# Voronoi cells of varieties

Seminar

Speaker

Madeleine Weinstein (University of California, Berkeley)

Date

05/06/2019 - 11:00 - 10:00Add to Calendar

`2019-06-05 10:00:00``2019-06-05 11:00:00``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.``Third floor seminar room (room 201, building 216)``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room (room 201, building 216)

Abstract

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.

Last Updated Date : 22/05/2019