Mathematical sciences seminar: Minimal Energy Point Sets and Equilibrium Measures on Manifolds



Professor Xingping Sun
Missouri State University, USA


The problem of distributing a large number of points uniformly on the surface of a manifold (e.g. the surface of a sphere or a doughnut) started out as a pure mathematical curiosity. Over the years, it has attracted the attention of biologists, chemists, electrical engineers, and physicists working in such diverse areas as viral morphology, molecular structure, global positioning system, compressed sensing, and electrostatics. The discovery of stable carbon-60 molecules with atoms arranged in a soccer ball pattern showcases an elegant mathematical structure, which has motivated scientists to hypothesize molecular structures of super-light and super-strong material. In electrostatics, locating identical point charges on sphere so that they are in equilibrium with respect to the Coulomb potential law is both challenging and fascinating. In digital communication, signals are often transmitted in packets. The process resembles sphere packing. The underlying mathematical principles are rich and broad, ranging from abstract algebra to potential analysis and statistics. In this talk, we will take a brief inspection of these mathematical tools and discuss their applications.

Speaker's Bio

Professor Xingping Sun is a full professors in Missouri State University. He obtained his PhD in Mathematics from University at Austinof Texas and is a well known expert in approximation theory, radial basis functions and numerical analysis. He was the deputy dean of School of Natural and Applied Science in Missouri State University.