Tony Feng (May 20, 2022): Enumerative arithmetic geometry and automorphic forms
Channel: Algebraic Geometry at Stanford
Date: 2022-05-21

The problem of counting vectors with given length in a lattice turns out to have much more structure than initially expected, and is connected with the theory of so-called automorphic forms. A geometric analogue of this problem is to count global sections of vector bundles on a curve over a finite field. The generating functions for such counts are special automorphic forms called theta series. In joint work with Zhiwei Yun and Wei Zhang, we find a family of generalizations of such counting problems in the enumerative geometry of arithmetic moduli spaces, which lead to generating functions that we call higher theta series. I will explain theorems and conjectures around these higher theta series.