Generating series of special divisors on arithmetic ball quotients

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 discuss some generalizations and applications of this result. In particular, we report on recent joint work with B. Howard, S. Kudla, M. Rapoport, and T. Yang, in which 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 in the sense of Arakelov geometry. If time permits, we address some applications to arithmetic theta lifts and the Colmez conjecture.