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
DOI:
https://doi.org/10.1090/S1079-6762-04-00130-1
Published electronically:
June 17, 2004
MathSciNet review:
2075897
Full-text PDF Free Access
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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
MR Author ID:
606578
ORCID:
0000-0001-9261-4656
Email:
cohn@microsoft.com
Abhinav Kumar
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138
MR Author ID:
694441
Email:
abhinav@math.harvard.edu
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.
