3 problems

Let $T$ be a regular tree and let $G\leqslant\operatorname{Aut}(T)$ be unimodular and transitive on the vertices of $T$. The group C$^*$-algebra of $G$ is CCR if it is liminal, a p…

Let $T$ be a regular tree and let $G\leqslant\operatorname{Aut}(T)$ be a non-amenable automorphism group acting minimally on $T$. Horan–Raum conjecture. The group $G$ is type I if…

Let $T$ be the infinite rooted binary tree, and let $\operatorname{Aut}(T)$ be its group of root- and parent-preserving automorphisms. The source proves that…