3 problems

Projectivity conjecture. $H$ is projective.

Kielak–Linton's agrarian generalization conjecture. The theorem remains true when every instance of $\mathbb Q$ is replaced by an arbitrary field $k$ and every $L^2$-Betti number…

Let $L$ be a flag complex, let $M$ be a covering of $L$, let $S\subseteq\mathbb Z$ satisfy $S+n=S$ for some $n>0$, and let $G_L^M(S)\rtimes n\mathbb Z$ be the associated CAT(0) cub…