Pre-talk for graduate students: 2pm "Green's functions over modular curves"

Main talk: 3-3:50pm

In this talk I will introduce my thesis work in progress to prove a Gross-Zagier formula for CM cycles over Shimura curves. The formula connects the global height pairing of special cycles in Kuga varieties over Shimura curves with the derivatives of the L-functions associated to weight-2k modular forms. As a key original ingredient of the proof, I will introduce some harmonic analysis on local systems over graphs, including an explicit construction of Green's function, which we apply to compute some local intersection numbers. Speaker(s): Boya Wen (Princeton University)