12 problems

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

Let $BS_{k,1}=\langle a,b\mid a^b=a^k\rangle$ for $k\ge 2$, where $x^y=y^{-1}xy$. A 1-relator group is a group admitting a presentation with one defining relator, and its Dehn func…

Let … be a Baumslag–Solitar group, with cogrowth series formed using the generating set $\{a^{\pm1},t^{\pm1}\}$. Baumslag–Solitar non-D-finiteness conjecture. If $M\neq N$, then th…

Let $G=\operatorname{BS}(1,k)=\langle a,b\mid b^{-1}ab=a^k\rangle$ with $k>1$, equipped with the standard normal form described above, and let the solution language of an equation…

Let $\operatorname{BS}(1,k)=\langle a,b\mid b^{-1}ab=a^k\rangle$ with $k>1$, equipped with the standard normal form in which every element is uniquely expressible as … where…

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 $B(\Gamma)$,…

Commuting-pairs language conjecture. The set

Let $G$ be a group with finite classifying space and no subgroup isomorphic to $\mathbb{Z}^2$. Let $\operatorname{BS}(m,n)$ denote the Baumslag–Solitar group with parameters $m,n$.…

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 $BS(p,q)=\langle a,t\mid t a^p t^{-1}=a^q\rangle$, and consider the growth of its horocyclic subgroup $\langle a\rangle$ with respect to the induced metric from the standard ge…

Let $BS(p,q)=\langle a,t\mid ta^pt^{-1}=a^q\rangle$, and consider the growth series of its horocyclic subgroup, consisting of elements represented by powers of the generator $a$. F…

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…