##### Department of Mathematics,

University of California San Diego

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### The New Faculty

## Mark Watkins

#### University of Bristol, UK

## Special values of $L$-functions: a meeting place of algebra and analysis

##### Abstract:

Starting with the examples of Dirichlet's class number formula and the Birch--Swinnerton-Dyer conjecture, we give a broad overview of the expected relations between the arithmetic of algebraic objects (such as varieties) and the special values of their $L$-functions. Our formulation will deliberately tend toward lowbrow and down-to-earth, rather than aiming for the highest possible generality. \vskip .1in \noindent Note: Watkins is not a new faculty member at UCSD, but he is visiting one (Stein) for the week.

Host: W. Stein

### October 27, 2005

### 1:00 PM

### AP&M 7321

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