Modularity and Bruhat--Tits stratification
It is well-known that the theta series of a positive definite quadratic lattice is a modular form. In this talk, I will present new modularity results for arithmetic theta series of some “parahoric" hermitian lattices of sign (n-1,1), which live on unitary Shimura varieties. One key step is to understand a local analog of the story, which happens on unitary Rapoport-Zink spaces. I will explain the use of Bruhat-Tits stratification studied by S. Cho in the computation.