Speaker: Michael Baake
Date: 12.07.2024 at 17:00
The recently discovered Hat is an aperiodic monotile for the Euclidean plane: Together with rotated and reflected copies, it can tile the plane, but only aperiodically. It is of interest to understand what kind of long-range order emerges, and how this compare with previous examples, such as the Taylor–Socolar monotile. To do so, methods from topology, dynamics and harmonic analysis are combined to show that the Hat tiling induces a dynamical system that is topologically conjugate to a primitive inflation tiling, the CAP, from which it then inherits a quasiperiodic structure with pure point spectrum and continuous eigenfunctions. In particular, it can be understood via a projection from four dimensions. A similar structure is present for the even more recent Spectre tiling, which is another aperiodic monotile for the plane, this time without needing a reflected version. This is joint work with Franz Gaehler and Lorenzo Sadun.