Single-valued Hodge, p-adic^2, and tropical integration

Abstract: I'll discuss 4 different types of single-valued integration on algebraic varieties -- one in the complex setting, one in the tropical setting, and two in the p-adic setting, and the relationships between them. In particular, I'll explain how to compute Vologodsky's "single-valued" iterated integrals on curves of bad reduction in terms of Berkovich integrals, and how to give a single-valued integration theory on complex varieties. Time permitting, I'll explain some potential arithmetic applications. This is a report on joint work in progress with Sasha Shmakov (in the complex setting) and Eric Katz (in the p-adic setting).

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar