Best and random approximation of convex bodies by polytopes

School of Mathematics Colloquium
Thursday, October 15, 2015 - 11:00am
1 hour (actually 50 minutes)
Skiles 006
Case Western Reserve University
How well can a convex body be approximated by a polytope? This is a fundamental question in convex geometry, also in view of applications in many other areas of mathematics and related fields. It often involves side conditions like a prescribed number of vertices, or, more generally, k-dimensional faces and a requirement that the body contains the polytope or vice versa. Accuracy of approximation is often measured in the symmetric difference  metric, but other metrics can and have been considered. We will present several results about these issues, mostly related to approximation by “random polytopes”.