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

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

Diffeomorphisms of discs, harmonic spinors and positive scalar curvature 11:10 Fri 17 Mar, 2017 :: Engineering Nth N218 :: Diarmuid Crowley :: University of Melbourne
Media...Let Diff(D^k) be the space of diffeomorphisms of the kdisc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have nonzero 8periodic 2torsion detected in real Ktheory. I will then discuss applications for spin manifolds M of dimension 6 or greater: 1) Our results input to arguments of Hitchin which now show that M admits a metric with a harmonic spinor. 2) If nonempty, space of positive scalar curvature metrics on M has nonzero 8periodic 2torsion in its homotopy groups which is detected in real Ktheory. This is part of joint work with Thomas Schick and Wolfgang Steimle. 

Fast approximate inference for arbitrarily large statistical models via message passing 15:10 Fri 17 Mar, 2017 :: Engineering South S111 :: Prof Matt Wand :: University of Technology Sydney
We explain how the notion of message passing can be used
to streamline the algebra and computer coding for fast
approximate inference in large Bayesian statistical models.
In particular, this approach is amenable to handling
arbitrarily large models of particular types
once a set of primitive operations is established.
The approach is founded upon a message passing formulation
of mean field variational Bayes that utilizes
factor graph representations of statistical
models. The notion of factor graph fragments is introduced
and is shown to facilitate compartmentalization of the
required algebra and coding. 

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


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

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

Onelayer liquid films loaded with selfpropelled particles and twolayer films under vibration 15:10 Fri 31 Mar, 2017 :: Engineering South S111 :: Dr Andriy Pototskyy :: Swinburne University of Technology
In the first part, we consider a colony of selfpropelled particles (swimmers) in a thin liquid film resting on a solid plate with deformable liquidgas interface. The local surface tension of the liquidgas interface is altered by the local density of swimmers due to the solutoMarangoni effect. Linear stability of the flat film and nonlinear time evolution is analyzed in case of the swarming interaction between the swimmers.
In the second part, we study the Faraday instability and nonlinear patterns in vibrated twolayer liquid films. For gravitationally stable twolayer films with a lighter fluid on top of the heavier fluid, we find squares, hexagons, quasiperiodic patterns with eightfold symmetry as well as localized states in the form of large scale depletion regions or finite depth holes, occurring at the interface and surface. For a RayleighTaylor unstable combination (heavier fluid above the light one) we show that external vibration increases the lifetime of the film by delaying or completely suppressing the film rupture. 

