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Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably, while their relevance has grown in practice as well. Here, the phenomenon of homometry shows various unexpected new facets, particularly so in the presence of disorder. After an introduction to the mathematical tools, we review pure point spectra, based on the Poisson summation formula for lattice Dirac combs, aiming at the diffraction formulas of perfect crystals and quasicrystals. We continue by considering classic deterministic examples with singular or absolutely continuous diffraction spectra, and we recall an isospectral family of structures with continuously varying entropy. We close with a summary of more recent results on the diffraction of dynamical systems of algebraic or stochastic origin.

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Michael Baake, Universität Bielefeld
Seminarraum Theoretische Physik
Contact: not specified