Number Theory Seminar

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 by Fargues-Scholze, and also provides a way to study the cohomology of Shimura varieties. In this talk, we first give a brief overview on this object, then present our recent result towards understanding its geometry in terms of a natural stratification called the Newton stratification.