##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Danny Neftin

#### University of Michigan

## The Sylow subgroups of the absolute Galois group of Q.

##### Abstract:

Following a question of Serre, the Sylow subgroups of the absolute Galois group of a p-adic field were studied and completely understood by Labute. However, the structure of the p-Sylow subgroups of the absolute Galois group of the field of rational numbers is much more subtle and mysterious. We make progress towards its determination via a surprisingly simple decomposition. Joint work with Lior Bary-Soroker and Moshe Jarden.

Host: Cristian Popescu

### February 5, 2015

### 1:00 PM

### AP&M 7321

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