Analysis Seminar

Uwe Grimm, Open University, UK

Pure point diffraction is one indicator of `order' for a given
structure. Apart from periodic arrangements, such as those found in
perfect crystals, examples of pure point diffractive structures
include model sets, which are obtained by a cut and project scheme
from a higher-dimensional lattice. While continuous diffraction is
traditionally attributed to the presence of `disorder', many
aperiodically ordered systems show singular or even absolutely
continuous diffraction, while the pure point part is essentially
absent.

In continuation of the talk by Michael Baake, this talk will look at
several instructive examples of such structures, and show how their
diffraction can be determined constructively. It will also touch on
the relation between the diffraction and the dynamical spectrum (of
the associated dynamical system under the translation action) and
highlight the role of (topological) factors in revealing the hidden
order in the structure.