Mathematical Sciences: Stability Properties of Geometric Inequalities

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The principal investigator will study the stability of geometric inequalities, a branch of integral and convex geometry. In particular he will investigate the stability of symmetrization procedures and analytic inequalities, and duals of Brunn- Minkowski theory. These studies will require the understanding of ellipsoids and cap bodies. This project involves mathematics at the overlap between geometry and probability theory. A typical problem might be to find the probability that a random line in two dimensions intersects a given square or other convex polygon. Solutions to these problems have a variety of applications in Operations Research and other applied areas. This investigator will continue his studies of similar problems in higher dimension.