Arithmetic statistics via graded Lie algebras

Abstract: I will explain how various results in arithmetic statistics by Bhargava, Gross, Shankar and others on $2$-Selmer groups of Jacobians of (hyper)elliptic curves can be organised and reproved using the theory of graded Lie algebras, following earlier work of Thorne. This gives a uniform proof of these results and yields new theorems for certain families of non-hyperelliptic curves. I will also mention some applications to rational points on certain families of curves.

number theory

Audience: researchers in the topic

Harvard number theory seminar