The common topic of the eleven articles in this volume is ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This emerging field of study is found at the crossroads of algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. The volume brings together contributions by leading specialists. Important advances in understanding the foundations of this new field are presented.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Mathematicians, physicists, crystallographers; graduate students.

Table of Contents

• M. Baake and R. V. Moody -- Similarity submodules and semigroups
• D. Barache, B. Champagne, and J.-P. Gazeau -- Pisot-cyclotomic quasilattices and their symmetry semigroups
• N. A. Bulenkov -- Three possible branches of determinate modular generalization of crystallography
• L. Chen, R. V. Moody, and J. Patera -- Non-crystallographic root systems
• L. W. Danzer -- Upper bounds for the lengths of bridges based on Delone sets
• N. P. Dolbilin and D. W. Schattschneider -- The local theorem for tilings
• A. Hof -- Uniform distribution and the projection method
• D. W. Schattschneider and N. P. Dolbilin -- One corona is enough for the Euclidean plane
• M. Schlottmann -- Cut-and-project sets in locally compact Abelian groups
• B. Solomyak -- Spectrum of dynamical systems arising from Delone sets
• G. van Ophuysen -- Non-locality and aperiodicity of \(d\)-dimensional tilings