University of Chicago
Department of Mathematics

Crystallography, number theory and coding theory give strong motivations for the study of (euclidean) lattices. A modern version of reduction theory introduces the notion of semistable lattice, and explains that any lattice is canonically an extension of semistable ones. We shall explain the relationship with the notion of semistability for vector bundles (and for filtered vector spaces), evoke a common framework, and discuss the following delicate (open) question: is the tensor product of two semistable lattices semistable?