PDEA Seminar: Zeros of multiple orthogonal polynomials with respect to Angelesco systems on the unit circle

Abstract:

General properties of orthogonal polynomials are mostly studied for measures supported on either the real line or the unit circle. The related of notion of multiple orthogonal polynomial has been studied extensively over the last few decades, but only on the real line. In this talk I will present some very recent development on the unit circle. This concerns an analogue to a century-old result of Angelescu about the uniqueness and zero location of multiple orthogonal polynomials. I will also present some motivation for why one may be interested in studying general orthogonal polynomials, multiple orthogonal polynomials, and their zeros. This includes applications to both number theory and numerical integration.

This is a seminar in the PDEs and Applications seminar series.