New developments on non-commutative quasicrystals

The theory of mathematical quasicrystals essentially goes back to work of Meyer in the 70’s, who investigated aperiodic point sets in Euclidean space. Shechtman’s discovery of physical quasicrystals (1982, Nobel prize for Chemistry 2011) via diffraction experiments triggered a boom of the mathematical analysis of the arising scatter patterns. Recent years have seen some progress in understanding the geometry, Fourier theory and dynamics of well-scattered, aperiodic point sets in non-commutative groups. We explain some of those developments from the viewpoint of approximation of certain key quantities arising from the underlying group actions via a notion of convergence of dynamical systems. One particular focus in this context will be on sufficient criteria to ensure unique ergodicity of the dynamical system associated with a point set.

Based on joint projects with Siegfried Beckus and Michael Björklund/Tobias Hartnick.