NT Seminar: Explicit modularity in genus 2 

We discuss what it means for a genus 2 curve X over the rationals to be modular. In joint work with Andrew Booker, Jeroen Sijsling, Drew Sutherland, and Dan Yasaki, to every genus 2 curve X we discuss conjectures and theorems that attach to X a modular form with a matching L-function. The precise description depends on the structure of the endomorphism algebra of the Jacobian of X. We also establish three typical cases of modularity, in joint work with Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, and 
David Yuen.