Szego Seminar: Bounds on the Volumes of Difference Bodies

Abstract: I will explore some fundamental results in convex geometry, a field first laid out by Brunn and Minkowski at the end of the 19th century. We will consider their famous lower bound on the volume of the sum of convex bodies and ask to what degree this can be generalized, as well as – as Blaschke did – whether we can obtain a corresponding upper bound. The latter question will lead us towards the fruitful Rogers-Shephard inequality for difference bodies.