14 December 2017
Speaker: Prof Barry Simon (Caltech)
Title: 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 Gamboa, Nagel and Rouault who obtain the sum rules using large deviations for random matrices.
Time and Venue: 3.00pm in Room S-2.08 (see the map), KCL.
For more information: King’s Analysis Seminar’s website