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Talk

Curves, degenerations, and Hirota varieties

  • Yelena Mandelshtam (University of California, Berkeley)
E1 05 (Leibniz-Saal)

Abstract

The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases, Riemann's theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This is based on joint work with Daniele Agostini, Claudia Fevola, and Bernd Sturmfels.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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