Algebraicity of higher Green functions at CM points

Contact: Pieter Moree (moree@mpim...)

By the classical theory of complex multiplication, the modular j-function takes algebraic values at CM points.
It is an interesting question to ask about the algebraic nature of other types of automorphic functions at CM points.
For the automorphic Green function at integral parameters, Gross and Zagier conjectured in the 1980s that their values at
CM points are essentially logarithms of algebraic numbers. In this talk, we will discuss recent progress toward this conjecture and its generalization to the setting of orthogonal Shimura varieties. This is partly joint with Jan Bruinier and Tonghai Yang.