On the long-rang order of (planar) monotiles

Mathphys Analysis Seminar

The recently discovered monotiles of the Euclidean plane enforce tilings without any periods, but still have a stong form of long-range order. In fact, the Hat and the Spectre tilings are quasiperiodic and can be described as projection tilings. Their structure can be analysed with methods from topology, dynamical systems and harmonic analysis. This is compared to other monotiles and monocovers, and we briefly comment on known results in 3-space.