New Zealand Mathematical Society

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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

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


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.