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Introduction to quasi-crystals. (Introduction aux quasicristaux.) (French) Zbl 0924.52015

Séminaire Bourbaki. Volume 1997/98. Exposés 835–849. Paris: Société Mathématique de France, Astérisque. 252, 81-103, Exp. No. 838 (1998).
This is an informal introduction to some of the questions and results that emerged from the discovery of quasicrystals in the early eighties. The author focuses on aspects where he has substantially contributed himself, such as diffraction, projection method, tiling theory and local structures. Also, topological properties are discussed, and how they are relevant for the distinction of different types of order.
For further information, the interested reader should consult the references [‘Lectures on quasicrystals.’ ed. by F. Hippert and D. Gratias (1994)] and [‘Beyond quasicrystals’ ed. by F. Axel and D. Gratias (1994; Zbl 0880.00009)] of this survey, or (for more mathematical developments) the book “The mathematics of long-range aperiodic order” (1997; Zbl 0861.00015) ed. by R. V. Moody.
For the entire collection see [Zbl 0911.00019].

MSC:

52C23 Quasicrystals and aperiodic tilings in discrete geometry
82D25 Statistical mechanics of crystals
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