Aperiodic order and pure point diffraction

TL;DR

This paper provides an accessible introduction to mathematical diffraction theory, emphasizing pure point diffraction, its characterizations, models from cut and project schemes, and outlines open problems in the field.

Contribution

It offers a comprehensive overview of pure point diffraction, including characterizations and models, along with a discussion of open problems in mathematical diffraction theory.

Findings

Various characterizations of pure point diffraction

Models arising from cut and project schemes

List of open problems in the field

Abstract

We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project schemes. We finish with a list of open problems.