Modularity of higher theta series

Modularity of theta functions is an important cornerstone in the theory of automorphic forms and L-functions. A few years ago, joint work of myself with Zhiwei Yun and Wei Zhang constructed objects called higher theta functions, and conjectured their modularity. We recently completed the proof of this conjecture. So far this sounds like an abstract for a number theory talk, but the proof involves a crucial use of motivic homotopy theory, and I will highlight that. Specifically, motivic homotopy theory enters through a formalism that we call the “sheaf-cycle correspondence”, an enhancement of Grothendieck’s sheaf-function correspondence.

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