Sep 22. 2021, 11:00 — 12:00

In work with Jack Thorne, we find the average size of the 3-Selmer group for a family of genus-2 curves by analyzing a graded Lie algebra of type . In this talk, I will give examples of graded Lie algebras and show that they naturally arise when looking at families of algebraic curves. I'll talk about the role Lie theory plays in my work with Thorne, and about a new construction that extends our methods.