简介

While theoretical and mathematical tools exists to describe the properties (electrons, phonons, diffraction, transport) of crystals (periodic solids) are available, it is still an open problem to do the same for aperiodic ones. Since 1980, many progress have been made to fill this hole, especially by using the framework of Noncommutative Geometry. The present research program concerns (i) the description of the structure of such materials, using tiling theory and tiling spaces (ii) transport properties for electrons and the effect of magnetic field, disorder (quantum Hall effect), dissipation.