##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Nolan Wallach

#### UCSD

## Whittaker Theory II: The proof of the Whittaker Plancherel Theorem

##### Abstract:

Today the main emphasis in local number theory (i.e the Local Langlands) is on the finite places. In charactacteristic 0 the infinite place is the ''elephant in the room''. This is especially true in the Whittaker Theory in which serious difficulties separate the infinite from the finite places. Whittaker models were developed to help the study of Fourier coefficients at cusps of non-holomophic cusp forms (i.e Maass cusp forms) through representation theory. The first of these lectures will start with an explanation of the role of Whittaker models in the theory of automorphic forms. It will continue with a description of the main results. The second lecture will explain the proof of the Whittaker Plancherel Theorem.

Host: Cristian Popescu

### October 18, 2018

### 2:00 PM

### AP&M 7321

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