CRM Monograph Series 2000; 379 pp; hardcover Volume: 13 ISBN10: 0821826298 ISBN13: 9780821826294 List Price: US$96 Member Price: US$76.80 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, selfaffine 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 selfsimilar 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 gaplabeling, 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 copublished with the Centre de Recherches Mathématiques. Readership 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 uptodate 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 uptodate account of the present state of knowledge and monitors the rapid evolution of this intriguing field."  CMS Notes Table of Contents  M. Baake and R. V. Moody  Selfsimilar 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: Cutandproject sets with preassigned 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 Wulffshape
 D. Damanik  Gordontype arguments in the spectral theory of onedimensional quasicrystals
 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
