A conceptual breakthrough in sphere packing

@article{Cohn2016ACB,
  title={A conceptual breakthrough in sphere packing},
  author={Henry Cohn},
  journal={arXiv: Metric Geometry},
  year={2016}
}
  • Henry Cohn
  • Published 5 November 2016
  • Mathematics
  • arXiv: Metric Geometry
This expository paper describes Viazovska's breakthrough solution of the sphere packing problem in eight dimensions, as well as its extension to twenty-four dimensions by Cohn, Kumar, Miller, Radchenko, and Viazovska. 
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58 Citations
Background Citations
15
Methods Citations
3
Results Citations
1

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We give a unified description of the modular and quasi-modular functions used in Viazovska's proof of the best packing bounds in dimension 8 and the proof by Cohn, Kumar, Miller, Radchenko, and…
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References

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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…
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We improve on the lower bounds for the optimal density of sphere packings. In all sufficiently large dimensions the improvement is by a factor of at least 10, 000; along a sparse sequence of…
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…
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she announced her spectacular result in the paper titled ‘The sphere packing problem in dimension 8’ [10] on the arXiv-preprint server. Only one week later, on 21 March 2016, Henry Cohn, Abhinav…
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