Seminars

Upcoming

Speaker: Professor Alessandro Sfondrini (IAS, Princeton & Padova University Italy)

Time: Monday 27th November, 2pm

Location: Seminar Room  (Room 113)  Maths and Computer Science  (C026)

Title: Integrability on the string worldsheet

Abstract: I will present how integrability can be used to compute exact observables in string theory and in AdS/CFT. This blackboard lecture will not assume any knowledge of these topics, but only basic notions from quantum field theory.


Speaker: Professor Hiroshi Matano (Meiji Univ)

Time: Thursday 30th November, 2pm

Location: Seminar Room  (Room 113)  Maths and Computer Science  (C026)

Title: Front propagation in an epidemiological model with mutations

Abstract: In this talk, I will discuss propagation properties of a 2-species reaction-diffusion system that comes from an epidemiological model with two types of pathogens, the wild type and the mutant type. The reaction-diffusion system is of a hybrid nature, in the sense that it is of the cooperative type in the area where the solutions are small, while it is of the competitive type where the solutions are relatively large. Such a system was first studied by Griette and Raoul in 2016, then later by Griette and Alfaro, Girardin, Crooks and other people.  In this talk, I will consider the problem under the spatially periodic environment and show, among other things, the existence of traveling waves and discuss whether or not the so-called linear determinacy holds for the speed of spreading fronts whose initial data is compactly supported. This is joint work with Quentin Griette.


Past Seminars

Speaker: Prof. Philip Candelas FRS

Time: Wednesday 2nd August 2023, 11am

Location: Seminar Room  (Room 113)  Maths and Computer Science  (C026)

Title: Arithmetic of Black Holes, Rank 2 Attractors and String theory


Speaker: Dr. Rong Wang (Australian National University)

Time: Friday 9th December 2022, 10am

Location: Seminar Room  (Room 113)  Maths and Computer Science  (C026)

Title: Long-time dynamics of some diffusive epidemic models with free boundaries

Abstract: We consider the long-time dynamics of two epidemic models with free boundaries, one with local diffusion and the other with nonlocal diffusion. We show that both models are well-posed, and their long-time dynamical behaviours are characterized by a spreading-vanishing dichotomy. When spreading persists, we also determine the spreading speed. For the local diffusion model, we show that the spreading speed is always finite, determined by an associated semi-wave problem. For the nonlocal diffusion model, a threshold condition is found in terms of the kernel functions appearing in the nonlocal diffusion terms, such that the spreading speed is finite precisely when this condition is satisfied; when this condition is not satisfied, we show that the spreading speed is infinite, namely accelerated spreading happens. This talk is based on joint works with Professor Yihong Du as well as ongoing work with both Prof. Du and Dr. Wenjie Ni.


Speaker: Prof. Fernando Quiros (Univ. Autonoma Madrid)

Time: Friday 9th December 2022, 11:30am

Location: Seminar Room  (Room 113)  Maths and Computer Science  (C026)

Title: Large-time behaviour in non-local heat equations with memory

Abstract: I will review recent results, in collaboration with Carmen Cortázar (PUC, Chile) and Noemí Wolanski (IMAS-UBA-CONICET, Argentina), on the large-time behaviour of solutions to nonlocal heat equations involving a Caputo time derivative. Such derivatives introduce memory effects that yield new phenomena that are not present in classical diffusion equations.


Speaker: Hiroshi Matano (Meiji University, Tokyo)

Time: Thursday 9th June 2022, 2:00pm.

Location: Seminar Room  (Room 113)  Maths and Computer Science  (C026)

Title: Stability of fronts of bidomain models

Abstract: Bidomain models are widely used to simulate electrical signal transmissions in the heart. Mathematically bidomain models are expressed in terms of pseudo-differential equations involving a Fourier integral operator that is anisotropic. Despite their importance in cardiac electrophysiology, systematic mathematical studies of bidomain models
started only relatively recently.  As the bidomain models usually have strong anistropy, the stability of fronts depends on the direction of
its motion.  In 2016, we considered bidomain Allen-Cahn type equations on ${\bf R}^2$ and revealed the deep relation between the linear stability of a planar wave and the so-called Frank diagram (joint work with Yoichiro Mori, CPAM 2016).  In this talk, I will present our recent results on the nonlinear stability of a planar wave of bidomain Allen-Cahn type equations and also show some numerical simulations of pulse waves of the bidomain FitzHugh-Nagumo system that are noticeably different from those of the conventional FitzHugh-Nagumo systems. This is joint work with Yoichiro Mori, Mitsunori Nara and Koya Sakakibara.

Speaker: Masoud Ganji (University of New England)

Time: Thursday 11th November 2021, 10:00am.

