Seminar in Real and Complex Geometry

Thursday, June 6, 2019, 17:00-18:00, Schreiber building, room 209

Madeleine Weinstein (Berkeley)

Voronoi Cells of Varieties


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.