KP Solitons from Tropical Limits

In this talk, we study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes all tau functions arising from such a sum. After introducing solitons solutions, we compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces. This is joint work with Daniele Agostini, Yelena Mandelshtam and Bernd Sturmfels.