Seminar on Banach and Metric Space Geometry

Date: March 3, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Beatrice-Helen Vritsiou, University of Michigan

Title: Selberg-type integrals and the variance conjecture for the operator norm

Abstract: We will discuss the variance conjecture from Asymptotic Convex Geometry in the case of unit balls of the p-Schatten norms in different classical subspaces of square matrices (e.g. the subspaces of symmetric or Hermitian matrices). In particular, we will show how to resolve the conjecture for the unit ball of the operator norm in all these subspaces (this improves upon previous joint work with J. Radke). By Random Matrix Theory results, the question in such cases can be reduced to estimation of integrals of highly symmetric distributions, which may be more amenable to analytic or combinatorial techniques. In the case of the operator norm, integrals of the corresponding symmetric distributions (at least some specific instances of them) have been analysed by Selberg and others, and we manage to use the nice expressions they have found for them.