Aperiodic order and pure point diffraction

Abstract

The paper gives a leisurely introduction to mathematical diffraction theory with a focus on pure point diffraction. In particular, various characterizations of pure point diffraction and common models arising from cut and project schemes are discussed. It finishes with a list of open problems.

Keywords:

• diffraction
• quasicrystals

Acknowledgements

It is my pleasure to acknowledge helpful discussions with Michael Baake when I was preparing the talk at ‘Quasicrystals – The Silver Jubilee’, Tel Aviv, 2007, out of which this article arose. I take this opportunity to thank the organizers for the invitation to a highly enjoyable conference. Financial support from the German Science Foundation (DFG) is gratefully acknowledged.