Yelena Mandelshtam, IAS Princeton
The Kadomtsev-Petviashvili (KP) equation is a partial differential equation whose study yields fascinating connections between integrable systems, algebraic geometry, and combinatorics. In this talk I will describe some of the various approaches to connecting KP solutions to algebraic objects such as algebraic curves (due to Krichever) and the positive Grassmannian (due to Sato and later Kodama-Williams). I will then discuss recent and ongoing work to build bridges between these approaches.