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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, May 30, 2024}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape Lior Tenenbaum 
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  (Technion)
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will talk about
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{\Large\bfseries Periodic approximation of substitution subshifts\par}
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\textsc{Abstract:}
In studying higher dimensional Schrödinger operators of quasicrystals, one is lead to find
suitable periodic approximations. This means in particular that the spectrum converges as a set
to the limiting spectrum. It turns out that for this to hold, the convergence of the underlying dynamical systems is exactly what is needed. This is the starting point of the present talk.

We focus on aperiodic subshifts defined through symbolic substitutions. These substitution subshifts provide models of aperiodic ordered systems. We find natural sequence candidate of subshifts to approximate the aforementioned substitution subshift. We characterize when these sequences converge, and if so at what asymptotic rate. Some well-known examples of substitution subshifts are discussed during the talk. We will also discuss the motivation for this characterization, arising from an attempt to study higher
dimensional quasi-crystals. This is based on a Joint work with Ram Band, Siegfried Beckus and Felix Pogorzelski.








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