Roever Mini-Symposium: "Thrifty Approximations of Convex Bodies by Polytopes"
Alexander Barvinok, University of Michigan
Abstract: I’ll discuss how well an arbitrary (higher-dimensional) convex body can be approximated by a polytope with a given number of vertices. The case of a particular interest is when the body is centrally symmetric and the quality of approximation is measured with respect to the Banach-Mazur distance (assuming that the body contains the polytope, how much the polytope should be dilated to contain the body?). We are interested in coarse (few vertices), fine (many vertices) and intermediate (everything in between) approximations. Despite recent progress, the case of coarse approximations remains somewhat mysterious (more so, if the symmetry condition is dropped).
Host: Todd Kuffner
Tea @ 3:45pm in Cupples I, room 200