Enumerative arithmetic geometry and automorphic forms

Abstract: 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.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Tony Feng’s talk is taking place not in zoom-chat, but at tinyurl.com/2022-05-20-tf (and will be deleted after ~3-7 days).

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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