Open Problems and Conjectures related to the Theory of Mathematical Quasicrystals

TL;DR

This paper compiles open problems and conjectures in the mathematical theory of quasicrystals, aiming to foster cross-disciplinary research and advance understanding in this rapidly evolving field.

Contribution

It presents a curated list of open problems and conjectures from a collaborative workshop, highlighting diverse viewpoints and encouraging further research.

Findings

Identified key open problems in quasicrystal theory

Highlighted the need for cross-disciplinary approaches

Motivated future research directions

Abstract

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our meeting was to bring together researchers from a variety of disciplines with a common goal of understanding different viewpoints and approaches surrounding the theory of mathematical quasicrystals. The problems reflect this goal and this diversity and we hope that they will motivate further cross-disciplinary research and lead to new advances in our overall vision of this rapidly developing field.