AG Mathematische Physik, Jan Mazac (FAU): Diffraction of Hats and Spectres (and mathematical theory of diffraction in a nutshell)

Jan Mazac (FAU)

Diffraction of Hats and Spectres (and mathematical theory of
diffraction in a nutshell)

Abstract:

The mathematical theory of diffraction is a great tool to understand a
certain type of order in infinite objects, such as discrete point sets. This fact was
known to physicists and crystallographers for periodic structures already more than a
hundred years ago. Since the late ’90, there has been a very solid way to treat also
non-periodic structures, and, in the talk, we will briefly review this theory. The recently discovered tiles Hat and Spectre provide nice examples of
such structures, as they can tile the plane in an aperiodic way only.

In the talk, we show that the resulting tiling is quasiperiodic and can
be obtained as a projection of a periodic structure in four dimensions. In other words, the tiling
is mutually locally derivable with a model set.

It is known that such sets have a pure-point diffraction spectrum. We
then provide the images of the diffraction spectrum, and we discuss the method to obtain them.