# Operator Theory Seminar

Speaker:
Benjamin Hayes (University of Virginia)
Topic:
A random matrix approach to the Peterson-Thom conjecture

Abstract:
The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on $L^{2}$-Betti numbers. We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjornsen theorem whose validity would imply the Peterson-Thom conjecture. This random matrix conjecture is related to recent work of Collins-Guionnet-Parraud.

Event Date:
October 6, 2020 - 1:30pm to 2:20pm
Location:
Online & 309 VAN
Calendar Category:
Seminar
Seminar Category:
Operator Theory