Stochastik AG

Christoph Richard

Titel: Modulated crystals and almost periodic measures

Abstract:
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Modulated crystals and quasicrystals are both modulated quasicrystals, a
class of point sets introduced by de Bruijn in 1987. With appropriate
weight functions and modulation functions, modulated quasicrystals
themselves constitute a substantial subclass of strongly almost periodic
point measures. We re-analyse these structures using methods from modern
mathematical diffraction theory, thereby providing a coherent view over
that class. Similarly to de Bruijn’s analysis, we find stability with
respect to almost periodic modulations. This is joint work in progress
together with Jeong-Yup Lee (Soul), Daniel Lenz (Jena), Bernd Sing
(Barbados) and Nicolae Strungaru (Edmonton).