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Electronic Research Announcements
Electronic Research Announcements
ISSN 1079-6762

The densest lattice in twenty-four dimensions


Authors: Henry Cohn and Abhinav Kumar
Journal: Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 58-67
MSC (2000): Primary 11H31, 52C15; Secondary 05B40, 11H55
Published electronically: June 17, 2004
MathSciNet review: 2075897
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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.


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Additional Information

Henry Cohn
Affiliation: Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399
Email: cohn@microsoft.com

Abhinav Kumar
Affiliation: Department of Mathematics, Harvard University, Cambridge, MA 02138
Email: abhinav@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-04-00130-1
PII: S 1079-6762(04)00130-1
Received by editor(s): April 14, 2004
Published electronically: June 17, 2004
Additional Notes: Kumar was supported by a summer internship in the Theory Group at Microsoft Research.
Communicated by: Brian Conrey
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.