Speaker: Salim Tayou (Harvard)
Title: Mixed mock modularity of special divisors
Abstract: Since the work of Jacobi, Gauss, and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla, Millson, and Borcherds have proved that the generating series of special divisors on orthogonal 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 is a mixed mock modular form. More precisely, we find an explicit completion using theta series associated to the rays in the cone decomposition. The proof relies on intersection theory at the boundary of the Shimura variety. This recovers and refines recent results of Bruinier and Zemel. The result of this talk is joint work with Philip Engel and François Greer.
