Approximating Convex Bodies and Applications
Also on zoom:https://umd.zoom.us/j/96718034173?pwd=clNJRks5SzNUcGVxYmxkcVJGNDB4dz09 A recent series of results has established the central role that convex approximation plays in solving a number of computational problems in multidimensional real Euclidean space. These include applications such as computing the diameter of a point set, Euclidean minimum spanning trees, bichromatic closest pairs, width kernels, nearest neighbor searching, and lattice-based cryptography. In this talk, I will present recent results on efficient coverings and approximations of convex bodies. This is achieved through a combination of methods, both new and classical, including Delone sets in the Hilbert metric, Macbeath regions, and John ellipsoids. We will explore the development of these methods and discuss how they can be applied to various geometric optimization problems.