Speaker: Nathan Jones, UCLA
Title: "Almost all elliptic curves are Serre curves"
Abstract: A Serre curve is an elliptic curve defined over Q whose torsion subgroup, roughly speaking, has as much Galois symmetry as possible. In this talk, I will define this notion more precisely and sketch a proof of a theorem that, when counted according to height, almost all elliptic curves are Serre curves. If time permits, I will discuss an application of this theorem to the Lang-Trotter conjecture.