Seminar of Research Training Group
Towards quasicrystals in non-commutative spaces
Tuesday November 24, 2015 16:15:00 CET
Tuesday November 24, 2015 17:45:00 CET
In 2011, Dan Shechtman was awarded the Nobel prize in chemistry for his discovery of physical quasicrystals. Via diffraction experiments, he observed in 1982 that for some materials, there are interference patterns whose symmetries are not compatible with crystallographic structures in three-dimensional space. This triggered the mathematical examination of those structures as Dirac combs over uniformly discrete point sets in Euclidean space.
In the past decades, mathematical diffraction theory evolved into a beautiful and rich research topic combining various disciplines such as functional analysis, fourier analysis and dynamical systems. One method to obtain a large class of interesting quasicrystals is via so-called cut-and-project schemes, introduced by Meyer in the 70s. This talk presents the basics of diffraction for cut-and-project schemes over locally compact abelian groups and describes how the theory can be extended to the non-commutative case.
This is joint work with Michael Björklund (Chalmers Göteborg) and
Tobias Hartnick (Technion Haifa).
SR 5, Helmholtzweg 4