design for percolation and general random graph models (Part I) 09:30 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge
The problem of optimal arrangement of nodes of a random weighted graph
is discussed in this workshop. The nodes of graphs under study are fixed, but
their edges are random and established according to the so called
edgeprobability function. This function is assumed to depend on the weights
attributed to the pairs of graph nodes (or distances between them) and a
statistical parameter. It is the purpose of experimentation to make inference on
the statistical parameter and thus to extract as much information about it as
possible. We also distinguish between two different experimentation scenarios:
progressive and instructive designs.
We adopt a utilitybased Bayesian framework to tackle the optimal design problem
for random graphs of this kind. Simulation based optimisation methods, mainly
Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We
study optimal design problem for the inference based on partial observations of
random graphs by employing data augmentation technique. We prove that the
infinitely growing or diminishing node configurations asymptotically represent
the worst node arrangements. We also obtain the exact solution to the optimal
design problem for proximity (geometric) graphs and numerical solution for
graphs with threshold edgeprobability functions.
We consider inference and optimal design problems for finite clusters from bond
percolation on the integer lattice $\mathbb{Z}^d$ and derive a range of both
numerical and analytical results for these graphs. We introduce innerouter
plots by deleting some of the lattice nodes and show that the ÃÂÃÂ«mostly populatedÃÂÃÂ
designs are not necessarily optimal in the case of incomplete observations under
both progressive and instructive design scenarios. Some of the obtained results
may generalise to other lattices. 

Inference and optimal design for percolation and general random graph models (Part II) 10:50 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge
The problem of optimal arrangement of nodes of a random weighted graph
is discussed in this workshop. The nodes of graphs under study are fixed, but
their edges are random and established according to the so called
edgeprobability function. This function is assumed to depend on the weights
attributed to the pairs of graph nodes (or distances between them) and a
statistical parameter. It is the purpose of experimentation to make inference on
the statistical parameter and thus to extract as much information about it as
possible. We also distinguish between two different experimentation scenarios:
progressive and instructive designs.
We adopt a utilitybased Bayesian framework to tackle the optimal design problem
for random graphs of this kind. Simulation based optimisation methods, mainly
Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We
study optimal design problem for the inference based on partial observations of
random graphs by employing data augmentation technique. We prove that the
infinitely growing or diminishing node configurations asymptotically represent
the worst node arrangements. We also obtain the exact solution to the optimal
design problem for proximity (geometric) graphs and numerical solution for
graphs with threshold edgeprobability functions.
We consider inference and optimal design problems for finite clusters from bond
percolation on the integer lattice $\mathbb{Z}^d$ and derive a range of both
numerical and analytical results for these graphs. We introduce innerouter
plots by deleting some of the lattice nodes and show that the ÃÂÃÂÃÂÃÂ«mostly populatedÃÂÃÂÃÂÃÂ
designs are not necessarily optimal in the case of incomplete observations under
both progressive and instructive design scenarios. Some of the obtained results
may generalise to other lattices. 

Routing in equilibrium 15:10 Tue 21 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Timothy Griffin :: University of Cambridge
Media...Some path problems cannot be modelled
using semirings because the associated
algebraic structure is not distributive. Rather
than attempting to compute globally optimal
paths with such structures, it may be sufficient
in some cases to find locally optimal paths 
paths that represent a stable local equilibrium.
For example, this is the type of routing system that
has evolved to connect Internet Service Providers
(ISPs) where link weights implement
bilateral commercial relationships between them.
Previous work has shown that routing equilibria can
be computed for some nondistributive algebras
using algorithms in the BellmanFord family.
However, no polynomial time bound was known
for such algorithms. In this talk, we show that
routing equilibria can be computed using
Dijkstra's algorithm for one class of nondistributive
structures. This provides the first
polynomial time algorithm for computing locally
optimal solutions to path problems. 

