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Optimal Distribution of Points on Spheres

By Vivian Healey

September 28, 2011

#### Abstract

Given n points on S^m and a potential energy function that causes them to repel each other, which configurations of the points minimize the energy? I will present some tools for attacking this problem, talk a bit about polytopes (n dimensional polyhedra), and then present the answer given by Cohn and Kumar in their 2007 paper "Universally Optimal Distribution of Points on Spheres."