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November 2018

Events in October 2018

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

I will survey our current understanding of "quantum symmetries", the mathematical models of topological order, in particular through the formalism of fusion categories. Our very limited classification results to date point to nearly all examples being built out of data coming from finite groups, quantum groups at roots of unity, and cohomological data. However, there are a small number of "exceptional" quantum symmetries that so far appear to be disconnected from the world of classical symmetries as studied in representation theory and group theory. I'll give an update on recent progress understanding these examples.
Interactive theorem proving for mathematicians
15:10 Fri 5 Oct, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University

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

In a series of recent papers, Freed, Hopkins and Teleman put forth a deep result which identifies the twisted K -theory of a compact Lie group G with the representation theory of its loop group LG. Under suitable conditions, both objects can be enhanced to the Verlinde algebra, which appears in mathematical physics as the Frobenius algebra of a certain topological quantum field theory, and in algebraic geometry as the algebra encoding information of moduli spaces of G-bundles over Riemann surfaces. The Verlinde algebra for G with nice connectedness properties have been well-known. However, explicit descriptions of such for disconnected G are lacking. In this talk, I will discuss the various aspects of the Freed-Hopkins-Teleman Theorem and partial results on an extension of the Verlinde algebra arising from a disconnected G. The talk is based on work in progress joint with David Baraglia and Varghese Mathai.
Random walks
15:10 Fri 12 Oct, 2018 :: Napier 208 :: A/Prof Kais Hamza :: Monash University

A random walk is arguably the most basic stochastic process one can define. It is also among the most intuitive objects in the theory of probability and stochastic processes. For these and other reasons, it is one of the most studied processes or rather family of processes, finding applications in all areas of science, technology and engineering. In this talk, I will start by recalling some of the classical results for random walks and then discuss some of my own recent explorations in this area of research that has maintained relevance for decades.
How long does it take to get there?
11:10 Fri 19 Oct, 2018 :: Engineering North N132 :: Professor Herbert Huppert :: University of Cambridge

In many situations involving nonlinear partial differential equations, requiring much numerical calculation because there is no analytic solution, it is possible to find a similarity solution to the resulting (still nonlinear) ordinary differential equation; sometimes even analytically, but it is generally independent of the initial conditions. The similarity solution is said to approach the real solution for t >> tau, say. But what is tau? How does it depend on the parameters of the problem and the initial conditions? Answers will be presented for a variety of problems and the audience will be asked to suggest others if they know of them.
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 non-linear 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.
Local Ricci flow and limits of non-collapsed regions whose Ricci curvature is bounded from below
11:10 Fri 26 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg

We use a local Ricci flow to obtain a bi-Holder correspondence between non-collapsed (possibly non-complete) 3-manifolds with Ricci curvature bounded from below and Gromov-Hausdorff limits of sequences thereof. This is joint work with Peter Topping and the proofs build on results and ideas from recent papers of Hochard and Topping+Simon.
Bayesian Synthetic Likelihood
15:10 Fri 26 Oct, 2018 :: Napier 208 :: A/Prof Chris Drovandi :: Queensland University of Technology

Complex stochastic processes are of interest in many applied disciplines. However, the likelihood function associated with such models is often computationally intractable, prohibiting standard statistical inference frameworks for estimating model parameters based on data. Currently, the most popular simulation-based parameter estimation method is approximate Bayesian computation (ABC). Despite the widespread applicability and success of ABC, it has some limitations. This talk will describe an alternative approach, called Bayesian synthetic likelihood (BSL), which overcomes some limitations of ABC and can be much more effective in certain classes of applications. The talk will also describe various extensions to the standard BSL approach. This project has been a joint effort with several academic collaborators, post-docs and PhD students.
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