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Aperiodic order in quasicrystals and diffraction

(Prof. Dr. Marc Keßeböhmer)

The classical mathematical topic of aperiodic order has experienced a renaissance in recent years, following the discovery of the closely related physical phenomenon of quasicrystal (2011 Nobel Prize in Chemistry Dan Shechtman). The project aims to determine the autocorrelation and diffraction (the Fourier transform of the autocorrelation) for so-called Dirac combs and to approximate them graphically on the computer - aperiodic order corresponds here to purely atomic diffraction measures. Further information can be found in Aperiodic order. Known algorithms are to be optimized in such a way that a high accuracy of the results is guaranteed at a justifiable expenditure of time. In addition, effective error estimation should also be implemented.

Basic knowledge of calculus, linear algebra, measure theory and numerics is recommended. The duration of the work within the working group should be at least four weeks. In addition, a written paper and a final presentation in the seminar are expected. For further information and requirements, please refer to the module and course catalog of the Department of Mathematics.

A written presentation of this project can be found here.