## PIMS/ UBC Distinguished Colloquium: Barry Simon

- Date: 03/23/2017
- Time: 15:00

University of British Columbia

Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large Deviations.

After defining the spectral theory of orthogonal polynomials on the unit circle (OPUC) and real line (OPRL), I'll describe Verblunsky's version of Szego's theorem as a sum rule for OPUC and the Killip--Simon sum rule for OPRL and their spectral consequences. Next I'll explain the original proof of Killip--Simon using representation theorems for meromorphic Herglotz functions. Finally I'll focus on recent work of Gambo, Nagel and Rouault who obtain the sum rules using large deviations for random matrices.

Date: Thursday March 23, 2017

**Please note special time: 3:00pm**

Location: ESB 2012

A light reception will be hosted at PIMS, ESB 4133 from 2:30pm- 3:00pm.