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Modularity and Bruhat--Tits stratification

Algebra and Number Theory Seminar

Modularity and Bruhat--Tits stratification
Series: Algebra and Number Theory Seminar
Location: Zoom Meeting
Presenter: Zhiyu Zhang, MIT

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.