Beth Romano: Arithmetic statistics through graded Lie algebras

Given a Lie algebra of type E, one can build families of algebraic curves. In joint work with Jack Thorne, we have used the invariant theory of graded Lie algebras to analyze the Selmer sets of these curves. In my talk I'll focus on the beautiful relationship between the original Lie algebras and the resulting curves, and on the role Lie theory plays in our analysis.