Algebra and Geometry Seminar

The geometric Satake equivalence establishes a link between two categories: the category of perverse sheaves on the Hecke stack and the category of finitely generated representations of the Langlands dual group. It has many important applications in the study of the geometric Langlands program and number theory. In this talk, the speaker will discuss the integral coefficient geometric Satake equivalence in mixed characteristic case. This generalizes the previous results of Lusztig, Ginzburg, Mirkovic-Vilonen, and Zhu. Time permitting, the speaker will discuss the application of this result in constructing a Jacquet-Langlands transfer.