Title: Embedding of a 3-dimensional CR manifold and 4-dimensional Lorentzian geometry

Abstract: CR manifolds can be described as generalisations of real submanifolds of the complex space. Abstract 3-dimensional CR manifolds are defined by a co-dimension one distribution D and a field of endomorphisms J on D such that J^2=-id. The question of when a 3-dimensional CR manifold is embeddable into C^2 has been a fundamental problem for decades. In more recent years a criterion was presented by Hill, Lewandowski and Nurowski, who used the notion of shearfree metrics and Maxwell fields to relate the embedding problem to Lorentzian geometry. In this talk,  which is based on my thesis, I will introduce the notion of Fefferman-Robinson-Trautmann metric and explain that the existence of such Lorentzian metric on a line bundle over the CR manifold is equivalent to the embeddability of the CR manifold.  This is a joint publication with Gerd in 2018.

Speaker: Yihong Du (University of New England)

Time: Friday 22nd October 2021, 11:00am.

Title: Spreading profile of a diffusive competition model with free boundaries

Abstract: In this talk I will discuss some recent results on a two species diffusive competition model with free boundaries, which are concerned with the complete classification of the spreading profiles of the two species in the weak-strong competition case. I will explain how to reach the conclusion that there are exactly five different types of long-time dynamical behaviour for this system. The talk is based on theoretical work with Chang-Hong Wu, and numerical work with K. Khan, Shuang Liu and Tim Schaerf.


Speaker: Gerd Schmalz (University of New England)

Time: Friday 8th October 2021, 11:00am.

Title: CR manifolds and the embeddabilty problem

Abstract: CR-manifold is a hybrid of a real and a complex manifold, where the Cauchy-Riemann equations only make sense in certain directions. Examples of CR manifolds are real hypersurfaces, or more generally, real submanifolds of the complex space. Abstract CR structures on a 2n+k-dimensional manifold M can be given by specifying a 2n-dimensional subbundle D of the tangent  bundle and a smooth field of linear endomorphisms J on D such that J^2=-id. It is a fundamental question when such abstract CR manifold can be (locally) realised as a submanifold of C^N. This can be expressed as solubility of a system of PDE.

For k=0 this question is answered by the classical Newlander-Nirenberg theorem. The Kuranishi-Webster theorem deals with the case k=1, n>2. The case n=1 is notoriously difficult. In his thesis Masoud obtained an  interesting result that relates realisability to the existence of certain 4-dimensional space times. I will talk about a recent result with Cowling, Ottazzi (UNSW) and Masoud that establishes realisability if there exist complex vector fields whose commutators are in a sense close to the commutators of a (finite-dimensional) Lie algebra. This generalises a result by Hill and Nacinovich for solvable Lie algebras.


Speaker: Yihong Du (University of New England)

Time: Tuesday 23rd March 2021, 1:30pm.

Location: C026  Mathematics, Statistics and Computer Science, Room 113

Title: The Fisher-KPP nonlocal diffusion equation with free boundary

Abstract: Propagation has been modelled by reaction-diffusion equations since the pioneering works of Fisher and Kolmogorov-Peterovski-Piskunov (KPP). Much new developments have been achieved in the past a few decades on the modelling of propagation, with traveling wave and related notions playing a central role. In this talk, I will discuss some recent results on the Fisher-KPP equation with free boundary and "nonlocal diffusion".  A key feature of this nonlocal version of the problem is that the propagation may or may not be determined by traveling waves.  There is a threshold condition on the kernel function which determines whether the propagation has (a) a finite speed determined by traveling waves, or (b) an infinite speed (known as accelerated spreading). Some sharp estimates of the spreading rate in both cases (a) and (b) will be presented in the talk.


Speaker: Adam Harris (University of New England)

Time: Thursday 19th November 2020, 3pm.

Title: Branch Loci of Stochastic Binary Games

Abstract: I will give a brief overview of the rudiments of Game Theory, as it relates to the simplest two-player / two-strategy examples (such as Prisoners' Dilemma) and the concept of Equilibrium. Individual games can be distinguished by the settings of external parameters, but internal degrees of freedom are also introduced when player behaviour is modelled stochastically. Points of equilibrium are then seen as generating a branched covering of the internal parameter space. For binary games this covering is a surface defined real-analytically, so the classification and description of its branch locus is naturally related to the theory of stable mappings and their singularities. One of the ambitions of this theory, as originally conceived by Rene Thom, is to apply the general classification of such phenomena to a far-reaching science of Catastrophes which would re-shape the study of dynamical systems. It is well-known that this program was considered controversial when it was put forward half a century ago, but the introduction of  stochastic modelling in Economic Game Theory has led to a revival more recently. The context of stochastic binary games is in fact  sufficiently elementary for us to have carried out a classification that is both explicit and essentially constructive, with little more than a classic Theorem of Whitney on smooth surface-maps and a real-analytic statement of the Weierstrass Preparation Theorem as tools.


Speaker: Tim Schaerf (University of New England)

Time: Thursday 12th November 2020, 3pm.

