Overview
- Presents an evolving research area in which many different mathematical theories meet
- Yields a pool of interesting examples for various abstract mathematical theories
- Following D. Shechtman being awarded the 2011 Nobel Prize in chemistry for the discovery of quasicrystals, the mathematical study of periodically ordered tilings has enjoyed renewed interest
Part of the book series: Progress in Mathematics (PM, volume 309)
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Table of contents (11 chapters)
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Front Matter
Keywords
About this book
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically?
Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics.
This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
Editors and Affiliations
Bibliographic Information
Book Title: Mathematics of Aperiodic Order
Editors: Johannes Kellendonk, Daniel Lenz, Jean Savinien
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-0903-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2015
Hardcover ISBN: 978-3-0348-0902-3Published: 29 June 2015
eBook ISBN: 978-3-0348-0903-0Published: 05 June 2015
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XII, 428
Number of Illustrations: 42 b/w illustrations, 17 illustrations in colour
Topics: Convex and Discrete Geometry, Dynamical Systems and Ergodic Theory, Operator Theory, Number Theory, Global Analysis and Analysis on Manifolds