Monday Analysis Seminar (2018/12/3) Discretizing Manifolds via Riesz Energy Minimization and Riesz polarization Maximization

2018-12-3 16:30 - 2018-12-3 18:00
Faculty of Science Building #3 Room 210
Nattapong Bosuwan (Mahidol University, Thailand)
The problem of determining $N$ points on a $d$-dimensional manifold that are in some sense uniformly distributed over its surface has applications to such diverse fields as crystallography, electrostatics, nano manufacture, viral morphology, molecular modeling, global positioning and others.

There also are a variety of mathematical needs for the discretization of manifolds such as statistical sampling, quadrature rules, starting points for Newtons method, computer-aided geometric design, interpolation schemes, and finite element tesselation. In my talk, we discuss the asymptotic behaviors (as $N \rightarrow \infty$) of minimum $N$-point Riesz $s$-energy configurations and maximum $N$-point Riesz $s$-polarization configurations when $s > 0.$ We show that for some certain numbers of s, our optimal configurations are `good points" for discretizing some subsets of the $d$-dimensional Euclidean space $\mathbb{R}^d$ in the uniformly distributed sense.

Monday Analysis Seminar