Speaker: Curt McMullen
Title: Minkowski's conjecture, well-rounded lattices and topological dimension
Abstract: Classical sphere packing concerns lattices L in Rn with the Euclidean metric. Even a conjectural description of the densest packings is not known. Minkowski conjectured, however, that Zn is the densest lattice if we replace the Euclidean metric with the norm N(x) = x1 x2 .... xn. We will discuss a topological approach to this conjecture, and its relation to conjectures of Littlewood and Margulis.