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Self organization by local interaction: good point sets on a sphere or on other manifolds

Hold Date
2017-02-24 12:00〜2017-02-24 13:00
Lecture Room S W1-C-504, West Zone 1, Ito campus, Kyushu University
Object person
Johann Brauchart (Institute of Analysis and Number Theory at Graz University of Technology, Graz, Austria)

The question of how to distribute many points evenly on the sphere occurs in a surprising number of problems in various fields of science and engineering ranging from physics over chemistry to geodesy and mathematics.  A classic example from physics is Thomson's problem of determining the minimal potential energy distribution of N electrons on the unit sphere that repel each other with a force given by Coulomb's law. A general principle to generate good point sets is to optimize w.r.t. a suitable criterion such as ``generalized energy'’. In my talk I will present results from my research, in particular, concerning Quasi-Monte Carlo numerical integration methods and discuss the concept of ``hyperuniformity'' in the compact setting.