The real thing 12:10 Wed 3 Aug, 2011 :: Napier 210 :: Dr Paul McCann :: School of Mathematical Sciences
Media...Let x be a real number. This familiar and seemingly innocent assumption opens up a world of infinite variety and information. We use some simple techniques (powers of two, geometric series) to examine some interesting consequences of generating random real numbers, and encounter both the best flash drive and the worst flash drive you will ever meet. Come "hold infinity in the palm of your hand", and contemplate eternity for about half an hour. Almost nothing is assumed, almost everything is explained, and absolutely all are welcome. 

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. 

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


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. 

Estimating transmission parameters for the swine flu pandemic 15:10 Fri 23 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Kathryn Glass :: Australian National University
Media...Following the onset of a new strain of influenza with pandemic potential, policy makers need specific advice on how fast the disease is spreading, who is at risk, and what interventions are appropriate for slowing transmission. Mathematical models play a key role in comparing interventions and identifying the best response, but models are only as good as the data that inform them. In the early stages of the 2009 swine flu outbreak, many researchers estimated transmission parameters  particularly the reproduction number  from outbreak data. These estimates varied, and were often biased by data collection methods, misclassification of imported cases or as a result of early stochasticity in case numbers. I will discuss a number of the pitfalls in achieving good quality parameter estimates from early outbreak data, and outline how best to avoid them.
One of the early indications from swine flu data was that children were disproportionately responsible for disease spread. I will introduce a new method for estimating agespecific transmission parameters from both outbreak and seroprevalence data. This approach allows us to take account of empirical data on human contact patterns, and highlights the need to allow for asymmetric mixing matrices in modelling disease transmission between age groups. Applied to swine flu data from a number of different countries, it presents a consistent picture of higher transmission from children. 

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

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

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. 

The mechanics of plant root growth 15:10 Fri 30 Mar, 2012 :: B.21 Ingkarni Wardli :: Dr Rosemary Dyson :: University of Birmingham
Media...Growing plant cells undergo rapid axial elongation with negligible
radial expansion: high internal turgor pressure causes viscous
stretching of the cell wall. We represent the cell wall as a thin
fibrereinforced viscous sheet, providing insight into the geometric and
biomechanical parameters underlying bulk quantities such as wall
extensibility and showing how either dynamical changes in material
properties, achieved through changes in the cellwall microstructure, or
passive fibre reorientation may suppress cell elongation. We then
investigate how the action of enzymes on the cell wall microstructure
can lead to the required dynamic changes in macroscale wall material
properties, and thus demonstrate a mechanism by which hormones may
regulate plant growth.


The KazdanWarner equation 12:10 Mon 2 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Damien Warman :: University of Adelaide
Media...We look at an equation arising from the differentialgeometric problem of specifying the scalar curvature of a manifold. 

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. 

Mathematical modelling of the surface adsorption for methane on carbon nanostructures 12:10 Mon 30 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Olumide Adisa :: University of Adelaide
Media...In this talk, methane (CH4) adsorption is investigated on both graphite and in the region between two aligned singlewalled carbon nanotubes, which we refer to as the groove site. The LennardâJones potential function and the continuous approximation is exploited to determine surface binding energies between a single CH4 molecule and graphite and between a single CH4 and two aligned singlewalled carbon nanotubes. The modelling indicates that for a CH4 molecule interacting with graphite, the binding energy of the system is minimized when the CH4 carbon is 3.83 angstroms above the surface of the graphitic carbon, while the binding energy of the CH4âgroove site system is minimized when the CH4 carbon is 5.17 angstroms away from the common axis shared by the two aligned singlewalled carbon nanotubes. These results confirm the current view that for larger groove sites, CH4 molecules in grooves are likely to move towards the outer surfaces of one of the singlewalled carbon nanotubes. The results presented in this talk are computationally efficient and are in good agreement with experiments and molecular dynamics simulations, and show that CH4 adsorption on graphite and groove surfaces is more favourable at lower temperatures and higher pressures. 

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.


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.


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. 

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


The 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. 

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.


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.) 

