##### Department of Mathematics,

University of California San Diego

****************************

### Math 269 - Combinatorics

## Alex Lubotzky

#### Hebrew University of Jerusalem

## From Ramanujan graphs to Ramanujan complexe

##### Abstract:

Ramanujan graphs are k-regular graphs with optimal bounds on their eigenvalues. They play a central role in various questions in combinatorics and computer secience. Their construction is based on the work of Deligne and Drinfeld on the Ramanujan conjecture for GL(2). The recent work of Lafforgue which settles the Ramanujan conjecture for GL(n) over function fields opens the door to study of Ramanujan complexes: these are higher dimensional analogues which are obtained as quotients of the Bruhat-Tits building of PGL(n) over local fields.

Host: Efim Zelmanov

### April 20, 2004

### 4:00 PM

### AP&M 7321

****************************