A counterexample to the coarse Menger conjecture
Nguyen, T
Scott, A
Seymour, P
Journal of Combinatorial Theory, Series B
volume 173
68-82
(13 Feb 2025)
We are delighted to announce PROMYS Europe 2025,
Fri, 24 Jan 2025
14:00 -
Fri, 31 Jan 2025
16:00
L6
INTRODUCTION TO DISCRETE ENERGY ON RECTIFIABLE SETS
Ed Saff
(Vanderbilt University)
Abstract
Discrete and continuous energy problems that arise in a variety of scientific contexts are introduced, along with their fundamental existence and uniqueness results. Particular emphasis will be on Riesz and Gaussian pair potentials and their connections with best-packing and the discretization of manifolds. The latter application leads to the asymptotic theory (as N → ∞) for N-point configurations that minimize energy when the potential is hypersingular (short-range). For fixed N, the determination of such minimizing configurations on the d-dimensional unit sphere S d is especially significant in a range of contexts that include coding theory, discrete geometry, and physics. We will review linear programming methods for proving the optimality of configurations on S d , including Cohn and Kumar’s theory of universal optimality. The following reference will be made available during the short course: Discrete Energy on Rectifiable Sets, by S. Borodachov, D.P. Hardin and E.B. Saff, Springer Monographs in Mathematics, 2019.
Sessions:
Friday, 24 January 14:00-16:00
Friday, 31 January 14:00-16:00
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