Modularity of special cycles in orthogonal and unitary Shimura varieties

Since the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms. In this talk, I will explain an extension of these results to toroidal compactifications where we prove that the generating series of divisors is a mixed mock modular form. This recovers and refines earlier results of Bruinier and Zemel. The results of this talk are joint work with Philip Engel and François Greer.

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For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html