Abstract: With motivation coming from symbolic dynamics, logic, tiling theory, mathematical physics, and more, quasicrystals generated by substitution processes have been studied intensively for more than 50 years. In this talk I will give an overview of the types of structures encountered in the field and how dynamical systems theory forms the foundational approach to their study. I'll also introduce you to some diffraction theory and explain the relatively new `renormalization' approach to answering key questions about the structure of quasicrystals.
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