Thomas Wolfs

My research interests are oriented towards (multiple) orthogonal polynomials, random matrix theory, harmonic analysis and analytic number theory.

My doctoral research involves the construction of multiple orthogonal polynomials with applications in analytic number theory and random matrix theory. Essential in our approach are tools from harmonic analysis (Mellin and Laplace transform). Initially, the focus of my PhD was on solving certain Diophantine problems related to irrationality, see here for more details. In this direction, we constructed the current best rational approximants for Euler's constant and provided explicit irrationality proofs for values of hypergeometric E-functions. Remarkably, the underlying multiple orthogonal polynomials had a natural interpretation as average characteristic polynomials of products of certain random matrices. Intrigued by this phenomenon, my focus shifted towards random matrix theory. Currently, we are describing similar properties for random matrices induced by polynomial ensembles of derivative type.