##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Alireza Salehi Golsefidy

#### Princeton University

## Affine sieve and expanders

##### Abstract:

\indent I will talk about the fundamental theorem of affine sieve (joint with Sarnak). The main black box in the proof of this result will be also explained. It is a theorem on a necessary and sufficient condition for a finitely generated subgroup of SL(n,Q) under which the Cayley graphs of such a group modulo square free integers form a family of expanders (joint with Varju).

### January 24, 2011

### 2:00 PM

### Halkin Room

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