Browsing by Author "Damanik, David"

Now showing 1 - 6 of 6
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    Aperiodic Order and Spectral Properties
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Baake, Michael; Damanik, David; Grimm, Uwe
    Periodic structures like a typical tiled kitchen floor or the arrangement of carbon atoms in a diamond crystal certainly possess a high degree of order. But what is order without periodicity? In this snapshot, we are going to explore highly ordered structures that are substantially nonperiodic, or aperiodic. As we construct such structures, we will discover surprising connections to various branches of mathematics, materials science, and physics. Let us catch a glimpse into the inherent beauty of aperiodic order!
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    Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators
    (Zürich : EMS Publ. House, 2012) Damanik, David; Jitomirskaya, Svetlana
    This Arbeitsgemeinschaft discussed the spectral properties of quasi-periodic Schrödinger operators in one space dimension. After presenting background material on Schrödinger operators with dynamically defined potentials and some results about certain classes of dynamical systems, the recently developed global theory of analytic one-frequency potentials was discussed in detail. This was supplemented by presentations on an important special case, the almost Mathieu operator, and results showing phenomena exhibited outside the analytic category.
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    Aspects of Aperiodic Order
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2023) Baake, Michael; Cortez, María Isabel; Damanik, David; Strungaru, Nicolae
    The theory of aperiodic order expanded and developed significantly since the discovery of quasicrystals, and continues to bring many mathematical disciplines together. The focus of this workshop was on harmonic analysis and spectral theory, dynamical systems and group actions, Schrödinger operators, and their roles in aperiodic order - with links into a full range of problems from number theory to operator theory.
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    Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals
    (Zürich : EMS Publ. House, 2014) Damanik, David; Grimm, Uwe
    The dynamical (or von Neumann) spectrum of a dynamical system and the diffraction spectrum of the corresponding measure dynamical system are intimately related. While their equivalence in the case of pure point spectra is well understood, this workshop aimed at an appropriate extension to systems with mixed spectra, building on recent developments for systems of finite local complexity and for certain random systems from the theory of point processes. Another focus was the question for connections between Schr¨odinger and dynamical spectra.
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    Mini-Workshop: The Pisot Conjecture - From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets
    (Zürich : EMS Publ. House, 2009) Damanik, David; Lenz, Daniel
    This mini-workshop brought together researchers with diverse backgrounds and a common interest in facets of the Pisot conjecture, which relates certain properties of a substitution to dynamical properties of the associated subshift.
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    Spectral Structures and Topological Methods in Mathematical Quasicrystals
    (Zürich : EMS Publ. House, 2017) Damanik, David; Kellendonk, Johannes; Lenz, Daniel
    The mathematical theory of aperiodic order grew out of various predecessors in discrete geometry, harmonic analysis and mathematical physics, and developed rapidly after the discovery of real world quasicrystals in 1982 by Shechtman. Many mathematical disciplines have contributed to the development of this field. In this meeting, the goal was to bring leading researchers from several of them together to exchange the state of affairs, with special focus on spectral aspects, dynamics and topology.