分野別セミナー

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.