3:00 p.m., Friday (March 17, 2006)
University of Victoria
Dynamics in the Theory of Diffraction in Systems with Long-range Aperiodic Order
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
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.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).