##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Dimitri Shlyakhtenko

#### UCLA

## Free entropy dimension and the first $L^2$-Betti number

##### Abstract:

Free entropy dimension and the first $L^2$ Betti number are both numeric invariants of discrete groups; one comes from Voiculescuâ€™s free probability theory and is defined by using finite matrices to ``approximateâ€™â€™ the group, while the other comes from geometric group theory and is of cohomological nature. Somewhat surprisingly, the two numbers are related. I will describe this connection and talk about some applications to von Neumann algebras.

Host: Adrian Ioana

### June 1, 2017

### 4:00 PM

### AP&M 6402

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