Symmetric power functoriality for modular forms

Abstract: One prediction of the Langlands program is that all 'reasonable' L-functions should arise from automorphic forms. For example, the modularity theorem of Wiles, Breuil, Conrad, Diamond and Taylor identifies the Hasse-Weil L-function of an elliptic curve defined over the rationals with the L-function of a modular form. More generally, the symmetric power L-functions of elliptic curves should be the L-functions of higher rank automorphic forms. This prediction is closely related to the arithmetic of the elliptic curve (e.g. the Sato-Tate conjecture). I will discuss this circle of ideas, including some recent work with Jack Thorne in which we prove automorphy of these symmetric power L-functions.

number theory

Audience: researchers in the topic

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11