Joint IAS/Princeton University Number Theory Seminar

I will start by explaining Quillen's notion of a superconnection, and then will use it to define some natural differential forms on period domains parametrizing Hodge structures. For hermitian symmetric domains, we will show that this construction recovers the forms introduced by Kudla and Millson. We will discuss the properties of these forms and how they allow to generalize results on special cycles in Shimura varieties to arithmetic quotients of period domains.