Time: 7th August (Wednesday) 10:00 - 11:00
Speaker: Prof. Tongseok Lim(Institute of Mathematical Sciences, ShanghaiTech University)
Place: #701, Natural Science Building, Hanyang University
Title : On the optimal formation of interacting particles -- maximal variance problem and its generalization
We study the geometry of minimizers of an interaction energy, which is a Lyapunov functional for the aggregation equation. 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 yield to 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 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.
In this workshop, we discuss recent progress in hyperbolic partial differential equations and kinetic equations. The aim of this workshop is to promote communications and to encourage collaborations between young researchers.
Time : May 3rd (Friday) 09:30 -- 17:30
Place : Natural Sciences Bldg #702
Take off at Hanyang Univ. subway station (exit #2) and climb the stairway. The natural science building is located at the top of the hill.
If you bring your car, please park at 한양종합기술연구원(HIT) or 행원파크.("P" symbol in the map)