Two classes of network structures that enable efficient information transmission 15:10 Fri 7 Sep, 2012 :: B.20 Ingkarni Wardli :: A/Prof Sanming Zhou :: The University of Melbourne
Media...What network topologies should we use in order to achieve efficient information transmission? Of course answer to this question depends on how we measure efficiency of information dissemination. If we measure it by the minimum gossiping time under the storeandforward, allport and fullduplex model, we show that certain Cayley graphs associated with Frobenius groups are `perfect' in a sense. (A Frobenius group is a permutation group which is transitive but not regular such that only the identity element can fix two points.) Such graphs are also optimal for alltoall routing in the sense that the maximum load on edges achieves the minimum. In this talk we will discuss this theory of optimal network design. 

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


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. 

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. 

Asymptotic independence of (simple) twodimensional Markov processes 15:10 Fri 1 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Guy Latouche :: Universite Libre de Bruxelles
Media...The onedimensional birthand death model is one of the basic processes in applied probability but difficulties appear as one moves to higher dimensions. In the positive recurrent case, the situation is singularly simplified if the stationary distribution has productform. We investigate the conditions under which this property holds, and we show how to use the knowledge to find productform approximations for otherwise unmanageable random walks. This is joint work with Masakiyo Miyazawa and Peter Taylor. 

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. 

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. 

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. 

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. 

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. 

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

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.


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. 

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. 

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. 

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. 

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.) 

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. 

How the leopard got his spots 14:10 Mon 14 Oct, 2013 :: 7.15 Ingkarni Wardli :: Dr Ed Green :: School of Mathematical Sciences
Media...Patterns are everywhere in nature, whether they be the spots and stripes on animals' coats, or the intricate arrangement of different cell types in a tissue. But how do these patterns arise? Whilst every cell contains a plan of the organism in its genes, the cells need to organise themselves so that each knows what it should do to achieve this plan. Mathematics can help biologists explore how different types of signals might be used to control the patterning process. In this talk, I will introduce two simple mathematical theories of biological pattern formation: Turing patterns where, surprisingly, the essential ingredient for producing the pattern is diffusion, which usually tends to make things more uniform; and the KellerSegel model, which provides a simple mechanism for the formation of multicellular structures from isolated single cells. These mathematical models can be used to explain how tissues develop, and why there are many spotted animals with a stripy tail, but no stripy animals with a spotted tail. 

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.


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.


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. 

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. 

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. 

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. 

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. 

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. 

Computing with groups 15:10 Fri 30 May, 2014 :: B.21 Ingkarni Wardli :: Dr Heiko Dietrich :: Monash University
Media...Groups are algebraic structures which show up in many branches of
mathematics and other areas of science; Computational Group Theory is
on the cutting edge of pure research in group theory and its interplay
with computational methods.
In this talk, we consider a practical aspect
of Computational Group Theory: how to represent a group in a computer,
and how to work with such a description efficiently. We will first
recall some wellestablished methods for permutation group; we will
then discuss some recent progress for matrix groups. 

Optimal transportation and MongeAmpere type equation 15:10 Fri 13 Jun, 2014 :: B.21 Ingkarni Wardli :: Professor XuJia Wang :: Centre for Mathematics and its Applications, Australian National University
Media...The optimal transportation is to find an optimal mapping of transferring one mass density to another one such that the total cost is minimised. This problem was first introduced by Monge in 1781. Monge's cost function is propositional to the distance the mass is transferred, namely c(x,y)=xy, but more general costs are allowed. The optimal transportation has found a variety of applications and has been extensively studied since then. In 1940s Kantorovich introduced a dual functional, by which one can determine the optimal mapping through the associated potential function, for a large class of cost functions.
The potential function satisfies a MongeAmpere type equation, which is a fully nonlinear partial differential equation arising also in geometric problems related to the Gauss curvature, and has been studied by Aleksandrov, Calabi, Nirenberg, Pogorelov, ChengYau, and Caffarelli, among many others. In this talk we will first introduce the optimal transportation and review the existence of optimal mappings. We then focus on the regularity of the optimal mappings. By studying the associated MongeAmpere equation, sharp conditions on the cost function have been found by the speaker and his collaborators. For Monge's cost function xy, which does not satisfy the sharp conditions, we have also obtained the existence of optimal mappings, and established interesting regularity and singularity results for the mapping. 

