5 problems

Direct-product profinite rigidity conjecture. If a finitely presented residually free group $\Gamma$ has the same finite quotients as $F\times F'$, then

Absolute profinite rigidity conjecture for lattices. All lattices in

Remeslenikov's conjecture. Finitely generated free groups are profinitely rigid: every finitely generated, residually finite group with the same finite quotients as $F$ is isomorph…

Let $\mathcal{M}$ and $\mathcal{N}$ be hyperbolic $3$-manifolds. Their profinite completions are the inverse limits of their finite quotient groups. The manifolds are commensurable…

Let $G$ and $H$ be lattices in $PSL_2(\mathbb{C})$, and let $\widehat{G}$ and $\widehat{H}$ denote their profinite completions. Bridson–Reid conjecture. If … then … This is a profi…