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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.
David Mount is a professor in the Department of Computer Science at the University of Maryland with a joint appointment in the University's Institute for Advanced Computer Studies (UMIACS). He received his Ph.D. from Purdue University in Computer Science in 1983, and started at the University of Maryland in 1984. In 2001 he was a visiting professor at the Hong Kong University of Science and Technology.
He has written over 170 research publications on algorithms for geometric problems, particularly problems with applications in image processing, pattern recognition, information retrieval, and computer graphics. He currently serves on the editorial boards of Computational Geometry: Theory and Applications and the International Journal of Computational Geometry & Applications. He has served on the editorial boards of ACM Transactions on Spatial Algorithms and Systems, ACM Trans. on Mathematical Software, and Pattern Recognition.