Soumya Sankar : Counting points on stacks and elliptic curves with a rational N-isogeny

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

March 17, 2023, 1 p.m.

In

Zoom

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 work of Ellenberg, Satriano and Zureick-Brown, among others, 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. Time permitting, I will also talk about ongoing work with Jennifer Park on counting elliptic curves of higher degree.

Please note this talk is on Zoom. Link: https://uic.zoom.us/j/83309314462?pwd=K0xPMmVmQTB1WDMwQTkwRGZrVSs2dz09