##### Department of Mathematics,

University of California San Diego

****************************

### Math 243 - Functional Analysis Seminar

## Hui Tan

#### UCSD

## Spectral gap characterizations of property (T) for II$_1$ factors

##### Abstract:

For property (T) II$_1$ factors, any inclusion into a tracial von Neumann algebra has spectral gap, and therefore weak spectral gap. I will discuss characterizations of property (T) for II$_1$ factors by weak spectral gap in inclusions. I will explain how this is related to the non-weakly-mixing property of the bimodules containing almost central vectors, from which we also obtain a characterization of property (T).

Host: David Jekel

### March 29, 2022

### 10:00 AM

Zoom

Please email djekel@ucsd.edu for details

****************************