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Universally optimal distribution of points on spheres
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points).
New upper bounds on sphere packings I
We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related
A variational principle for domino tilings
1.1. Description of results. A domino is a 1 x 2 (or 2 x 1) rectangle, and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps. In
A group-theoretic approach to fast matrix multiplication
  • Henry Cohn, C. Umans
  • Mathematics
    44th Annual IEEE Symposium on Foundations of…
  • 24 July 2003
A new, group-theoretic approach to bounding the exponent of matrix multiplication is developed, including a proof that certain families of groups of order n/sup 2+o(1)/ support n /spl times/ n matrix multiplication.
The sphere packing problem in dimension 24
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and
The Shape of a Typical Boxed Plane Partition
Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all
Approximate common divisors via lattices
This work analyzes the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem and develops a corresponding lattice-based list decoding algorithm for Parvaresh-Vardy and Guruswami-Rudra codes, which are multivariate extensions of Reed-Solomon codes.
An $L^p$ theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions
A theory of limits for sequences of sparse graphs based on graphons is introduced, which generalizes both the existing $L^\infty$ theory of dense graph limits and its extension by Bollob\'as and Riordan to sparse graphs without dense spots.
Sparse Exchangeable Graphs and Their Limits via Graphon Processes
By generalizing the classical definition of graphons as functions over probability spaces to functions over $\sigma$-finite measure spaces, this work can model a large family of exchangeable graphs, including the Caron-Fox graphs and the traditional exchangeable dense graphs as special cases.
Local statistics for random domino tilings of the Aztec diamond
We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will