##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Zhiwei Yun

#### MIT

## Motives and the inverse Galois problem

##### Abstract:

We will use geometric Langlands theory to solve two problems concerning number fields. One is Serre's question of whether there exist motives over $\Bbb Q$ with motivic Galois group of type $E_8$ or $G_2$; the other is the concrete question of whether there are Galois extensions of $\Bbb Q$ with Galois group $E_8(p)$ or $G_2(p)$ (the finite simple groups of Lie type), for sufficiently large primes $p$. The answer to both questions is ``YES". Please note the change of day for this week's colloquium.

Host: Cristian Popescu

### January 23, 2012

### 3:00 PM

### AP&M 6402

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