##### Department of Mathematics,

University of California San Diego

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### Math 211 A00 - Algebra Seminar

## Nir Avni

#### Northwestern University

## Model theory of higher rank arithmetic groups

##### Abstract:

I'll describe a new rigidity phenomenon of lattices in higher rank semisimple groups. Specifically, I'll explain why the theories of such groups can't have (finitely generated) deformations, why these groups have a very rich collection of definable subgroups, and finish by discussing a conjecture saying that being a higher rank arithmetic lattice is a first-order property. Based on joint works with Alex Lubotzky and Chen Meiri.

Host: Alireza Salehi Golsefidy

### November 1, 2021

### 2:00 PM

### Meeting ID: 939 5383 2894, Password: structures

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