6 problems

Direct-product conjecture. $S$ has a subgroup of finite index that is itself a direct product of $n$ or fewer limit groups.

Characterization conjecture. The group $G$ is elementarily equivalent to a non-abelian free group if and only if $G$ is a non-elementary hyperbolic fully residually free tower.

Let $G$ be a limit group, and let $H$ be a finite index supergroup of $G$. The limit-group supergroup conjecture. The group $H$ has property (LR). This is motivated by Wilton's the…

A limit group is a finitely generated subgroup of a group obtained from a free group by finitely many extensions of centralizers, and it is one-ended when it has one end. For a gro…

Let $G$ be a locally compact group, and let $F_2$ denote the free group of rank two. A group has a dense copy in $G$ if it contains a subgroup isomorphic to that group whose image…

Let $L_1,\ldots,L_n$ be non-abelian limit groups with $n\geq 2$, let $D=L_1\times\cdots\times L_n$, and let $H\leq D$ be a subdirect product that intersects each factor non-trivial…