About the speaker:
Mikhail Kapranov is a professor at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, specializing in algebra, algebraic geometry, mathematical physics, and category theory. With Israel Gelfand and Andrei Zelevinsky, he co-authored the influential book Discriminants, Resultants, and Multidimensional Determinants. He previously held positions at Yale University, the University of Toronto, Northwestern University, Cornell University, and the Steklov Institute. He graduated from Lomonosov Moscow State University and received his PhD from the Steklov Institute under the supervision of Yuri Manin.
Abstract:
A classic result of Minkowski (1895) says that any finite collection of vectors summing to 0 can be realized as the weighted normals to the faces of a unique, up to translations, convex polytope. This may have a significance for scattering theory, if we think of the vectors as the momenta of the incoming and outgoing particles. A polyhedral subdivision of the polytope given by the Minkowski problem gives a "scattering diagram", i.e., a graph with edges labelled by momenta satisfying momentum conservation at each vertex. We can then interpret the 1959 paper of Landau that introduced Landau singularities, to deduce that a regular subdivision (admitting a strictly convex PL-function) produces a singularity of an appropriate Feynman integral corresponding to the dual graph of the subdivision. This gives an interesting class of "polyhedral" Landau singularities.
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