Arithmetic of Shimura Varieties
The theory of Shimura varieties lies at the intersection of number theory, algebraic geometry, and the theory of automorphic representations. It plays a key role in the Langlands program as a source of Galois representations attached to automorphic forms. More recently, S. Kudla has conjectured a relationship between the Arakelov intersection theory of arithmetic cycles on integral models of Shimura varieties and the Fourier expansions of automorphic forms.
Amir-Khosravi's research fits within this general framework of investigating the relationship between the arithmetic geometry of Shimura varieties on the one hand, and the number theoretic information encoded in analytic objects on the other. More specifically, Amir-Khosravi is interested in extensions of these ideas to analogues of Shimura varieties arising from groups with compact factors.