Joint IAS/Princeton University Number Theory Seminar

Eisenstein series, p-adic deformations, Galois representations, and the group G_2

I will explain some recent work on special cases of the Bloch-Kato conjecture for the symmetric cube of certain modular Galois representations. Under certain standard conjectures, this work constructs nontrivial elements in the Selmer groups of these symmetric cube Galois representations; this works by $p$-adically deforming critical Eisenstein series in a generically cuspidal family of automorphic representations, and then constructing a lattice in the associated family of Galois representations, all for the exceptional group $G_2$. While I will touch on all of these aspects of the construction, I will mainly focus on the Galois side in this talk.

Date & Time

April 01, 2021 | 4:30pm – 5:30pm

Location

Remote Access

Speakers

Sam Mundy, Princeton University

Affiliation

Columbia University

Event Series

Categories

Notes

Zoom link password hint: the three digit integer that is the cube of the sum of its digits.

Video link: https://www.ias.edu/video/eisenstein-series-p-adic-deformations-galois-…