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Séminaire du LJLL - 12 04 2019 14h00 : E. Saff
Edward Saff (Université Vanderbilt)
Discretizing manifolds with minimal energy
Résumé
Minimal discrete energy problems arise in a variety of scientific contexts, such as crystallography, nanotechnology, information theory, and viral morphology, to name but a few. Our goal is to analyze the structure of configurations generated by optimal (and near optimal) N-point configurations that minimize the Riesz s-energy over a bounded surface in Euclidean space. The Riesz s-energy potential is simply given by 1/r^s, where r denotes the distance between pairs of points, and is a generalization of the familiar Coulomb potential. We show how such potentials and their minimizing point configurations are ideal for use in sampling surfaces (and even generating a "near perfect" poppy-seed bagel). Connections to the recent breakthrough results by H. Cohn et al. on best-packing and universal optimality in 8 and 24 dimensions will be discussed.