91É«ÇéƬ

2:00pm, Wednesday 24 June 2026

Abstract

I will discuss recent work establishing upper bounds for moments of analytic ranks of elliptic curves over number fields. The approach is to study moments of the 1-level density of elliptic curve L-functions. The proof combines tools from arithmetic geometry and analytic number theory, including counting of points of bounded height on weighted projective stacks, the explicit formula for L-functions, and estimates for sums of class numbers. Part of this work is joint with Saahil Sharma.