## NZMS Seminar Series

The NZMS is currently setting up a regular seminar series with talks held via Zoom.

**Wednesday 29 September 2021, 3pm**

**Sione Ma'u, University of Auckland: The extremal function of a real convex body**

https://massey.zoom.us/j/84190393386?pwd=RkVlMmIxbHFOcTUxcGdUVHpKeDhjdz09

The extremal function (or pluricomplex Green function of logarithmic growth) associated to a regular compact set K is important in polynomial approximation. In one complex variable it is a classical Green function for the complement with pole at infinity: zero on K, harmonic on the complement of K in the complex plane, and grows logarithmically as one goes to infinity. In several variables the extremal function is zero on K, maximal on the complement of K and grows logarithmically as one goes to infinity.

In this talk I will describe basic properties of the extremal function in one and several variables: its importance in approximation, and what "maximal" means (which is not the same as harmonic, except in the complex plane).

Then I will explain how to compute the extremal function of a convex body in $R^n$ (considered as a subset of $C^n$). In one variable the extremal function of a real interval e.g. -1,1 is well-known, given in terms of the inverse Joukowski function.

**Wednesday 13 October 2021, 3pm**

**Shaun Cooper, Massey University: The Rogers-Ramanujan continued fraction**

Video: https://youtu.be/FO5jpSCZJfc

Just over 100 years ago, an unknown clerk from India wrote some letters to Cambridge mathematician G. H. Hardy. About certain results in one of the letters, Hardy later wrote

*“(they) defeated me completely; I had never seen anything in the least like them before”*

and concluded

*"A single look at them is enough to show that they could only be written down by a mathematician of the highest class.”*

I will describe these particular results, put them in a modern context, and outline some recent developments.

**Wednesday 27 October 2021, 3pm**

**David Bryant, University of Otago: Minkowski diversities**

https://otago.zoom.us/j/98054569910?pwd=ODJKS2RDaStDcUpZR2docElMK0ZXQT09

The *circumradius* of a set of points in R^n is the minimum amount you need to scale a unit ball in order to contain them. Replace the ball with a convex body K and you have the *generalised circumradius*. We characterise which functions on bounded subsets of R^n correspond to a generalised circumradius for some choice of K. We then discuss the harder question of determining when a function on a finite powerset can be realised as the generalised circumradius defined on some finite set. The results mix convex analysis, the theory of mathematical diversities and ideas from metric geometry.

**Wednesday 10 November, 3pm**

**Dion O'Neale, University of Auckland: Modelling COVID-19 in Aotearoa NZ on a bipartite contact network of 5 million individuals **

Video: https://youtu.be/LK-B_zMKH_o

Many of the models used for rapid policy advice during the COVID-19 pandemic have relied on simplifying assumptions about the homogeneity of individuals. However, we know that risk factors for exposure, transmission, and poor outcomes are not evenly distributed across society. We have built a stochastic model of infection dynamics that runs on an empirically derived bipartite contact network of the ~5 million people in Aotearoa New Zealand. The contact network includes spatial information, and individual demographic information, along with distinct ‘transmission contexts’ including dwellings, workplaces, and schools, built from linked data in the Statistics NZ Integrated Data Infrastructure. This network is the underlying structure on which we run a stochastic contagion process to model the spread of COVID-19, which includes explicit representation of the testing and contact tracing processes. We have used this model to estimate the probable outcomes of COVID outbreaks in Aotearoa and to evaluate the effect of non-pharmaceutical interventions including 'Alert Level' changes. In particular, we find that this heterogeneity (network structure) means that the effect of different interventions does not combine linearly.

** Wednesday 1 December, 9.00 am – 4.30 pm**

**Manawatū–Wellington Applied Mathematics Conference**

Organised by Robert McLachlan. Video: https://youtu.be/w8aXAayfbsI

9.00 am Keynote: Vivien Kirk, Mathematics from physiology?

9.45 am Break

10.00 am Carlo Laing, Periodic solutions of a theta neuron subject to delayed self-feedback

10.20 am Sishu Muni, Globally resonant homoclinic tangencies

10.40 am Brandon Jones, Mathematical models of microbial growth

11.00 am Break

11.20 am John Butcher, Isomeric trees with applications to Runge-Kutta method

11.40 am Christina Lin, Modelling housing feature impacts on sale values in newly developed suburb

12.00 pm Winston Sweatman, Symmetric families of periodic orbits with four- and five-bodies

12.20 pm Break

1.00 pm Keynote: Mark McGuinness, Under pressure: Volcanic bombs that don't explode

1.45 pm Break

2.00 pm Nicholas Witte, Beyond Toeplitz matrices: Modulated or slanted systems

2.20 pm Howard Cohl, Special values for continuous $q$-Jacobi polynomials and applications

2.40 pm Graham Weir, Power loss in soft magnetic materials

3.00 pm Break

3.20 pm Brendan Harding, Inertial migration of spherical particles in curved ducts having a trapezoidal cross-section

3.40 pm Dimitrios Mitsotakis, Recent advances in the theory of nonlinear and dispersive water waves

4.00 pm Robert McLachlan, Functional equivariance of numerical integrators

** Thursday 2 December, 2 pm**

**Juliette Unwin, Imperial College London: Modelling COVID-19: A British perspective**

Video: https://youtu.be/NElieXNZT0U

Late 2019 / early 2020, reports of a novel pathogen spreading around China began to be discussed in the Department of Infectious Disease Epidemiology at Imperial College that I worked in. Little did we know at that point, the scale to which this global pandemic response would reach. During this seminar I’m going to give an overview of the modelling that went on at Imperial over the past few years from the perspective of a member of the COVID-19 response team. I’ll share most insights about the particular projects I was involved in - developing a new method for modelling Rt (the time varying reproduction number), estimating proportions of cases not detected in an outbreak, and now global orphanhood estimates from COVID.