Apparaît dans la collection : Cycles on moduli spaces / Cycles sur les espaces de modules

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, when these cycles are corrected by certain boundary cycles, the resulting generating series is still a modular form in the case of divisors in orthogonal Shimura varieties and cycles of codimension up to the middle degree in the cohomology of unitary Shimura varieties, thereby partially answering a conjecture of Kudla.