Generating series of CM cycles and (Arithmetic) Fundamental Lemma over reals
Prof. Tonghai Yang
2025-06-19 14:30-15:30
MCM610
Speaker: Prof. Tonghai Yang (University of Wisconsin-Madison)
Time: 14:30-15:30 June 19, 2025 (Thursday)
Venue: MCM610
Title: Generating series of CM cycles and (Arithmetic) Fundamental Lemma over reals
Abstract: In this talk, we will describe a generating series or arithmetic CM cycles in unitary Shimura varies, which is expected to be modular. Next, we describe a possible `arithmetic relative trace formula’ with one side being the arithmetic intersection between our generating series and a known arithmetic theta series of arithmetic divisors, and the other side is a derivative of `theta integrals’ which is known to be modular. So the identity gives some evidence of the modularity conjecture. Finally proof of the conjectured identity is reduced to (arithmetic) fundamental lemma and transfers, a lot of which was known to Wei Zhang and others. We propose a fundamental lemma (and prove it too) and an arithmetic fundamental lemma at infinity. This is a preliminary joint work with A. Mihatsch and S. Sankaran.
