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SUMMARY:Workshop / Seminar:Combinatorics Seminar -- Curves\, degenerations\, and Hirota Varieties
DESCRIPTION:The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems\, algebraic geometry\, and algebraic combinatorics. 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 and has a nice combinatorial description based on the Delaunay polytope. 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 talk is based on joint work with Daniele Agostini\, Claudia Fevola\, and Bernd Sturmfels.
UID:110147-21824403@events.umich.edu
URL:https://events.umich.edu/event/110147
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall
CONTACT:
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