Mathematics Colloquium
ED SAFF
Vanderbilt
Title: Energy bounds for minimizing Riesz and Gauss configurartions
Date: Friday, March 8, 2019 [POSTPONED]
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm
Abstract. Utilizing frameworks developed by Delsarte, Yudin and Levenshtein, we deduce linear programming lower bounds (as N tends to infinity) for the Riesz energy of N-point configurations on the d-dimensional unit sphere in the so-called hypersingular case; i.e, for non-integrable Riesz kernels of the form |x - y|^{-s} with s > d. As a consequence, we immediately get (thanks to the Poppy-seed bagel theorem) lower estimates for the large N limits of minimal hypersingular Riesz energy on compact d-rectifiable sets. Furthermore, for the Gaussian potential exp(-a |x - y|^2) on R^p, we obtain lower bounds for the energy of infinite configurations having a prescribed density.