Aperiodic order via dynamical systems: Diffraction for sets of finite local complexity

TL;DR

This paper introduces diffraction theory for aperiodic order using dynamical systems, emphasizing pure point diffraction, reviewing recent results, and presenting a new uniform Wiener/Wintner type theorem that generalizes previous findings.

Contribution

It provides a comprehensive introduction to diffraction for aperiodic sets and introduces a novel uniform Wiener/Wintner type result extending earlier work.

Findings

Review of recent results in diffraction theory for aperiodic order

Presentation of a new uniform Wiener/Wintner type theorem

Sketches of proofs for key results

Abstract

We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform Wiener/Wintner type result generalizing various earlier results of this type.