Speaker: Prof. Heejong Lee，Korea Institute for Advanced Study

Title: Serre weight conjectures and modularity lifting for GSp4

Language: English

Time & Venue: 2026.04.17 10:00-12:00 MCM110

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.

During the first half of the 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. SL2(Fp), GSp4(Fp)) and the geometry of p-adic local Galois representations. This part will focus on examples of modular forms and associated Galois representations, keeping the exposition elementary.

During the second half of the talk, I will explain the proof of Serre weight conjectures for GSp4 and how to deduce modularity lifting by combining Serre weight conjectures with Breuil-Mezard conjecture (a la Feng-Le Hung-Lin) and certain weight shifting mod p differential operators on GSp4 Shimura varieties (a la Ortiz). This is based on a joint work with Daniel Le and Bao V. Le Hung.

(This is a series seminar organized by Yiwen Ding, Yongquan Hu, Liang Xiao on p-adic Langlands Program at MCM110 on each Friday. Please see more information on the official website.)