The Langlands reciprocity associates a Galois representation with a certain modular form/automorphic representation. One can ask how this association reflects structures on both sides. For example, the weights of modular forms/automorphic representations are matched by the Hodge-Tate weights of Galois representations. The weight part of Serre's conjecture is a mod p analogue of this structural correspondence.
In this talk, we introduce the weight part of Serre's conjecture and its role in the Langlands program. Then, we discuss a novel idea proving the conjecture for the group GSp4 under technical assumptions. This is based on a joint work with Daniel Le and Bao Viet Le Hung.
Note: This is a part of Webinar in Number Theory series(https://www.math.u-bordeaux.fr/~pthieull/LIA/webinars_NT.html), organized by YoungJu Choie (POSTECH), Bo-Hae Im (KAIST), Dohyeong Kim (Seoul National Univeristy), Chol Park (UNIST), Tuan Ngo Dac (CNRS - Université de Caen Normandie). For the Zoom link, contact Dohyeong Kim(dohyeongkim@snu.ac.kr).