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D. B. Cohen, C. Goodman-Strauss, and the author proved that a hyperbolicgroup admits an "SA SFT" if and only if it has at most one end. This paper hastwo distinct parts: the first is a conversation explaining what an SA SFT isand how they may be of use. In the second part I attempt to explain both oldand new ideas that go into the proof. References to specific claims in theoriginal paper are given, with the hope that any interested reader may be ableto find the details there more accessible after reading this exposition.

Strongly aperiodic SFTs on hyperbolic groups: where to find them and why we love them