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Directions in Mathematical Quasicrystals
Edited by: Michael Baake, Universität Tübingen, Germany, and Robert V. Moody, University of Alberta, Edmonton, AB, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Monograph Series
2000; 379 pp; hardcover
Volume: 13
ISBN-10: 0-8218-2629-8
ISBN-13: 978-0-8218-2629-4
List Price: US$91 Member Price: US$72.80
Order Code: CRMM/13

This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order. A number of the articles deal with the sophisticated mathematical ideas that are being developed from physical motivations.

Many prominent mathematical aspects of the subject are presented, including the geometry of aperiodic point sets and their diffractive properties, self-affine tilings, the role of $$C^*$$-algebras in tiling theory, and the interconnections between symmetry and aperiodic point sets. Also discussed are the question of pure point diffraction of general model sets, the arithmetic of shelling icosahedral quasicrystals, and the study of self-similar measures on model sets.

From the physical perspective, articles reflect approaches to the mathematics of quasicrystal growth and the Wulff shape, recent results on the spectral nature of aperiodic Schrödinger operators with implications to transport theory, the characterization of spectra through gap-labeling, and the mathematics of planar dimer models.

A selective bibliography with comments is also provided to assist the reader in getting an overview of the field. The book will serve as a comprehensive guide and an inspiration to those interested in learning more about this intriguing subject.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Graduate students and research mathematicians; mathematical physicists; theoretical physicists; theoretical materials scientists.

Reviews

"This collection provides ideal reference material for researchers who are active in the field as well as for any mathematician or theoretical physicist who is interested to learn more about this fascinating topic. It gives an up-to-date account of the present state of knowledge and monitors the rapid evolution of this intriguing field."

-- CMS Notes

"This is the fascinating realm of aperiodic order that is addressed by the contributions collected in the book ... contains articles that explore ... sometimes astonishing connections to many areas of mathematics ... This collection provides ideal reference material for researchers who are active in the field as well as for any mathematician or theoretical physicist who is interested to learn more about this fascinating topic. It gives an up-to-date account of the present state of knowledge and monitors the rapid evolution of this intriguing field."

-- CMS Notes

• M. Baake and R. V. Moody -- Self-similar measures for quasicrystals
• G. Bernuau and M. Duneau -- Fourier analysis of deformed model sets
• J. C. Lagarias -- Mathematical quasicrystals and the problem of diffraction
• P. A. B. Pleasants -- Designer quasicrystals: Cut-and-project sets with pre-assigned properties
• M. Schlottmann -- Generalized model sets and dynamical systems
• A. Weiss -- On shelling icosahedral quasicrystals
• J. Kellendonk and I. F. Putnam -- Tilings, $$C*$$-algebras, and $$K$$-theory
• J. Bellissard, D. J. L. Herrmann, and M. Zarrouati -- Hulls of aperiodic solids and gap labeling theorems
• K. Böröczky, Jr., U. Schnell, and J. M. Wills -- Quasicrystals, parametric density, and Wulff-shape
• D. Damanik -- Gordon-type arguments in the spectral theory of one-dimensional quasi-crystals
• R. Kenyon -- The planar dimer model with boundary: A survey
• A. Vince -- Digit tiling of euclidean space
• M. Baake and U. Grimm -- A guide to quasicrystal literature
• Index
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