The periodic tiling conjecture asserts that any finite subset of a lattice Z^d that tiles that lattice
by translations, in fact tiles periodically. In this work we disprove this conjecture for …

An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of
its automorphism group. In this paper we obtain a structure theorem for locally finite quasi …

In this article we study domino snake problems on finitely generated groups. We provide
general properties of these problems and introduce new tools for their study. The first is the …

We look at constructions of aperiodic subshifts of finite type (SFTs) on fundamental groups of
graph of groups. In particular, we prove that all generalized Baumslag-Solitar groups (GBS) …

A subshift of finite type is a set of tilings of a group subject to a finite number of local
constraints, where the group acts by translation. In recent years, much progress has been …

Let G; H be two countable amenable groups. We introduce the notion of group charts, which
gives us a tool to embed an arbitrary H-subshift into a G-subshift. Using an entropy addition …

We introduce a notion of “simulation” for labelled graphs, in which edges of the simulated
graph are realized by regular expressions in the simulating graph, and we prove that the …

Strongly aperiodic subshifts of finite type on hyperbolic groups Page 1 Ergod. Th. & Dynam. Sys.,
(2022), 42, 2740–2783 © The Author(s), 2021. Published by Cambridge University Press. This is an …

We extend the classical Domino problem to any tiling of rhombus-shaped tiles. For any
subshift X of edge-to-edge rhombus tilings, such as the Penrose subshift, we prove that the …

In [1] we construct aperiodic tile sets on the Baumslag-Solitar groups BS (m, n). Aperiodicity
plays a central role in the undecidability of the classical domino problem on Z 2, and …