##### Department of Mathematics,

University of California San Diego

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### Number Theory Seminar

## Skip Garibaldi

#### Emory Univ. and CCR La Jolla

## Algebraic groups with the same tori

##### Abstract:

If two simple linear algebraic groups have the same F-isomorphism classes of maximal F-tori, are the two groups necessarily isomorphic? When F is a number field, it is an old question attributed to Shimura. We describe the recent solution to this question (which relies on the notion of weak commensurability introduced by Gopal Prasad and Andrei Rapinchuk) and its connection with the question "Can you hear the shape of a drum?" for arithmetic quotients of locally symmetric spaces.

Host: Cristian Popescu

### November 15, 2012

### 1:00 PM

### AP&M 7321

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