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.


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. 

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. 

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

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. 

Neural Development of the Visual System: a laminar approach 15:10 Fri 29 Aug, 2014 :: N132 Engineering North :: Dr Andrew Oster :: Eastern Washington University
Media...In this talk, we will introduce the architecture of the visual
system in higher order primates and cats. Through activitydependent
plasticity mechanisms, the left and right eye streams segregate in the
cortex in a stripelike manner, resulting in a pattern called an ocular
dominance map. We introduce a mathematical model to study how such a
neural wiring pattern emerges. We go on to consider the joint
development of the ocular dominance map with another feature of the
visual system, the cytochrome oxidase blobs, which appear in the center
of the ocular dominance stripes. Since cortex is in fact comprised of
layers, we introduce a simple laminar model and perform a stability
analysis of the wiring pattern. This intricate biological structure
(ocular dominance stripes with "blobs" periodically distributed in their
centers) can be understood as occurring due to two Turing instabilities
combined with the leadingorder dynamics of the system. 

Neural Development of the Visual System: a laminar approach 15:10 Fri 29 Aug, 2014 :: This talk will now be given as a School Colloquium :: Dr Andrew Oster :: Eastern Washington University
In this talk, we will introduce the architecture of the visual system in higher order primates and cats. Through activitydependent plasticity mechanisms, the left and right eye streams segregate in the cortex in a stripelike manner, resulting in a pattern called an ocular dominance map. We introduce a mathematical model to study how such a neural wiring pattern emerges. We go on to consider the joint development of the ocular dominance map with another feature of the visual system, the cytochrome oxidase blobs, which appear in the center of the ocular dominance stripes. Since cortex is in fact comprised of layers, we introduce a simple laminar model and perform a stability analysis of the wiring pattern. This intricate biological structure (ocular dominance stripes with 'blobs' periodically distributed in their centers) can be understood as occurring due to two Turing instabilities combined with the leadingorder dynamics of the system. 

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). 

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. 

Geometric singular perturbation theory and canard theory to study travelling waves in: 1) a model for tumor invasion; and 2) a model for wound healing angiogenesis. 15:10 Fri 17 Oct, 2014 :: EM 218 Engineering & Mathematics Building :: Dr Petrus (Peter) van Heijster :: QUT
In this talk, I will present results on the existence of smooth and shocklike travelling wave solutions for two advectionreactiondiffusion models.
The first model describes malignant tumour (i.e. skin cancer) invasion, while the second one is a model for wound healing angiogenesis.
Numerical solutions indicate that both smooth and shockfronted travelling wave solutions exist for these two models.
I will verify the existence of both type of these solutions using techniques from geometric singular perturbation theory and canard theory.
Moreover, I will provide numerical results on the stability of the waves and the actual observed wave speeds.
This is joint work with K. Harley, G. Pettet, R. Marangell and M. Wechselberger. 

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. 

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. 

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. 

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. 

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. 

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. 

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.


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. 

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. 

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.


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. 

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

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. 

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. 

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.


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. 

Harmonic Analysis in Rough Contexts 15:10 Fri 13 May, 2016 :: Engineering South S112 :: Dr Pierre Portal :: Australian National University
Media...In recent years, perspectives on what constitutes the ``natural" framework within which to conduct various forms of mathematical analysis have shifted substantially. The common theme of these shifts can be described as a move towards roughness, i.e. the elimination of smoothness assumptions that had previously been considered fundamental. Examples include partial differential equations on domains with a boundary that is merely Lipschitz continuous, geometric analysis on metric measure spaces that do not have a smooth structure, and stochastic analysis of dynamical systems that have nowhere differentiable trajectories.
In this talk, aimed at a general mathematical audience, I describe some of these shifts towards roughness, placing an emphasis on harmonic analysis, and on my own contributions. This includes the development of heat kernel methods in situations where such a kernel is merely a distribution, and applications to deterministic and stochastic partial differential equations. 

