4 problems

$L^2$-Hall characterization conjecture. The following conditions should be equivalent:

Let $G$ be a group, and let $B(\Gamma)$ be a right-angled Baumslag–Solitar–Artin group whose underlying undirected graph is a star graph. Suppose that $G$ is virtually $B(\Gamma)$,…

For an integer $k\geq 2$, let $BS(1,k)=\langle a,t\mid tat^{-1}=a^k\rangle$, and let a finite generating set mean any finite generating set of this group. The Baumslag–Solitar tran…

Let $\mathrm{BS}(N,N)$ be the Baumslag–Solitar group, and let $g_{n,0}$ denote the number of trivial words of length $n$ in it. Write $\mu_N$ for the exponential growth rate and…