Speaker:  Roy Zhao (University of California Berkeley)

Title: Heights on quaternionic Shimura varieties

Abstract:  We give an explicit formula for the height of a special point on a quaternionic Shimura variety in terms of Faltings heights of CM abelian varieties. This is a generalization of the work of Yuan and Zhang on proving the averaged Colmez conjecture. We also show an application of this formula to the Andre-Oort conjecture, which was recently proven by Pila, Shankar, and Tsimerman.