##### Department of Mathematics,

University of California San Diego

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### Algebra

## Alex Lubotzky

#### Hebrew University of Jerusalem

## Subgroup growth of Lattices in Semisimple Lie groups

##### Abstract:

The subgroup growth of a group is the study of the number of its index n subgroups as a function of n. We will present some sharp estimates on this growth for lattices L in higher rank semi-simple Lie groups G. A surprising phenomenom is that this growth depends only on the root system of G and not on L. In the most general case, the results depend on the generalized Riemann Hyphothesis but a number of results can be also proved unconditionally.

Host: Efim Zelmanov

### April 19, 2004

### 3:00 PM

### AP&M 7321

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