Friday, March 25, 2016 (4:00 p.m. in Yost 306)

Title: The Surface Area Deviation of the Euclidean Ball and a Polytope

Student: Steven Hoehner

Advisor: Elisabeth Werner (Professor, Case Western Reserve University)

Committee Members: Harsh Mathur (CWRU Physics), Carsten Schuett (Christian-Albrechts-Universitaet zu Kiel), Wojbor Woyczynski (CWRU MAMS)

Abstract: The approximation of convex bodies by polytopes has numerous applications to many areas of mathematics and the mathematical sciences. There is extensive literature on this subject. Most of the known results deal with approximation by inscribed or circumscribed polytopes. However, much less is known in the case of generally positioned polytopes. The main point of this thesis is to address exactly that point: we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the surface area deviation. Part of this thesis will appear in “The surface area deviation of the Euclidean ball and a polytope” by S. Hoehner, C. Schuett, and E. Werner (Preprint, 2016). The main results are joint work with Dr. Carsten Schuett and Dr. Elisabeth Werner.