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Minimal Discrete Energy and Maximal Polarization

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This talk concerns minimal energy point configurations as well as maximal polarization (Chebyshev) point configurations on manifolds, which are optimization problems that are asymptotically related to best-packing and best-covering. In particular, we discuss how to generate N points on a d-dimensional manifold that have the desirable local properties of well-separation and optimal order covering radius, while asymptotically having a uniform distribution (as N grows large). Even for certain small numbers of points like N=5, optimal arrangements with regard to energy and polarization can be challenging problems. Connections to the very recent major breakthrough on best-packing results in R8 and R24 will also be described.

This talk is part of the Applied and Computational Analysis series.

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