Dynamics in the Theory of Diffraction in Systems with Long-range Aperiodic Order.

Abstract: The distinguishing feature of a system with long-range aperiodic order (e.g. Penrose tilings or quasicyrstals) is the distinctive nature of its diffraction, namely the prominent appearance of many bright spots, or Bragg peaks as they are called.

An important technique in the study of long-range aperiodic order is the use of dynamical systems. The associated spectral theory is closely associated with the diffraction and this has proven to be a useful angle on the subject. Nonetheless, the connection between diffraction and dynamics is not particularly straightforward and it is not yet fully understood.

In the talk we will introduce the concepts, defining diffraction, showing how we obtain dynamical systems from aperiodic systems, and giving some indication of the way in which dynamical systems play an important part in the theory. We then look more closely at the relation between diffraction and dynamics and survey some recent work , still in progress, that we hope sheds some useful light on this.