##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Gordan Savin

#### University of Utah

## Inverse Problem in Galois Theory

##### Abstract:

In a couple of recent works with Khare and Larsen we have developed a method to construct finite Lie groups of type $C_n, B_n$ and $G_2$ (and potentially more) as Galois groups over the field of rational numbers. The main tools are functorial lifts and self-dual automorphic forms on $GL(n)$ as a source of $l$-adic representations (Kottwitz, Clozel, Harris-Taylor). In this talk I will discuss how one can control the image of the $l$-adic representation by picking local components of automorphic representations: deeply embedded tame parameters and Jordan subgroups, as main tools.

Host: Wee Teck Gan

### April 21, 2008

### 3:00 PM

### AP&M 7218

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