Martin Raum (Goteborg): The geometric unitary Kudla Conjecture

Kudla and Millson proved that the generating series of cohomology classes associated with special cycles on orthogonal and unitary Shimura varieties is modular. This yields Siegel modular forms and Hermitian modular forms. In later work, Kudla conjectured that the analogous generating series of cycles in the Chow group is modular, too. The orthogonal case of the conjecture was established more than 10 years ago. We resolve the conjecture in the unitary case. In this talk, we explain in particular the role of automatic convergence results in the theory: how they arise and what techniques we currently have to prove them.

Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).