##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Alex Ghitza

#### Colby College

## Galois representations (mod p) and modular forms

##### Abstract:

The relation between modular forms and Galois representations is more popular than ever, thanks to recent progress on the Fontaine-Mazur conjecture by Kisin, and on Serre's conjecture by Khare and Wintenberger. After a short introduction to this circle of ideas, I will discuss ongoing work on higher-dimensional generalizations, in the context of Gross' philosophy of modular Galois representations. I will attempt to make the talk as self-contained and accessible as possible.

Host: Wee Teck Gan

### January 25, 2007

### 2:00 PM

### AP&M 7321

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