Colloquium Mathematics - Hadleigh Frost, IAS Princeton

Title: A Gentle Introduction to Positive Geometry and Positive Physics

Abstract:

Positive geometry refers to the study of a broad class of real, positive spaces—polytopes, Grassmannians, moduli spaces—with rich boundary structures. Such spaces are central to some recent developments in theoretical physics. In this talk, I will introduce some of these developments and explain how Teichmüller spaces fit into this framework in a surprisingly simple way. The "positive point of view" leads to new results about gauge and string theory, and interesting new formulas for Weil-Petterson volumes and theta functions. I will highlight some open questions/mysteries about connections of this work to integrable systems.