4 problems

Let $G$ be a finitely generated group. Recall that $G$ is virtually free if it has a finite-index free subgroup. Ballier and Stein's conjecture. The group $G$ has decidable domino…

For integers $p,q\geq 2$, let ${\mathsf{DL}(p,q)}$ be the Diestel–Leader graph, and let the unlabelled graph mean this graph considered without its standard edge labelling. A seede…

Let $G$ be a one-ended word-hyperbolic group, meaning a word-hyperbolic group with one end. Let the surface group of genus $2$ be the fundamental group of a closed orientable surfa…

Weak-aperiodicity conjecture. $G$ has no weakly aperiodic SFT if and only if it is virtually cyclic.