##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis Seminar

## Krishnendu Khan

#### University of Iowa

## On some structural rigidity results of group von Neumann algebras

##### Abstract:

In this talk I will present examples of property (T) type II1 factors with trivial fundamental group, thus, providing progress towards the well-known open questions of Connes'94 and Popa'06. We will show that the semidirect product feature is an algebraic feature that survive passage to group von Neumann algebras for a class of inductive limit of property (T) groups arising from geometric group theory. Using Popa's deformation/rigidity in conjunction with group theoretic methods we proved that the acting group can be completely recoverable from the von Neumann algebra as well as the limit action of the acting group. In addition, the fundamental group of the group von Neumann algebras associated to these limit groups are trivial, which contrasts the McDuff case. This is based on a joint work with S. Das.

Host: David Jekel

### May 17, 2022

### 11:00 AM

AP&M 7218 and Zoom

Email djekel@ucsd.edu for Zoom details

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