Seminar: Frank Vallentin (University of Cologne)


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(Meeting ID: 849 0964 5595, Passcode: 772448)


Speaker: Frank Vallentin (University of Cologne)

Title: Extremal lattice problems (not in the bible)

Lattices (discrete subgroups of n-dimensional Euclidean spaces) are ubiquitous objects in mathematics.

Typical classes of extremal lattice problems are finding good lattices with respect to some parameter, for instance minimizing packing density, maximizing covering density, or minimizing the quantization constant. The "bible" on these extremal lattice problems is the book "Sphere packings, lattices, and groups" [SPLAG] by Conway and Sloane. The first edition appeared in 1988. In the third edition from 1998 and one finds on p. xv the following quote "like the bible, [SPLAG] contains no proofs. This is of course only half true."

Science and technology advances and there is need for lattices which are good for other parameters or properties not yet treated in the bible, like minimizing potential energy, max-min polarization, minimizing Euclidean distortion, coloring the Voronoi cells, or polynomial time decodability.

In this talk I will introduce some of these extremal lattice problems, explain (combinatorial) techniques to attack them, and review open problems.