Title: On stable transfer operators and functorial transfer kernels Abstract: Langlands introduced stable transfer operators as a fundamental part of his proposal of Beyond Endoscopy. They are intended to be used in comparisons of his proposed refinements of stable trace formulas, in an analogous role to that of endoscopic transfer operators in the theory of […]

Title: Local-global compatibility over function fields Abstract: We show that V. Lafforgue's global Langlands correspondence is compatible with Fargues–Scholze's semisimplified local Langlands correspondence. As a result, we canonically lift Fargues–Scholze's construction to a non-semisimplified local Langlands correspondence for fields of characteristic ≥ 5. We also deduce that Fargues–Scholze's construction agrees with that of Genestier–Lafforgue, answering a question of Fargues–Scholze, Hansen, […]

Title: Harris-Venkatesh plus Stark Abstract: The class number formula describes the behavior of the Dedekind zeta function at s=0 and s=1. The Stark and Gross conjectures extend the class number formula, describing the behavior of Artin L-functions and p-adic L-functions at s=0 and s=1 in terms of units and class numbers. The Harris-Venkatesh conjecture describes […]