3 papers
math.DS2025
Katsura-Exel-Pardo self-similar actions, Putnam's binary factors and their limit spaces
Jeremy B. Hume, Michael F. Whittaker
We show that the dynamical system associated by Putnam to a pair of graph embeddings is identical to the shift map on the limit space of a self-similar groupoid action on a graph.…
math.OA2024
C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states
Zahra Afsar, Nathan Brownlowe, Jacqui Ramagge +1
We introduce the notion of a self-similar action of a groupoid on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodu…
math.MG2024
Planar aperiodic tile sets: from Wang tiles to the Hat and Spectre monotiles
Tinka Bruneau, Michael F. Whittaker
A brief history of planar aperiodic tile sets is presented, starting from the Domino Problem proposed by Hao Wang in 1961. We provide highlights that led to the discovery of the Ta…