Abstract: In 80s, Gross and Zagier discovered and proved a deep and well-known formula between derivative of an L-function and the height of some ‘CM’ point on an elliptic curve--Gross-Zagier formula, which gives partial answer the Birch and Swinnerton-Dyer conjecture. In the process, they also proved a beautiful factorization formula for the difference of CM values of the j-function. In addition, they also gave a conjecture about the algebraicity of the CM values of higher Green functions.  In this talk, we will look at the these work in terms of  regularized theta lifting, and outline  a proof of their algebraicity conjecture.  This talk is based on joint work with collaborators, including J. Bruinier, S. Kudla, Yingkun Li, Dongxi Ye, Hongbo Yin, and Peng Yu among others.

Bio-Sketch: Tonghai Yang got his  PhD degree at University of Maryland and is currently a professor at University of Wisconsin-Madison. He is an AMS fellow. In addition, he has run a small charity (Hometown Education Foundation) since 2004 to help over 1300 poor students in rural China a year.