Abstract: The theorem of the title states that if K is a number field, then any representation ρ:GK→GL2(C) with projective image S4 arises from automorphic forms. Wiles famously used this theorem in the case K=Q, together with a group-theoretic coincidence, to establish the automorphy of the mod 3 representations attached to elliptic curves over Q. The rest of the story you know. We will discuss what goes wrong with this argument when studying elliptic curves over more general number fields, and what one can do instead.
As usual, the seminar will be preceded by various study groups, starting at 1200.
The talks will be preceded by tea/coffee in Imperial’s common room (room 549 Huxley) from 3:30.