##### Department of Mathematics,

University of California San Diego

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### RTG colloquium

## Kiran Kedlaya

#### UCSD

## Models for modular forms: part 1

##### Abstract:

Modular forms, being some of the most fundamental objects in number theory, have a habit of appearing in many different contexts; such coincidences turn out to be extremely useful for computational purposes. I'll describe three different constructions that give the action of the Hecke operators on certain spaces of modular forms: the classical method of modular symbols (Manin), the``method of graphs'' based on isogenies among supersingular elliptic curves (Mestre-Oestrele), and a less well-known method based of reduction of quadratic forms (Birch).

Host: James McKernan

### November 8, 2017

### 3:00 PM

### AP&M 6402

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