数学科学研究所
Insitute of Mathematical Science

Seminar: Isodiametry, variance, and regular simplices from particle interactions

Seminar| Institute of Mathematical Sciences

Time14:00-15:00, Oct 15, Thuesday

LocationRoom S408, IMS


Speaker: Tongseok Lim, IMS


Abstract: We study the geometry of minimizers for the interaction energy functional. When the interaction potential is mildly repulsive, it is known to be hard to characterize those minimizers due to the fact that they break the rotational symmetry, suggesting that the problem is unlikely to be resolved by the usual convexity or symmetrization techniques from the calculus of variations. We prove that, if the repulsion is mild and the attraction is sufficiently strong, the minimizer is unique up to rotation and exhibits a remarkable simplex-shape rigid structure. As the first crucial step we consider the maximum variance problem of probability measures under the constraint of bounded diameter, whose answer in one dimension was given by Popoviciu in 1935.



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