Aperiodic tilings have been big news recently, with the discovery of the hat monotile (or “einstein”). Aperiodic Order is the mathematical study of decorations of space that do not periodically repeat but still enjoy a rich structure of global order. The theory is diverse, intersecting areas such as Topology, Dynamical Systems, Symbolic Dynamics, Fourier Analysis, Diophantine Approximation, Discrete Geometry and Noncommutative Geometry. In this talk I will give an overview of the main constructions of aperiodically ordered patterns and introduce some of the tools that have been used to study them.
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