##### Department of Mathematics,

University of California San Diego

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### Joint Algebra/Number Theory

## Lisa Carbone

#### Rutgers University

## Trees and group actions

##### Abstract:

If a group G acts on a tree X we may determine the precise structure of G byapplying machinery of Bass and Serre for reconstructing the group action. We use this to give structure theorems for certain subgroups of $SL_2 $ over a on-archimedean local field, and of groups associated to Kac-Moody Lie algebras over finite fields. Of special interest are lattice subgroups and their congruence subgroups.

Host: Audrey Terras

### December 5, 2002

### 1:30 PM

### AP&M 7321

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