Speaker: Prof. Barry Simon (CalTech)
Title: Poncelet’s Theorem, Paraorthogonal Polynomials and the Numerical Range of Truncated
GGT Matrices
Event: The talk was given as the second lecture of the 2019-2020 DeLong Lecture Series at the
University of Colorado, Boulder
Abstract: During the last 20 years there has been a considerable literature on a collection of related mathematical topics: higher degree versions of Poncelet’s Theorem, certain measures associated to some finite Blaschke products and the numerical range of finite dimensional completely non-unitary contractions with defect index 1. I will explain that without realizing it, the authors of these works were discussing Orthogonal Polynomials on the Unit Circle (OPUC). This will allow us to use OPUC methods to provide illuminating proofs of some of their results and in turn to allow the insights from this literature to tell us something about OPUC. This is joint work with Andrei Martínez-Finkelshtein and Brian Simanek.
