##### Department of Mathematics,

University of California San Diego

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### Representation Theory

## Martin Kimball

#### Caltech

## Modularity in four dimensions

##### Abstract:

Langlands conjectured that a continuous complex Galois representation can be associated to an automorphic ''representation'' such that their $L$-functions agree. We reduce the problem for representations into $GL(4)$ with solvable image into several cases. We prove that in certain cases, Langlands modularity conjecture holds. In particular, we obtain a new case of Artin s $L$-function conjecture.

Host: Wee Teck Gan

### February 10, 2004

### 1:30 PM

### AP&M 7321

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