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UID:60c96b32fcf024254b175f5a8acb3b5a
CATEGORIES:Special Colloquium
CREATED:20221028T110543
SUMMARY:Lewis lectures III - Five point energy minimization
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: In this talk I will quickly survey some results about energy mini
 mizing configurations of points on the sphere, and then explain how to use 
 the computer to solve Thomson's 5-electron problem by showing that the tria
 ngular bi-pyramid is the configuration of electrons on the sphere which min
 imizes the electrostatic potential. (Yes.) I'll also explain how to use the
  computer to rigorously establish the more general result that the triangul
 ar bi-pyramid is the energy minimizer with respect to all power law potenti
 als up to about exponent 15.05, at which point the answer changes to a fami
 ly of pyramids with square base.  The team of Melnyk, Knopf, and Smith disc
 overed this phase transition in the late 1970s.   As in the other talks, I'
 ll demonstrate the software I wrote to help solve these problems.  I'll als
 o discuss the advantages and shortcomings of a computer-assisted approach l
 ike this.  <br />
CONTACT:Richard Schwartz - Brown University
DTSTAMP:20260828T093749
DTSTART;TZID=America/New_York:20221110T140000
DTEND;TZID=America/New_York:20221110T150000
SEQUENCE:0
TRANSP:OPAQUE
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