##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Stefaan Vaes

#### K.U. Leuven

## Von Neumann Algebras with a Unique Cartan Decomposition

##### Abstract:

The subject of this talk is at the crossroads of functional analysis, ergodic theory and group theory. Using a construction by Murray and von Neumann (1943), ergodic actions of countable groups on probability spaces give rise to algebras of operators on a Hilbert space, called von Neumann algebras. In a joint work with Sorin Popa, we proved that such crossed product von Neumann algebras by free groups or, more generally, by hyperbolic groups have a unique Cartan subalgebra. I will explain this result and its consequences for the classification of crossed products by free groups.

Adrian Ioana

### March 7, 2013

### 3:00 PM

### AP&M 6402

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