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. 

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. 

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.


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. 

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. 

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.


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

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.


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. 

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. 

Lagrangian transport in deterministic flows: from theory to experiment 16:10 Tue 16 May, 2017 :: Engineering North N132 :: Dr Michel Speetjens :: Eindhoven University of Technology
Transport of scalar quantities (e.g. chemical species, nutrients, heat) in deterministic flows is key to a wide range of phenomena and processes in industry and Nature. This encompasses length scales ranging from microns to hundreds of kilometres, and includes systems as diverse as viscous flows in the processing industry, microfluidic flows in labsonachip and porous media, largescale geophysical and environmental flows, physiological and biological flows and even continuum descriptions of granular flows.
Essential to the net transport of a scalar quantity is its advection by the fluid motion. The Lagrangian perspective (arguably) is the most natural way to investigate advection and leans on the fact that fluid trajectories are organized into coherent structures that geometrically determine the advective transport properties. Lagrangian transport is typically investigated via theoretical and computational studies and often concerns idealized flow situations that are difficult (or even impossible) to create in laboratory experiments. However, bridging the gap from theoretical and computational results to realistic flows is essential for their physical meaningfulness and practical relevance. This presentation highlights a number of fundamental Lagrangian transport phenomena and properties in both twodimensional and threedimensional flows and demonstrates their physical validity by way of representative and experimentally realizable flows. 

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. 

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. 

Exact coherent structures in high speed flows 15:10 Fri 28 Jul, 2017 :: Ingkarni Wardli B17 :: Prof Philip Hall :: Monash University
In recent years, there has been much interest in the relevance of nonlinear solutions of the NavierStokes equations to fully turbulent flows. The solutions must be calculated numerically at moderate Reynolds numbers but in the limit of high Reynolds numbers asymptotic methods can be used to greatly simplify the computational task and to uncover the key physical processes sustaining the nonlinear states. In particular, in confined flows exact coherent structures defining the boundary between the laminar and turbulent attractors can be constructed. In addition, structures which capture the essential physical properties of fully turbulent flows can be found. The extension of the ideas to boundary layer flows and current work attempting to explain the law of the wall will be discussed.


Conway's Rational Tangle 12:10 Tue 15 Aug, 2017 :: Inkgarni Wardli 5.57 :: Dr Hang Wang :: School of Mathematical Sciences
Media...Many researches in mathematics essentially feature some classification problems. In this context, invariants are created in order to associate algebraic quantities, such as numbers and groups, to elements of interested classes of geometric objects, such as surfaces. A key property of an invariant is that it does not change under ``allowable moves'' which can be specified in various geometric contexts. We demonstrate these lines of ideas by rational tangles, a notion in knot theory.
A tangle is analogous to a link except that it has free ends. Conway's rational tangles are the simplest tangles that can be ``unwound'' under a finite sequence of two simple moves, and they arise as building blocks for knots. A numerical invariant will be introduced for Conway's rational tangles and it provides the only known example of a complete invariant in knot theory.


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. 

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. 

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. 

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. 

