Arithmetic statistics and graded Lie algebras

Jef Laga

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.

https://www.ias.edu/video/arithmetic-statistics-and-graded-lie-algebras