Symmetric power functoriality for Hilbert modular forms
Symmetric power functoriality for Hilbert modular forms

Jack Thorne, Cambridge University
IAS  Simonyi Hall Seminar Room SH101
Online Talk
Zoom Link: https://princeton.zoom.us/j/92021955230?pwd=dWxyZXRUaVJmaWQyWWVjVWJoTllpdz09
Symmetric power functoriality is one of the basic cases of Langlands' functoriality conjectures and is the route to the proof of the SatoTate conjecture (concerning the distribution of the modulo p point counts of an elliptic curve over Q, as the prime p varies). I will discuss the proof of the existence of the symmetric power liftings of Hilbert modular forms of regular weight. The proof uses automorphy lifting theorems, automorphic forms on unitary groups, and the geometry of Shimura varieties, as well as the fact that Spec Z is simply connected.
This is joint work with James Newton.