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Yelena Mandelshtam (University of California, Berkeley): Hirota varieties

Ort: MPI für Mathematik in den Naturwissenschaften Leipzig, Inselstr. 22, E1 05 (Leibniz-Saal)

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 study the Hirota variety associated to familiar Delaunay polytopes, in particular characterizing it for the g-cube. If time permits, we will also compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces and present an algorithm that finds a soliton solution from a rational nodal curve.

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Beginn: July 23, 2021, 10 a.m.

Ende: July 23, 2021, 11 a.m.