Special Year Seminar I

The Kadomtsev-Petviashvili (KP) Equation has deep connections to algebraic curves, with solutions constructed from Riemann theta functions in the style of Krichever. As a curve undergoes tropical degeneration, its theta function simplifies to a finite sum of exponentials supported on a combinatorial structure closely related to Voronoi cells. The resulting solutions are soliton solutions, which have a well-known connection to the positive Grassmannian (following e.g. Kodama and Williams). In this talk, I’ll discuss ongoing work with Simonetta Abenda, Türkü Özlüm Çelik, and Claudia Fevola, exploring how the combinatorial structure of these soliton solutions reflects the geometry of their underlying tropical curves.