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Kissing Numbers, Sphere Packings, and Some Unexpected Proofs

by Florian Pfender, Gunter M. Ziegler

Award: Chauvenet Prize

Year of Award: 2006

Publication Information: Notices of the AMS, September 2004, pp. 873-883

Summary:   A review of the sphere packing and kissing number problems, the kissing configurations in dimensions four, eight, and twenty-four, a sketch of Delsarte’s method and how it was applied for the kissing number problem in dimensions eight and twenty-four, and also an elegant construction of the Leech lattice in dimension twenty-four.

Read the Article (The file is 11.38 MB.)

About the Authors

Florian Pfender studied mathematics at Technische Universität (TU) Berlin, and got his Ph.D. from Emory University with Ron Gould in 2002. After holding a postdoctoral position at Emory University, he is currently a postdoctoral fellow at the DFG Research Center Matheon, at TU Berlin.  His main research interests are in the areas of graph theory and discrete geometry.  Outside of mathematics, he spends most of his time playing, coaching and organizing ultimate frisbee.

Günter M. Ziegler studied mathematics and physics at Munich University, and got his Ph.D. in mathematics from M.I.T. with Anders Björner in 1987. He is a professor of mathematics at Technische Universität (TU) Berlin since 1995, and a member of the DFG Research Center Matheon “Mathematics for Key Technologies.” The focus of his work is on discrete geometry (polytopes!) and combinatorics, with special interest in algebraic and topological methods. He is the author of Lectures on Polytopes (Springer 1995) and of Proofs from THE BOOK (with Martin Aigner, Springer 1998). His honors include a Gerhard Hess Prize of the German Science Foundation in 1994, and a Leibniz Prize in 2001.

Subject classification(s): Geometry and Topology
Publication Date: 
Monday, November 17, 0008

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