Integrable Systems Seminar
Friday, February 28, 2003, 4:00pm, 218 Physics
Jean Bellissard (Georgia Tech, Department of Mathematics)
Tilings, Aperiodic media and their Noncomutative Geometry

Abstract:

Aperiodic solids can be described though point sets representing the ideal position of their atoms at zero temperature. Equivalently such sets can be represented by their Voronoi tiling. Among such sets, the one that are both "repetitive" with "finite type" have special interest. We give a description of such class of point set in term of a dynamical system called the "Hull". A classification theorem permits to describe the Hull up to conjugacy. The homology and the cohomology of the underlying space are also computable. It allows to classify ergodic invariant measures. Another point of view comes from the canonical C*-algebra associated with the dynamical system. The K-theory of such algebra has also some application in Physics or in PDE theory, such as the "gap labeling theorem". This lecture will give an overview of this theory.

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