Title: CM Values Associated to Special Cycles on Shimura Varieties

Abstract: Kudla has a program inspired by theta functions and the work of Hirzebruch and Zagier in 1976. Its main goal is to prove that the generating functions arisen from certain arithmetic cycles on orthogonal Shimura varieties are actually modular. As part of the program, Kudla also conjectured a formula that relates the height pairing of the arithmetic cycles with some proper cycles with the central derivative of some Siegel Eisenstein series. The infinite part of the height turns out to be CM values of special functions on Shimura varieties. In this talk, I will present the background of the problem and known results on CM values. If time permits, I will further talk about my work on its applications to Siegel 3-fold case.=