[SNU Number Theory Seminar 2022-08-08] Geometry of the $B_{dR}^+$-Grassmannian

The classical affine Grassmannian plays a pivotal role in geometric representation theory and the geometric Langlands program. Its p-adic analogue, known as the $B_{dR}^+$-Grassmannian, similarly plays a crucial role in the geometrization of the local Langlands correspondence, and also provides a way to study the cohomology of Shimura varieties. In this talk, we give a brief overview on this object and present a recent progress towards understanding its geometry.