Models, machine learning, and robotics: understanding biological networks 15:10 Fri 16 Mar, 2018 :: Horace Lamb 1022 :: Prof Steve Oliver :: University of Cambridge
The availability of complete genome sequences has enabled the construction of computer models of metabolic networks that may be used to predict the impact of genetic mutations on growth and survival. Both logical and constraintbased models of the metabolic network of the model eukaryote, the ale yeast Saccharomyces cerevisiae, have been available for some time and are continually being improved by the research community. While such models are very successful at predicting the impact of deleting single genes, the prediction of the impact of higher order genetic interactions is a greater challenge. Initial studies of limited gene sets provided encouraging results. However, the availability of comprehensive experimental data for the interactions between genes involved in metabolism demonstrated that, while the models were able to predict the general properties of the genetic interaction network, their ability to predict interactions between specific pairs of metabolic genes was poor. I will examine the reasons for this poor performance and demonstrate ways of improving the accuracy of the models by exploiting the techniques of machine learning and robotics.
The utility of these metabolic models rests on the firm foundations of genome sequencing data. However, there are two major problems with these kinds of network models  there is no dynamics, and they do not deal with the uncertain and incomplete nature of much biological data. To deal with these problems, we have developed the Flexible Nets (FNs) modelling formalism. FNs were inspired by Petri Nets and can deal with missing or uncertain data, incorporate both dynamics and regulation, and also have the potential for model predictive control of biotechnological processes.


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. 

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. 

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

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

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

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. 

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. 

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. 

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

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

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

Some advances in the formulation of analytical methods for linear and nonlinear dynamics 15:10 Tue 20 Nov, 2018 :: EMG07 :: Dr Vladislav Sorokin :: University of Auckland
In the modern engineering, it is often necessary to solve problems involving strong parametric excitation and (or) strong nonlinearity. Dynamics of micro and nanoscale electromechanical systems, wave propagation in structures made of corrugated composite materials are just examples of those. Numerical methods, although able to predict systems behavior for specific sets of parameters, fail to provide an insight into underlying physics. On the other hand, conventional analytical methods impose severe restrictions on the problem parameters space and (or) on types of the solutions.
Thus, the quest for advanced tools to deal with linear and nonlinear structural dynamics still continues, and the lecture is concerned with an advanced formulation of an analytical method. The principal novelty aspect is that the presence of a small parameter in governing equations is not requested, so that dynamic problems involving strong parametric excitation and (or) strong nonlinearity can be considered. Another advantage of the method is that it is free from conventional restrictions on the excitation frequency spectrum and applicable for problems involving combined multiple parametric and (or) direct excitations with incommensurate frequencies, essential for some applications.
A use of the method will be illustrated in several examples, including analysis of the effects of corrugation shapes on dispersion relation and frequency bandgaps of structures and dynamics of nonlinear parametric amplifiers. 
News matching "Higher geometric structures: stacks and gerbes" 
ARC success The School of Mathematical Sciences was again very successful in attracting Australian Research Council funding for 2008. Recipients of ARC Discovery Projects are (with staff from the School highlighted):
Prof NG Bean; Prof PG Howlett; Prof CE Pearce; Prof SC Beecham; Dr AV Metcalfe; Dr JW Boland:
WaterLog  A mathematical model to implement recommendations of The Wentworth Group.
20082010: $645,000
Prof RJ Elliott:
Dynamic risk measures.
(Australian Professorial Fellowship)
20082012: $897,000
Dr MD Finn:
Topological Optimisation of Fluid Mixing.
20082010: $249,000
Prof PG Bouwknegt; Prof M Varghese; A/Prof S Wu:
Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program.
20082010: $240,000
The latter grant is held through the ANU Posted Wed 26 Sep 07. 

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

ARC Grant 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. 

