Events for 02/21/2022 from all calendars

Colloquium - Ionut Chifan

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Ionut Chifan, University of Iowa

Description:
Title: Classification and rigidity for group von Neumann algebras
Abstract: In the 30’s Murray and von Neumann found a natural way to associate a von Neumann algebra L(G) to every countable group G. Classifying L(G) in terms of G emerged as a natural, yet quite challenging problem, as these algebras tend to have very limited memory of the underlying group. This is best illustrated by Connes’ celebrated result (’76) asserting that all icc amenable groups give rise to isomorphic von Neumann algebras; thus, in this case, besides amenability, L(G) does not retain any information on G.
In the non-amenable case the classification is wide-open and far more complex; instances when the von Neumann algebraic structure is sensitive to various algebraic group properties have been discovered via Popa’s eformation/rigidity theory. In this direction, a famous conjecture of Connes (’82) predicts that all icc property (T) groups G are completely recognizable from L(G). In my talk, I will introduce the first examples of property (T) groups which satisfy this conjecture. Our groups are called wreath-like products and arise naturally in the context of group theoretic Dehn filling. Wreath-like product groups can be also used to compute the automorphism groups and the fundamental groups of property (T) von Neumann algebras, a problem of independent interest, barely touched in the literature. For example, through a combination of group theoretic and von Neumann algebraic techniques, we show that for every finitely presented group Q, there exists a property (T) group G such that Out(L(G)) ∼= Q. This is based on a recent joint work with A. Ioana, D. Osin and B. Sun.