##### Department of Mathematics,

University of California San Diego

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### Colloquium

## Richard Taylor

#### Harvard University

## L-FUNCTIONS AND GALOIS THEORY

##### Abstract:

I will first recall some examples of L-functions and indicate some of the ways they have been important in algebraic number theory. I will then describe what appears to be their intimate connection with Galois theory (eg the Fontaine-Mazur conjectures), as well as touching on their relationship with algebraic geometry and automorphic forms. Finally, I will discuss what can be proved in this direction.

Host: Nolan Wallach

### October 16, 2003

### 4:00 PM

### AP&M 6438

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