researchseminars.org

Jef Laga (Cambridge)
2023-03-09 22:00 - 23:00 UTC | https://researchseminars.org/talk/UCSD_NTS/80/
Title: Arithmetic statistics via graded Lie algebras (https://researchseminars.org/talk/UCSD_NTS/80/)
by Jef Laga (Cambridge) as part of UCSD number theory seminar

Lecture held in APM 6402 and online.

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.

The talk will involve a mixture of representation theory, number theory and algebraic geometry and I will assume no familiarity with arithmetic statistics.

pre-talk at 1:20pm
