##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Sorin Popa

#### UCLA

## On the classification of II$_1$ factors arising from free groups acting on spaces'.

##### Abstract:

A famous problem of Murray and von Neumann (1943) asks whether the II$_1$ factors $L(\Bbb F_n)$ associated with free groups with $n$ generators, $\Bbb F_n$, are non-isomorphic for distinct $n$'s. While this problem is still open, its ``group measure space'' version, showing that the II$_1$ factors $L^\infty(X)\rtimes \Bbb F_n$ arising from free ergodic probability measure preserving actions $\Bbb F_n\curvearrowright X$ are non-isomoprphic for $n= 2, 3, ...$, independently of the actions, has been recently settled by Stefaan Vaes and myself. I will comment on this, as well as on related results by Gaboriau, Ozawa, Ioana, Peterson.

Host: Adrian Ioana

### April 12, 2012

### 4:00 PM

### AP&M 6402

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