##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Soumya Sankar

#### The Ohio State University

## Counting elliptic curves with a rational $N$-isogeny

##### Abstract:

The classical problem of counting elliptic curves with a rational N-isogeny can be phrased in terms of counting rational points on certain moduli stacks of elliptic curves. Counting points on stacks poses various challenges, and I will discuss these along with a few ways to overcome them. I will also talk about the theory of heights on stacks developed in recent work of Ellenberg, Satriano and Zureick-Brown and use it to count elliptic curves with an $N$-isogeny for certain $N$. The talk assumes no prior knowledge of stacks and is based on joint work with Brandon Boggess.

Host: Kiran Kedlaya

### March 4, 2021

### 1:00 PM

### Location: See https://www.math.ucsd.edu/\~{}nts/

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