5 problems

A straight edge of a tile is a line segment in its boundary that cannot be extended without leaving the boundary. A tile is weakly convex if, for every straight edge, the rest of t…

A substitution tiling is locally finite if, up to rigid motions, it contains only finitely many two-tile configurations. A tiling substitution has a linear expansion determined by…

Let $G$ be a connected graph, and let a labeling $l:V(G)\to\mathbb{R}^+$ be non-degenerate when the labeling satisfies the paper's non-degeneracy condition. Discreteness-local fini…

Zelmanov's conjecture. The group $G$ is locally finite.

Let $v$ be a group-word and $G$ a profinite group. The verbal subgroup $v(G)$ is the subgroup generated by all $v$-values in $G$. Local finiteness conjecture for torsion word value…