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New Zealand Mathematical
Society Colloquium

Run by the New Zealand Mathematical Society

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5 – 8 December 2016 : Victoria University, Wellington


NZMS Programme and Abstracts updated 5 December 1151

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Colloquium Programme

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Plenary Abstracts

Prof Roy Kerr

Quasars, Black Holes and Gravitational Waves

In 1963 it was realised that certain radio "stars" were enormously powerful objects in far distant galaxies, but the mechanism that drove them was a mystery. Serendipitously, I discovered the unique solution for rotating black holes at this time and it was fairly quickly realised that the accretion disc around one of these could supply the necessary energy. Since then we have observed such supermassive black holes at the centre of most large galaxies.

The most energetic objects in the universe are GRBs (Gamma Ray Bursters). These are generally considered to be hypernova from a very massive rotating star collapsing to a Black hole. However another theory is that they are caused by mergers of massive neutron stars or black holes.

In the last year Ligo has observed mergers of three pairs of rotating black holes, each 10-40 solar masses. The gravitational waves from these have been compared to templates calculated by a mixture of numerical and analytic solutions of Einstein's equations for such events.

Rachel Tappenden

University of Canterbury

It’s a Big (Data) World

Data Science is ubiquitous in modern optimisation literature. Many challenges arise when one applies optimisation methods to very large-scale problems, and in this talk we will investigate how traditional optimisation techniques can be adapted to work successfully in this data science niche. In particular, we will discuss how coordinate descent methods (some of the first optimisation methods to be developed) are once again finding favour in data science, due to their scalability, convergence guarantees, and wide applicability. The talk is intended to be introductory in nature.

Hinke Osinga

University of Auckland

The art of computing global manifolds

Global manifolds are the backbone of a dynamical system and key to the characterisation of its behaviour. They arise in the classical sense of invariant manifolds associated with saddle-type equilibria or periodic orbits and, more recently, in the form of finite-time invariant manifolds in system that evolve on multiple time scales. Dynamical systems theory relies heavily on the knowledge of such manifolds, because of the geometric insight that they can offer into how observed behaviour arises. In applications, global manifolds need to be computed and visualised so that quantitative information about the overall system dynamics can be obtained. This requires accurate numerical methods and a precise understanding of how the computations depend on various model parameters. The computation of global manifolds is a serious challenge, but an effort that pays off. This talk will focus on two case studies that represent the most recent developments in this area.

Geoff Whittle

Victoria University Wellington

What is Rota’s Conjecture — and why would you care?

Recently Jim Geelen, Bert Gerards and I announced that we had a proof of Rota’s Conjecture, which concerns matroids representable over finite fields. In this talk, rather than discuss the proof, I will attempt to give a feel for the milieu in which the conjecture arose and to communicate some of the reasons why, from the time I was a graduate student, I became fascinated with it.

Alexander Melnikov

Massey University

An algorithmic approach to classification problems.

A large part of classical mathematics seeks to characterise mathematical structures. For example, every vector space over a field is fully described by its dimension. A much more complicated example is the complicated description of finite simple groups, up to isomorphism. How can we compare two classification-type results? How can we measure the complexity of a classification problem? Is it possible to show that a class of mathematical structures is unclassifiable? These questions seem to be unrelated to algorithms. Remarkably, modern computability theory can be used to attack questions of this sort. We will discuss three recent applications of computability theory to classification problems in mathematics. These applications include a solution to a 60yo problem of Maltsev (joint with Ng).

Caroline Yoon

University of Auckland

Mathematical freedom, constraints and border crossings

Successful mathematical tasks often invite students to shuttle between the disparate states of creative freedom and attending to externally imposed constraints. This attentional back and forth can be dizzying, but often yields solutions that are less likely to occur when the student is restricted solely to either single state. How can we design mathematical tasks that encourage such productive tension? This talk will consider how we might incorporate common dichotomies into the mathematical experiences we provide for our students: freedom vs. constraint; work vs. play; messiness vs. structure; lectures vs. tutorials.

Ben Burton

University of Queensland

A theory for practical computational topology

Exact computation with knots and 3-manifolds is challenging - many fundamental problems are decidable but enormously complex, and many major algorithms have never been implemented. Even "simple" problems, such as recognising the unknot, have best-known algorithms that are worst-case exponential time. In practice, however, the story is different: modern software packages are surprisingly effective at solving complex topological problems that "should" be intractable. We discuss an ongoing research programme, based on an interplay between topology, graph theory and logic, that aims both to understand this behaviour in theory and to use it in practice for building fast mathematical software.