R. Moody 教授：講演概要 (Abstract)

　Long-range order or aperiodic order refers to the phenomenon of discrete systems of infinite extent which still have very evident order but are either partially or totally deficient in periodic symmetries. The order can appear in several ways, the most notable being the repetition of local structure (albeit aperiodically) and through the existence of a strong pure point component in the diffraction. Famous examples are the Penrose tilings, the Fibonacci substitution sequences, and the actual physical examples of quasi-crystalline materials.
　Just as in the case of statistical mechanics, it has proven extremely useful to study aperiodic structures not just as individuals in isolation, but rather as members of some larger family of closely related aperiodic structures; for example, all those objects whose local structures are indistinguishable up to translation. Thereby arise dynamical systems, and again, just as in statistical mechanics, the spectral theory of the associated dynamical system provides a powerful method of exploring the underlying geometry of the original structure that led to it.
　This lecture will explain this connection works and indicate some recent results that strongly link the dynamical and diffraction spectra.