Mathematikgebäude, Hörsaal E28

Minimal discrete energy problems arise in a variety of scientific contexts – such as crystallography, nanotechnology, information theory, and viral morphology, to name but a few. Our goal is to analyze the structure of configurations generated by optimal (and near optimal)-point configurations that minimize the Riesz s-energy over a sphere in Euclidean space R^d and, more generally, over a bounded manifold. The Riesz s-energy potential, which is a generalization of the Coulomb potential, is simply given by 1/r^s, where r denotes the distance between pairs of points. We show how such potentials for s>d and their minimizing point configurations are ideal for use in sampling surfaces.
Connections to the breakthrough results by Field's medalist M. Viazovska and her collaborators on best-packing and universal optimality in 8 and 24 dimensions will be discussed. Finally we analyze the minimization of a 'k-nearest neighbor' truncated version of Riesz energy that reduces the order N^2 computation for energy minimization to order N log N, while preserving global and local properties.

Mit dem Kolloquium feiern wir den 90. Geburtstag von Professor em. Dr. Manfred Reimer

Wissenschaftlicher Vortrag:
Prof. Dr. Edward B. Saff
Vanderbilt University, USA
Sampling with Minimal Energy: A talk in honor of Manfred Reimer's 90th birthday

Organisation: Fakultät für Mathematik und Freundesverein der Fakultät

Fakultät für Mathematik, TU Dortmund