Ulrik Enstad: Existence of Gabor frames over rational lattices

A Gabor system is a sequence of time-frequency translates of a single function (the window), often indexed over a lattice. It is an open problem whether every lattice of covolume less than one admits a Gabor frame with window in the Schwartz class. I will present some recent joint work with Hannes Thiel and Eduard Vilalta where we apply the radius of comparison for C*-algebras to make progress on this problem, obtaining some new partial results.