Ramification & singularity in arithmetic (T)GGP and Kudla program
Prof. Zhiyu Zhang
2025-06-20 11:00-12:00
MCM110
Speaker: Prof. Zhiyu Zhang (Stanford University)
Time: 11:00-12:00 June 20, 2025 (Friday)
Venue: MCM110
Title: Ramification & singularity in arithmetic (T)GGP and Kudla program
Abstract: Studying automorphic forms involves intricate (arithmetic) harmonic analysis questions. The finally proved FL and still-unsolved twisted FL have underpinned many breakthroughs in Langlands program. Similarly, recent proofs of AFL and Kudla-Rapoport conjecture both lead to some high dimensional (p-adic) Gross-Zagier formulas, after many years. Related advances are also anticipated for twisted AFL. But these advances rest on local-global assumptions which exclude Q. How to prove complete height formulas? To fully understand arithmetic geometry with harmonic analysis, there are new features and difficulties, especially ramification and singularity (e.g. Atiyah flops). I will discuss related conjectures and results of myself, Cho, He, Li, Luo, Mihatsch, Rapoport, Shi, Yang, Zhu, Zhang et al. To explain general patterns, I will focus on a global double induction method, blow ups, ramified global modularity and local duality conjecture of special divisors obtained in my PHD thesis, very recent advances, and analytic formulations on Whittaker expansion and orbital integrals for more test functions.
