##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Brian Longo

#### UCSD

## ``Super-approximation" for absolutely almost simple groups over the field of rational functions with coefficients in a finite field

##### Abstract:

In recent years, there have been major breakthroughs on the topic of super-approximation for algebraic groups, which is a qualitative version of strong approximation. Super-approximation has proven to be incredibly useful in many areas of both pure and applied Mathematics. We discuss the difficulties of super-approximation in positive characteristic, as well as recent new results for absolutely almost simple groups over $k(t)$, where $k$ is a finite field.

Advisor: Alireza Salehi Golsefidy

### May 9, 2016

### 12:00 PM

### AP&M 7321

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