Towards Topological Jacobi Forms

Tilman Bauer, KTH Royal Institute of Technology, Stockholm

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Jacobi forms are a two-variable generalization of modular forms, behaving like a modular form in the first variable and like an elliptic function in the other. They incorporate a number of interesting objects from arithmetic, such as theta series and Siegel modular forms. Using equivariant topological modular forms, building on ideas by Lurie and recent work by Gepner and Meier, I will construct a periodic ring spectrum TJF of topological Jacobi forms and give a relatively explicit computation of its homotopy groups. The question of the existence of a connective version of topological Jacobi forms is much harder and more interesting from an arithmetic point of view. I will present a feasible candidate for “weak” connective topological Jacobi forms. 

This is joint work with Lennart Meier.