Title: Local interactions in free-swimming captive Antarctic krill

Abstract: (Joint work with Dr Alicia Burns (University of Sydney), A/Prof Joseph Lizier (University of Sydney), Dr So Kawaguchi (Australian Antarctic Division), Dr Martin Cox (Australian Antarctic Division), Mr Rob King (Australian Antarctic Division), Prof Dr Jens Krause (Humboldt University and Leibniz-Institute of Freshwater Ecology and Inland Fisheries), and Prof Ashley Ward (University of Sydney))
Antarctic krill (Euphausia superba) are one of the most abundant and important animal species and are often described as the keystone species of the Southern Ocean, a species of such vital importance that if they were removed an entire ecosystem could collapse. During their lifetime these krill can form vast swarms, which confer potential safety in numbers, enhanced ability to track nutrient gradients, and improved energy efficiency while swimming.
The broad theory that underpins modern studies of collective motion is that group-level patterns of movement across many species arise due to the application of local rules of interaction that describe how individuals adjust their velocity in response to the relative positions and behaviours of their group mates. There are now several viable methods for trying to infer such interaction rules from experimentally derived trajectory data, including the simplest force-matching/averaging methods, machine learning based methods, and more complex statistical schemes.
This presentation will cover recent work aimed at better understanding krill swarming via the analysis of trajectory data using a force-matching/averaging method. My colleagues filmed the movements of relatively small groups of free-swimming Antarctic krill in aquaria at the Australian Antarctic Division in Kingston, Tasmania, using stereo-video cameras. The movements of individual krill were then tracked manually (in two spatial dimensions), with the identities of krill resolved across paired images from the stereo cameras, before projective geometry was applied to reconstruct the trajectories of the krill in three-dimensions. We then applied an averaging/force-matching method to examine the average changes in the components of the krill’s velocity as a function of the relative coordinates of neighbours, in a consistent frame of reference with respect to gravity and the velocity of individual krill. The averaging method was validated using data derived from an important simulation model for collective motion, and was found to accurately reflect the qualitative form of the interaction rules that drive the model. When applied to the krill, the averaging method reveals a clear, but complex pattern of turning and moderation of speed in response to the relative positions of neighbours. These patterns suggest the presence of social interactions being applied by krill when adjusting their velocity, but differ markedly in detail to the sorts of rules applied in a general individual based model for collective movement. In particular, the krill that we observed tended to slow down when their partners were “above” (in the relative coordinate system), or directly below, but increased speed when partners were to their front or rear. The krill also tended to turn in some form to avoid their neighbours, except those located below and to their front.
Given that the qualitative interaction rules suggested by our analysis differ from those applied in a standard model, we then sought to construct an individual-based model based around the turning responses of the krill (as a first attempt at developing a krill-specific model of collective motion). I’ll present some simulation output from this model, and discuss why I think it is wrong at the moment, plus show some results from an earlier prototype of the model which I’m sure are wrong (but are interesting to look at).
Overall this study represents an important step in better understanding the social elements that may contribute to the movement of krill swarms, and developing better informed models of these swarms.


Speaker: Norm Dancer (University of Sydney)

Time: Thursday 15th October 2020, 3pm.

Title: Convergence to equilibrium for some competing species models with large interactions

Abstract: We use limit problems and scaling arguments to prove, for a number of competing species models, the solution u(x,t) converges to an equilibrium as time goes to infinity.

This is based on joint work with Elaine Crooks (Swansea) Daniel Hauer (Sydney)


Speaker: David Robertson (University of New England)

Time: Thursday 24th September 2020, 3pm

Title: Totally Disconnected Locally Compact Groups

Abstract: A group G acting faithfully by homeomorphisms of the Cantor set is called piecewise full if any homeomorphism assembled piecewise from elements of G is itself an element of G. I will discuss when such a group admits a non-discrete totally disconnected locally compact group topology and describe a number of examples. This is joint work with Alejandra Garrido and Colin Reid.


Speaker: Gerd Schmalz (University of New England)

Time: Thursday 3rd September 2020, 3pm.

Title: Kähler, Sasakian & shearfree Einstein spacetimes of higher dimensions

Abstract: The relation between 4-dimensional spacetimes and 3-dimensional Cauchy-Riemann manifolds (CR manifolds) has been known and exploited by physicists for a long time. The famous Schwarzschild, Kerr and Taub-NUT solutions have nice realisations within this framework. It turns out that the corresponding CR manifold are even more special and feature a much more restrictive Sasakian structure. Sasakian manifolds can be considered as odd-dimensional analogues of Kähler manifolds and are in various ways intimately related to the latter. After an introduction into the topic I will present our construction of higher-dimensional Einstein spacetimes of Taub-NUT type, built on higher-dimensional Kähler manifolds.
This is joint work with D. Alekseevsky, M. Ganji and A. Spiro.