An introduction to aperiodically ordered systems and their diffraction

3^rd February 2020, 11:00 MIF, Βoardroom, Ground floor
Prof. Uwe Grimm
School of Mathematics & Statistics
The Open University, Milton Keynes, UK

Abstract

The talk will present an introductory overview on aperiodically ordered systems obtained from cut and project or inflation methods. The key methods and results will be illustrated by means of examples and pictures, leaving aside much of the mathematical details. For cut and project sets, the diffraction is well understood, and the general result and its application to examples will be discussed. In contrast, inflation systems are still only partially understood, and paradigms with different spectral type are presented. Finally, I will briefly discuss recent results on the Fourier transform of Rauzy fractals and the point spectrum of unimodular Pisot inflation tilings, which uses both the inflation and the projection structure.