4 problems

Let $S$ be a surface and let $G<\operatorname{Mod}(S)$ be parabolically geometrically finite, meaning that $G$ is relatively hyperbolic relative to a possibly trivial collection of…

Let $S$ be any surface of finite type, and let $g_1,\dots,g_l\in MCG(S)$. For a subset $A$ of a group, write $\langle\langle A\rangle\rangle$ for its normal closure. Dehn-filling c…

Let $S$ be a finite-type surface, let $\mathcal{MCG}(S)$ be its mapping class group, and let $\mathcal{B}=\{\phi_1,\dots,\phi_k\}$ be a collection of elements. For a positive integ…

Let $A_\Gamma$ be an Artin group, and let $\mathcal{C}(A_\Gamma)$ denote its graph of irreducible proper parabolic subgroups of finite type. The graph is considered for Artin group…