##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Aaron Pollack

#### Duke University

## Modular forms on exceptional groups

##### Abstract:

By a ``modular form'' for a reductive group $G$ we mean an automorphic form that has some sort of very nice Fourier expansion. The classic example are the holomorphic Siegel modular forms, which are special automorphic functions for the group $\mathrm{Sp}_{2g}$. Following work of Gan, Gross, Savin, and Wallach, it turns out that there is a notion of modular forms on certain real forms of the exceptional groups. I will define these objects and explain what is known about them.

### January 23, 2020

### 3:00 PM

### AP&M 6402

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