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Session S31 - Mathematical-Physical Aspects of Toric and Tropical Geometry

Monday, July 12, 14:45 ~ 15:45 UTC-3

KP Solitons from Tropical Limits

Yelena Mandelshtam

UC Berkeley, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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. We compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces and we present an algorithm that finds a soliton solution from a rational nodal curve.

Joint work with Daniele Agostini (MPI MiS Leipzig), Claudia Fevola (MPI MiS Leipzig) and Bernd Sturmfels (MPI MiS Leipzig and UC Berkeley).

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