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Explore the concept of K-hulls and K-strongly convex sets in Euclidean space through this 30-minute lecture. Delve into a general approach for analyzing the facial structure of K-strongly convex sets, drawing parallels to the established theory for polytopes. Examine the application of this theory to the case where A = Ξn represents a sample of n points uniformly distributed on a compact convex body K. Discover how the set of points x such that x+K contains the sample Ξn, when multiplied by n, converges in distribution to a zero cell of a specific Poisson hyperplane tessellation. Learn about the convergence in distribution of the f-vector of the K-hull of Ξn to a limiting random vector, as well as the convergence of all moments of the f-vector. This talk, presented by Ilya Molchanov at the Hausdorff Center for Mathematics, is based on joint work with Alexandr Marynych from Kiev.
