Kimball Martin — University of Oklahoma

Title: Galois orbits of modular forms and genus 2 curves.

Abstract: Modular forms are analytic functions that are of interest for several reasons in number theory, in particular for a connection with elliptic curves and abelian varieties.  A basic invariant of a modular (new)form is the size of its Galois orbit, i.e., the degree of its rationality field, yet we have few ways to prove theorems about this invariant.  I will discuss some results and conjectures about Galois orbits of newforms, and then focus on a closely related problem of counting abelian surfaces and genus 2 curves with RM.  This is joint work with Alex Cowan.