Extensions of the Gross-Zagier formula

Joint IAS/Princeton University Number Theory Seminar
Topic:Extensions of the Gross-Zagier formula
Speaker:Kartik Prasanna
Affiliation:University of Michigan
Date:Thursday, April 23
Time/Room:4:30pm - 5:30pm/S-101
Video Link:http://video.ias.edu/puias/2015/0423-KartikPrasanna

I will first discuss the general conjectural picture relating algebraic cycles to L-functions and some extensions of the Gross-Zagier formula involving $p$-adic L-functions. This leads naturally to the question of constructing algebraic cycles corresponding to the vanishing of certain Rankin-Selberg L-functions at the center of symmetry. Finally, I will outline some new constructions of such cycles, based on work in progress with A. Ichino.