# Faltings' Height of CM Cycles and Derivative of L-Functions

 JOINT IAS/PU NUMBER THEORY SEMINAR Topic: Faltings' Height of CM Cycles and Derivative of L-Functions Speaker: Tong Hai Yang Affiliation: The University of Wisconsin at Madison Date: Thursday, November 13 Time/Room: 4:30pm - 5:30pm/Fine Hall -- 214

In this talk, we first describe a systematic way to construct automorphic Green functions' for Kudla's special divisors on a Shimura variety of orthogonal type $(n, 2)$. We then give an explicit formula for their values at a CM cycle. This formula suggests a direct relation between the Faltings' height of these CM cycles with the central derivative of some Rankin-Selberg $L$-function. As an application, we also give an analytic proof' of the Gross-Zagier formula without computing the local intersection numbers at finite primes. This is a joint work with Jan Bruinier.