A joint seminar of the departments of

Mathematical Modeling and Numerical Analysis

and

Mathematical Foundations of Informatics

will be held on January 5th, 2023 (Thursday), at 3:00 pm in Room 403 of IMI – BAS.

A talk on

 Universal extrema of potentials of certain classes of spherical designs

will be delivered by Prof. Sergiy Borodachov, Towson University.

Abstract: We will discuss known results and our work on locations of absolute minima and maxima of the total potential of N points located on a higher-dimensional sphere that form a spherical design of the highest (in some sense) strength. The potential is a completely monotone function of the Euclidean distance squared. These results apply to a quite extensive list of particular spherical configurations. For power-law potentials and vertices of a regular polygon, regular simplex, cube, and cross-polytope, this problem was earlier solved in the papers by Stolarsky, Nikolov, and Rafailov.