Combinatorical and Algebraic Structures Seminar

Session details

Date: 21.3.2023
Speaker: Dirk Frettlöh, Universität Bielefeld
Title: Substitution tilings with transcendental inflation factor
Abstract: (spoluautoři: Alexey Garber (UT Rio Grande Valley), Neil Mãnibo (Univ. Bielefeld))
The mathematical theory of aperiodic order studies infinite structures with a high degree of local and global order. In most cases the structures are either infinite words (consisting of letters) or aperiodic tilings (consisting of tiles, hence in 1D: intervals of different lengths). Usually there are only finitely many types of letters, respectively tiles. Quite often the words or tilings are constructed via a substituion rule (i.e., inflate, subdivide). In this case the inflation factor is always an algebraic number. Only recently tilings with infinitely many tile types were studied in more detail w.r.t. their topological and dynamical properties. The question arose whether there are substitution rules with transcendental inflation factor (and then necessarily infinitely many letters resp. tile types). This talk explains concepts and background and gives an affirmative answer.

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