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Arithmetic statistics via graded Lie algebras

SEMINARS: NUMBER THEORY

When: October 19, 2022
3:00 pm - 4:00 pm
Where: Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Jef Laga - Princeton

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.