##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Chandrashekhar Khare

#### University of Utah

## Serre's modularity conjecture for Galois representations

##### Abstract:

In joint work with Jean-Pierre Wintenberger we have proved Serre's conjectures in some cases. Our work also leads to a strategy to prove the general case of Serre's conjecture. To get the strategy to work, one needs to generalize the modularity lifting results of Wiles and Taylor. These generalizations, while not yet carried out fully, seem relatively accessible. In my talk I will report on this work.

Host: Wee Teck Gan

### February 17, 2005

### 2:00 PM

### AP&M 7321

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