Speaker: Jan Bruinier (Darmstadt)

Date: January 12, 2017

Title: Generating series of special divisors on arithmetic ball quotients

Abstract: We report on joint work with B. Howard, S. Kudla, M. Rapoport, and T. Yang. A celebrated result of Hirzebruch and Zagier states that the generating series of Hirzebruch-Zagier divisors on a Hilbert modular surface is an elliptic modular form with values in the cohomology. We prove an analogue for special divisors on integral models of ball quotients. In this setting the generating series takes values in an arithmetic Chow group. If time permits, we discuss some applications to arithmetic theta lifts and the Colmez conjecture.