II. The P-adic and Mod p Langlands Program for GL2
Time: 2017-11-20
Published By: He Liu
Speaker(s): Yongquan Hu
Time: 10:00-12:00 November 29, 2017
Venue: Room 78201, Jingchunyuan 78, BICMR
At present, the mod p and p-adic Langlands correspondence is only well understood for the group GL2(Qp). One of the main difficulties in generalizing it to other groups is that very little is known about representation theory on automorphic side (except of GL2(Qp)). However, the recent work of Caraiani-Emerton-Gee-Geraghty-Paskunas-Shin suggests that one should seek such a correspondence in geometry, especially via the patching of automorphic forms.
My talk will mainly focus on the case of GL2. In my first (introductory) talk, I will tell the story of GL2(Qp), explaining the work of Breuil, Colmez, Paskunas, etc. In the second talk, I will discuss some folklore conjectures on the expected form of such a correspondence for GL2(F) (where F is an unramified extension of Qp) and explain some recent progress obtained recently by myself and Haoran Wang.
