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9 papers · 1 filter
From sphere packing to Fourier interpolation
Henry Cohn
Viazovska's solution of the sphere packing problem in eight dimensions is based on a remarkable construction of certain special functions using modular forms. Great mathematics has…
The Gaussian core model in high dimensions
Henry Cohn, Matthew de Courcy-Ireland
We prove lower bounds for energy in the Gaussian core model, in which point particles interact via a Gaussian potential. Under the potential function with $0…
Convex curves and a Poisson imitation of lattices
Nick Gravin, Fedor Petrov, Sinai Robins +1
We solve a randomized version of the following open question: is there a strictly convex, bounded curve γin the plane such that the number of rational points on γ, with denominator…
Three-point bounds for energy minimization
Henry Cohn, Jeechul Woo
Three-point semidefinite programming bounds are one of the most powerful known tools for bounding the size of spherical codes. In this paper, we use them to prove lower bounds for…
Rigidity of spherical codes
Henry Cohn, Yang Jiao, Abhinav Kumar +1
A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside f…
Order and disorder in energy minimization
Henry Cohn
How can we understand the origins of highly symmetrical objects? One way is to characterize them as the solutions of natural optimization problems from discrete geometry or physics…