##### Department of Mathematics,

University of California San Diego

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### Seminar in Operator Algebras

## Thomas Sinclair

#### UCLA

## Inner amenability and central sequences in group factors

##### Abstract:

We will show that every group admitting an unbounded quasi-cocycle into a mixing non-amenable representation is not inner amenable. We will discuss how our approach generalizes a recent result of Dahmani, Guirardel, and Osin on the non-inner amenability of so-called acylindrically hyperbolic groups. Other applications such as to central sequences in group-measure space algebras as well as some open problems will also be touched upon. This is based on joint work with Ionut Chifan and Bogdan Udrea.

Host: Adrian Ioana

### August 6, 2013

### 2:00 PM

### AP&M 5829

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