6 problems

Bounded packing conjecture for virtually polycyclic groups. Each subgroup of $P$ has bounded packing in $P$.

Let $M\in\operatorname{SL}(n,\mathbf{Z})$ have no eigenvalues on the unit circle, and let $G$ be a finitely generated group quasi-isometric to the associated group $\Gamma_M$. The…

Polycyclic cyclic escape conjecture. Every infinite finitely generated polycyclic group has the cyclic escape property.

Finite-Krull-dimension conjecture. The following assertions hold:

Baer's conjecture. If $\mathbb{Z}G$ is Noetherian, then $G$ is polycyclic-by-finite.

Let $N$ be a connected and simply connected nilpotent Lie group, and let $\Gamma\subseteq\operatorname{Aff}(N)$ act properly discontinuously and cocompactly on $N$; such an action…