9 problems

Let $A$) be an Artin group, with corresponding Coxeter group $W$. The standard parabolic subgroups of $A$ of finite type are the parabolic subgroups associated with finite standard…

Relative hyperbolicity conjecture. The group $G$ is hyperbolic relative to $\mathbf S$.

Let $G$ be a group that is hyperbolic relative to a finite family of subgroups $\{H_1,\ldots,H_n\}$. Denote by $\mathcal M=\mathcal L(G)$ the von Neumann algebra corresponding to…

Let $\mathcal{G}_{n,p}$ denote the Erdős–Rényi random graph, let $\Gamma\sim\mathcal{G}_{n,p}$, and let $W_{\Gamma}$ be the right-angled Coxeter group with presentation graph…

Let $(G,P)$ be a relatively hyperbolic group pair, meaning that $G$ is relatively hyperbolic relative to the collection of subgroups $P$. Assume that its Bowditch boundary is homeo…

Finite abelian hierarchy conjecture. Then $G$ should have the $L^2$-Hall property and satisfy the Geometric Hanna Neumann conjecture.

Let $G$ be a relatively hyperbolic diagram group. Free-product conjecture. Relatively hyperbolic diagram groups are free products. The claim gives a more precise form of the preced…

Relative hyperbolicity classification conjecture. $d4a2$ is relatively hyperbolic if and only if this HHS structure has isolated orthogonality.

Let $F$ be a free group, let $w\in F\setminus\{1\}$ have primitivity rank $\pi(w)=2$, and let $G=F/\langle\!\langle w\rangle\!\rangle$. Let $P<G$ be the peripheral subgroup supplie…