Foundations of Computational Mathematics, Budapest 2011: The State of the Art in Smale's 7th Problem

1. Points which maximise the product of their mutual distances (called elliptic Fekete points after [14]). 2. Points which minimise the sum of the inverse of their mutual distances (Thomson’s problem), and more generally which minimise some sum of potentials which depend on the mutual distances (like Riesz potentials). 3. Points which maximise the least distance between any pair. 4. Points which are the center of the optimal packing problem, that is, the problem of finding the smallest radius of a sphere such that one can place on its surface k non–overlapping circles of a given radius.

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