p-adic higher Green's functionsArithmetic Geometry and Representation Theory Research Seminar

by Hazem Hassan (Heidelberg University)

Tuesday Nov 10, 2026, 3:05 PM → 5:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Higher Green’s functions are higher weight analogues of differences of singular moduli. They encode local contributions to height pairings of Heegner cycles and recent work of Brown and Fonseca interprets them as periods of mixed motives. 

In this talk, I will briefly introduce higher Green’s functions and discuss their p-adic analogues in two examples. The first (joint work with Paolo Bordignon), identifies p-adic higher Green’s functions with local contributions to Nekovář's p-adic height pairing of Heegner cycles on Shimura curves. The second (from my thesis), relates p-adic higher Green’s functions to periods of higher weight rigid meromorphic cocyles. These periods should be connected to p-adic heights of the conjectured Stark—Heegner cycles (higher weight analogues of Stark—Heegner points).