Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Minkowski's 1905 Theorem That Good Lattice Sphere Packings Exist
Speaker: Neil Sloane, AT&T Labs
Date: Thursday, November 13, 2008 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
In 1905 Minkowski showed that there are lattice packings of equal spheres that are reasonably dense. This is one of the classical results in the "Geometry of Numbers". I will present one of the standard proofs of this, or rather of Hlawka's generalization. The argument is quite delicate, and predates the probabilistic method in combinatorics and the random coding argument in information theory. It gives some insight into how to choose good random lattices. The talk will contain nothing new, although we are hoping to apply the methods to a problem in data compression.