Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Thursday, Jan 6, 2022
Time: 4:00PM
Location: JWB 335
Spencer Leslie
Duke University
Title |
Periods, L-values, and stabilization |
Abstract |
The study of period integrals of automorphic forms originates in deep questions about cohomology of locally symmetric spaces. A particularly powerful tool for studying periods is a relative trace formula, which often allows one to relate these integrals to other arithmetic objects like L-functions. In this talk, I review some of this story, discuss the modern approach to relating period integrals to L-functions, and introduce a new case of interest: unitary Friedberg-Jacquet periods. These periods are conjecturally related to central values of certain L-functions and are thus connected to deep conjectures on the cohomology of the associated locally symmetric spaces. To prove these conjectural relationships, a promising approach is to use a relative trace formula. However, new problems (known as instability) arise in this setting that must be overcome if one is to prove this relation. I will discuss my work on a theory of endoscopy and stable relative trace formulae to overcome these problems. This gives a refinement of the relative trace formula amenable to proving this conjecture. |
Number Theory
Algebraic Geometry