A plausible strategy of proving the global geometric Langlands conjecture

2022.08.16（星期），09:00-10:00

2022.08.19（星期），09:00-10:00

点：Zoom会议：466-356-2952密码：mcm1234

要：In the previous colloquium talk, I introduced the (categorical unramified) global Geometric Langlands conjecture. In these two talks, I will explain a plausible strategy or project" of proving this conjecture, which is due to many people including Beilinson, Drinfeld, Laumon, Arikin, Gaitsgory, etc.. After that, I will talk about my works in this strategy. In particular, I will show the category of automorphic sheaves for G can be glued from categories of tempered automorphic sheaves for all the Levi subgroups of G. This will allow us to construct a functor from the automorphic side to the spectral side, and reduce the conjecture to its tempered version. Then the only missing point in the mentioned strategy is to show the Whittaker coefficient functor is fully faithful on tempered automorphic sheaves (which is unknown except for GL_n or PGL_n). I will only discuss this last point if time allows.