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The densest lattice in twenty-four dimensions
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The densest lattice in twenty-four dimensions
Henry Cohn and Abhinav Kumar
Abstract.
In this research announcement we outline the methods used in our
recent proof that the Leech lattice is the unique densest lattice
in $\mathbb{R}^{24}$. Complete details will appear elsewhere, but here we
illustrate our techniques by applying them to the case of lattice
packings in $\mathbb{R}^2$, and we discuss the obstacles that arise in
higher dimensions.
Copyright 2004 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 10 (2004), pp. 58-67
- Publisher Identifier: S 1079-6762(04)00130-1
- 2000 Mathematics Subject Classification. Primary 11H31, 52C15; Secondary 05B40, 11H55
- Key words and phrases.
- Received by editors April 14, 2004
- Posted on June 17, 2004
- Communicated by Brian Conrey
- Comments (When Available)
Henry Cohn
Microsoft Research,
One Microsoft Way, Redmond, WA 98052-6399
E-mail address: cohn@microsoft.com
Abhinav Kumar
Department of Mathematics,
Harvard University, Cambridge, MA 02138
E-mail address: abhinav@math.harvard.edu
Kumar was supported by a summer internship
in the Theory Group at Microsoft Research.
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