Operator Theory Seminar

Speaker:
Ionut Chifan
Topic:
On Connes Rigidity Conjecture

Abstract:

In this talk I will introduce a new class of groups, which we call \textit{wreath-like products}. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have strong fixed point properties including Kazhdan's property (T). In this paper, we establish several new rigidity results for von Neumann algebras of wreath-like products. In particular, we obtain the first continuum of property (T) groups whose von Neumann algebras satisfy Connes' rigidity conjecture and the first examples of W$^*$-superrigid groups with property (T). We also compute automorphism groups of von Neumann algebras of a wide class of wreath-like products; as an application, we show that for every finitely presented group $Q$, there exists a property (T) group $G$ such that $Out(L(G))\cong Q$.  This is based on new joint work with Adrian Ioana, Denis Osin and Bin Sun.

Event Date:
November 16, 2021 - 1:30pm to 2:20pm
Location:
VAN 309 or Online (See URL)
Calendar Category:
Seminar
Seminar Category:
Operator Theory