An Introduction to Orthogonal Polynomials on the Unit Circle
Speaker(s): Rostyslav Kozhan (Uppsala University)
Time: 10:00-11:00 March 30, 2026
Venue: Room 29, Quan Zhai, BICMR
In this talk, I will give an introduction to orthogonal polynomials on the unit circle from a spectral-theoretic perspective, including the Szegő recurrence and Verblunsky coefficients, the associated CMV matrix, the Christoffel-Darboux kernel, paraorthogonal polynomials, and asymptotic properties of the polynomials and their zeros. Time permitting, I will also touch on Szegő and strong Szegő theorems, connections to Toeplitz determinants, applications in approximation theory and random matrix theory, and recent developments related to multiple orthogonality.
