Integer partitions and Wronksian polynomials

Clare Dunning (University of Kent)

Tuesday 29th April 16:00-17:00 Maths 311B

Abstract

Partitions of integers play a role in a variety of fields including number theory, representation theory  and random matrix theory. They are also of independent interest in enumerative combinatorics.
I will use partitions to label certain Wronskian polynomials that arise in various applications including
- the excited-state sine-Gordon model in its massless limit
- various families of rational solutions associated with Painleve IV and Painleve V.
Curiously, it turns out that various properties of the partitions play a much more important role in these applications than simple labels.

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