An exposition of Wronskian polynomials

by Marco Stevens (KU Leuven)

Location: 200B.02.18, Leuven
Time: Wednesday February 27, 2019 at 10:30

Wronskian polynomials appear in a variety of contexts. For example, exceptional orthogonal polynomials are described in terms of Wronskians of classical orthogonal polynomials. Also there are rational solutions of Painlevé equations that are Wronskians of families of polynomials that satisfy the Appell property. In this talk, I will give an exposition on our contributions to the understanding of these polynomials. Most notably, I will discuss the combinatorial framework for studying these polynomials. This allows us to make connections to symmetric function theory and the characters of irreducible representations of the symmetric group. These connections are fruitful in both directions. Lastly, I will shine a light on our recent ideas involving the zeroes of Wronskian Hermite polynomials.

This is (finished and ongoing) joint work with Niels Bonneux (KU Leuven), Clare Dunning (University of Kent), Zachary Hamaker (University of Michigan) and John Stembridge (University of Michigan).