Bruhat-Tits buildings arise in the geometric representation theory of reductive groups. In recent years, the building associated to SL_d has proved to be a powerful combinatorial interface for the study of degenerations in algebraic and arithmetic geometry. In this talk, we will discuss some these developments, including the theory of Mustafin degenerations and their applications to the open problem of a p-adic Narasimhan-Seshadri theorem. If time permits, we will also study how the combinatorics of convex sets in Bruhat-Tits buildings relate to the theory of sub-ind-schemes of the affine Grassmannian of SL_d that parametrise invariant lattices of matrix algebras. This talk is based on joint work with Yassine El-Maazouz, Binglin Li, Gabriele Nebe, Mima Stanojkovski, Bernd Sturmfels and Annette Werner.
Combinatorics of Bruhat-Tits buildings and degenerations
02.05.2023 13:15 - 14:44
Organiser:
H. Grobner, A. Mellit
Location: