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Logarithmic Energy of Points on S^2

Stefan Steinerberger (University of Washington)
Monday, January 25, 2021 - 2:30pm to 3:30pm
Online via Zoom. Contact Zhen-Qing Chen for details.
I will discuss a very old problem that has an elementary formulation: how do you place n points on the standard sphere embedded in three dimensions in such a way that the product of all pairwise distances is as large as possible -- and how large does that product have to be? The idea is that this forces the points to be regularly spread out -- there are many known constructions but few rigorous results. The problem also arises in a different framework in mathematical physics (where it is related to the `crystallization conjecture').  I will give an introduction to all these things and discuss a recent new perspective that improves the known results on the size of the product -- the heat kernel on S^2 plays an important role.
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