Presented by:
Richard Schwartz
Date:
Friday 7th April 2017 - 16:00 to 17:00
Venue:
INI Seminar Room 1
Abstract:
Thomson's problem, which in a sense goes back to J.J.
Thomson's
1904 paper, asks how N points will arrange themselves on
the sphere (or the circle, or some other space) so as to minimize their total
electrostatic potential. Mathematicians
and physicists have also considered this problem with respect to other
potentials, such as power law potentials.
For special values of N, and the sphere of the appropriate dimension,
there are spectacular answers which say that the potential minimizers are
highly symmetric objects, such as the regular icosahedron or the E8 cell. In spite of this work, very little has been
proved about 5 points on the 2-sphere.
In my talk I will explain my computer assisted but
rigorous proof that there is a phase transition constant S=15.048... such that
the triangular bi-pyramid is the minimizer with respect to a power-law
potential if and only if the exponent is less or equal to S. (This constant was conjectured to exist in
1977 by
Melnyk-Knop-Smith.) The talk will have some colorful
computer demos.
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