On Cartan subalgebras of ${\rm II}_1$ factors arising from Bernoulli actions of weakly amenable groups

Hedrick Assistant Adjunct Professor Changying Ding; Department of Mathematics, University of California, Los Angeles

A conjecture of Popa states that the ${\rm II}_1$ factor arising from a Bernoulli action of a nonamenable group has a unique (group measure space) Cartan subalgebra, up to unitary conjugacy. In this talk, I will discuss this conjecture and show that it holds for weakly amenable groups with constant $1$ among algebraic actions. The proof involves the notion of properly proximal groups introduced by Boutonnet, Ioana, and Peterson.

To participate in the seminar remotely via Zoom, go to https://uiowa.zoom.us/j/95316149275