Voronoi cells of varieties

יום ד', 05/06/2019 - 10:00
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Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these Voronoi cells. Using intersection theory, we give a formula for the degrees of the algebraic boundaries of Voronoi cells of curves and surfaces. We discuss an application to low-rank matrix approximation. This is joint work with Diego Cifuentes, Kristian Ranestad, and Bernd Sturmfels.