Tobias Berger

Paramodularity of abelian surfaces

The key ingredient in Wiles' proof of Fermat's last theorem was to establish the modularity of elliptic curves. Despite many impressive advances in the Langlands programme the analogous question of modularity for abelian varieties of dimension 2 is still open. I will discuss what we know and present joint work with Kris Klosin (CUNY) on the modularity of abelian surfaces which have a rational torsion point.