8 problems

Boone--Higman conjecture. Every finitely generated group with solvable word problem embeds in a finitely presented simple group.

Let $G$ be a finitely generated group. The domino problem asks whether a given finite set of Wang tiles admits a tiling of $G$. Ballier–Stein conjecture. $G$ has undecidable domino…

Let $G$ be a finitely generated group. A strongly aperiodic subshift of finite type (SFT) is an SFT with no periodic configurations. The strongly aperiodic SFT conjecture. $G$ admi…

Let $G$ be a group and let $H\leq G$ be a subgroup of index $2$. Write $\operatorname{SMON}(K)$ for the submonoid membership problem in a group $K$. Finite-index submonoid membersh…

A Hopfian finitely presented group is a finitely presented group for which every surjective endomorphism is an automorphism; its word problem asks whether a given word represents t…

Undecidability conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually Abelian groups is not decidable.

Virtual specialness conjecture. Virtual specialness is an undecidable property of non-positively curved cube complexes.

Let $M$ be a closed, orientable, irreducible $3$-manifold. Algorithmic orientation-reversing symmetry conjecture. There is an algorithm that determines whether $M$ admits an orient…