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

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

Schlicht Envelopes of Holomorphy and Foliations by Lines Larusson, Finnur; Shafikov, R, Journal of Geometric Analysis 19 (373–389) 2009  Higher symmetries of the square of the Laplacian Eastwood, Michael; Leistner, Thomas, Symmetries and Overdetermined Systems of Partial Differential Equations, USA 17/07/08  The inner automorphism 3group of a strict 2group Roberts, David; Schreiber, U, Journal of Homotopy and Related Structures 3 (193–245) 2008  Geometric constructions of optimal linear perfect hash families Barwick, Susan; Jackson, WenAi, Finite Fields and Their Applications 14 (1–13) 2007  Prolongations of geometric overdetermined systems Branson, T; Cap, A; Eastwood, Michael; Gover, A, International Journal of Mathematics 17 (641–664) 2006  YangMills theory for bundle gerbes Varghese, Mathai; Roberts, David, Journal of Physics A: Mathematical and Theoretical (Print Edition) 39 (6039–6044) 2006  Bundle gerbes for ChernSimons and WessZuminoWitten theories Carey, Alan; Johnson, Stuart; Murray, Michael; Stevenson, Daniel; Wang, BaiLing, Communications in Mathematical Physics 259 (577–613) 2005  Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in Ktheory Kordyukov, Y; Varghese, Mathai; Shubin, M, Journal fur die Reine und Angewandte Mathematik 581 (193–236) 2005  Higher symmetries of the Laplacian Eastwood, Michael, Annals of Mathematics 161 (1645–1665) 2005  Smoothly parameterized ech cohomology of complex manifolds Bailey, T; Eastwood, Michael; Gindikin, S, Journal of Geometric Analysis 15 (9–23) 2005  Higher order accuracy in the gaptooth scheme for largescale dynamics using microscopic simulators Roberts, Anthony John; Kevrekidis, I, The ANZIAM Journal 46 (C637–C657) 2005  Smoothly parameterized Cech cohomology of complex manifolds Bailey, T; Eastwood, Michael; Gindikin, S, Journal of Geometric Analysis 15 (9–23) 2005  Bundle 2gerbes Stevenson, Daniel, Proceedings of the London Mathematical Society 88 (405–435) 2004  Gerbes, Clifford Modules and the index theorem Murray, Michael; Singer, Michael, Annals of Global Analysis and Geometry 26 (355–367) 2004  Geometric means, index mappings and entropy Comanescu, D; Dragomir, S; Pearce, Charles, chapter in Inequality theory and applications  Volume 3 (Nova Science Publishers) 85–96, 2003  Geometric means, index mappings and supermultiplicativity Pearce, Charles; Dragomir, S; Comanescu, D, chapter in Inequality theory and applications  Volume 2 (Nova Science Publishers) 193–201, 2003  Higgs fields, bundle gerbes and string structures Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 243 (541–555) 2003  The geometric triangle for 3dimensional SeibergWitten monopoles Carey, Alan; Marcolli, M; Wang, BaiLing, Communications in Contemporary Mathematics 5 (197–250) 2003  Higherorder statistical moments of waveinduced response of offshore structures via efficient sampling techniques Najafian, G; Burrows, R; Tickell, R; Metcalfe, Andrew, International Offshore and Polar Engineering Conference 3 (465–470) 2002  Twisted Ktheory and Ktheory of bundle gerbes Bouwknegt, Pier; Carey, Alan; Varghese, Mathai; Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 228 (17–45) 2002  A boundary element method for anisotropic inhomogeneous elasticity Azis, Mohammad; Clements, David, International Journal of Solids and Structures 38 (5747–5763) 2001  An edgeofthewedge theorum for hypersurface CR functions Eastwood, Michael; Graham, C, Journal of Geometric Analysis 11 (589–602) 2001  Hadamard and DragomirAgarwal inequalities, higherorder convexity and the Euler formula Dedio, L; Pearce, Charles; Peoario, J, Journal of the Korean Mathematical Society (–) 2001  A note on higher cohomology groups of Khler quotients Wu, Siye, Annals of Global Analysis and Geometry 18 (569–576) 2000  Bundle gerbes applied to quantum field theory Carey, Alan; Mickelsson, J; Murray, Michael, Reviews in Mathematical Physics 12 (65–90) 2000  Bundle gerbes: stable isomorphism and local theory Murray, Michael; Stevenson, Daniel, Journal of the London Mathematical Society 62 (925–937) 2000  Quasiquadrics and related structures De Clerck, F; Hamilton, N; O'Keefe, Christine; Penttila, T, Australasian Journal of Combinatorics 22 (151–166) 2000 
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