Some mathematical problems arising in the study of quasicrystals

Abstract

After briefly reviewing the projection method, some properties of quasicrystal structures obtained by projection are discussed. In particular, the connection between the Fourier spectra and the local isomorphism class of a quasicrystal is worked out. It is argued that quasicrystals have no residual entropy at T = 0. Finally, certain self-similarity properties of quasicrystals are discussed.