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Pop-up seminar in Number theory
Pop-up seminar in Number theory
Serre weight conjectures and modularity lifting for $\mathrm{GSp}_4$
Serre weight conjectures and modularity lifting for $\mathrm{GSp}_4$
Organizer
Speaker
Heejong Lee
Time
Tuesday, April 14, 2026 2:00 PM - 3:00 PM
Venue
A3-3-201
Online
Zoom 559 700 6085
(BIMSA)
Abstract
Given a Galois representation attached to a regular algebraic cuspidal automorphic representation, the Hodge-Tate weight of the Galois representation is matched with the weight of the automorphic representation. Serre weight conjectures are mod $p$ analogue of such a correspondence, relating ramification at $p$ of a mod $p$ Galois representation and Serre weights of mod $p$ algebraic automorphic forms. In this talk, I will discuss how to understand Serre weight conjectures and modularity lifting as a relationship between representation theory of finite groups of Lie type (e.g. $\mathrm{GSp}_4(\mathbb{F}_p)$) and the geometry of $p$-adic local Galois representations. Then I will explain the proof idea in the case of $\mathrm{GSp}_4$. This is based on a joint work with Daniel Le and Bao V. Le Hung.