3:00–4:00 pm
Eckhart Hall 5734 S University Ave, Room 202
Period Integrals of Algebraic Varieties
Abstract:
A period integral of a complex algebraic variety is the integral of an algebraic differential form along a topological cycle. While such integrals are transcendental in nature, they have had pervasive importance in algebraic and arithmetic geometry going back to the foundational work of Abel and Jacobi. The functions one obtains from taking period integrals in families of algebraic varieties moreover recur in many areas of mathematics. In this talk I will first survey how algebraic information can be extracted from period integrals, as well as their connection to various conjectural frameworks. I will then discuss recent progress on understanding the algebraic properties of period integrals in families and recent applications to Hodge theory, algebraic geometry, arithmetic geometry, and logic.
