Order and disorder in energy minimization

Details Order and disorder in energy minimization Order and disorder in energy minimization

2010-03-16

arxiv.org/abs/1003.3053v1

Proceedings of the International Congress of Mathematicians, Hyderabad, August 19-27, 2010, Volume IV, pages 2416-2443

Mathematics

Metric Geometry

to appear in Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010

Scientific paper

10.1142/9789814324359_0152

How can we understand the origins of highly symmetrical objects? One way is
to characterize them as the solutions of natural optimization problems from
discrete geometry or physics. In this paper, we explore how to prove that
exceptional objects, such as regular polytopes or the E_8 root system, are
optimal solutions to packing and potential energy minimization problems.

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