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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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J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups , third edition, Grundlehren der Mathematischen Wissenschaften 290
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T. C. Hales, Cannonballs and honeycombs , Notices Amer. Math. Soc. 47
2000
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H. Cohn and N. Elkies, New upper bounds on sphere packings I , Ann. of Math. (2) 157
2003
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T. C. Hales, A proof of the Kepler conjecture , Ann. of Math. (2) 162
2005
Cited alongside, same era.
H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices , Ann. of Math. (2) 170
2009
Cited alongside, same era.
A. Venkatesh, A note on sphere packings in high dimension , Int. Math. Res. Not. 2013
2013
Cited alongside, same era.
2015
Cited alongside, same era.
2015
Cited alongside, same era.
H. Cohn, Packing, coding, and ground states , PCMI 2014 lecture notes, 2016. arXiv: 1603.05202
2016
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2016
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2016
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2016
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M. S. Viazovska, The sphere packing problem in dimension 8 8 , preprint, 2016. arXiv: 1603.04246
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2016
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