Nathan Jones (University of Mississippi) An elliptic curve defined over the rational numbers is called a Serre curve if its torsion subgroup has "as much Galois symmetry as possible." In this talk, I will sketch a proof of the fact that, in an appropriately chosen one-parameter family of elliptic curves, almost all specializations are Serre curves. This is based on joint work with A. Cojocaru and D. Grant.