Energy and Polarization Problems
in Mathematics and Statistics, part I

The workshop will bring together researchers studying problems related to the equidistribution of point configurations, namely energy and polarization, which can be viewed as generalizations of the basic properties of separation and covering.

Energy minimization problems, both discrete and continuous, arise naturally in many areas of mathematics and science: discrete geometry, mathematical physics, approximation theory, flocking behavior, statistical mechanics, coding theory, etc. Polarization problems (also known as Chebyshev constants) are related max-min problems for potentials.

A number of interesting and unexpected phenomena in both energy minimization and polarization have been studied recently: universal optimality, discretization of minimizers, condensation and phase transitions, to name just a few. It turns out that the behavior of such minimizers is much more subtle than one would naturally expect.

The aim of this mini-workshop is to bring together a multifaceted group of researchers working in potential theory, approximation, gradient flows, point configurations, lattices, and partial differential equations who have recently made important contributions to energy minimization and polarization problems to report on their work and to collaborate in trying to resolve some of the fundamental questions in the field.