Linear Analysis Seminar

Date: April 21, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Michael Brannan, TAMU

Title: Quantum Cayley trees and the structure of orthogonal free quantum group factors

Abstract: In this talk I will survey some recent results on the structural theory of a class of II_1-factors arising from a family of discrete quantum groups, called the orthogonal free quantum groups FO_n. A question that has been around for some time is whether or not an orthogonal free quantum group factor L(FO_n) can be isomorphic to a free group factor L(F_k). We answer this question in the negative by proving that L(FO_n) is a strongly 1-bounded von Neumann algebra in the sense of Kenley Jung. We obtain this result by proving a certain spectral regularity result for the edge reversing operator on the quantum Cayley tree of FO_n and connect this result to a recent free entropy dimension result of Jung and Shlyakhtenko. This is joint work with Roland Vergnioux.