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

Abstract

In [9] D. B. Cohen, C. Goodman-Strauss, and the author proved that a hyperbolic group admits an "SA SFT" if and only if it has at most one end. This paper has two distinct parts: the first is a conversation explaining what an SA SFT is and how they may be of use. In the second part I attempt to explain both old and new ideas that go into the proof. References to specific claims in [9] are given, with the hope that any interested reader may be able to find the details there more accessible after reading this exposition.