9 problems

Let $G$ be an Artin-Tits group of spherical type, let $\mathcal C(G)$ be its curve graph, and let $\alpha\in G$. Suppose a vertex of $\mathcal C(G)$ has a finite orbit under…

Let $G$ be an Artin-Tits group of spherical type with rank $n$, let $\mathcal C(G)$ be the curve graph, and let $\alpha\in G$. Consider a vertex of $\mathcal C(G)$ with a finite or…

Let $\Sigma$ be a compact, connected, orientable surface, and let $\mathcal A$ be a multiarc and curve graph on $\Sigma$. For a witness $W$, let…

Let $\Sigma$ be a compact, connected, orientable surface, and let $\mathcal A$ be a multiarc and curve graph on $\Sigma$. A compact, essential subsurface $W\subset\Sigma$ is a witn…

Let $\alpha$ and $\beta$ be the endpoints of a shortest origami edge-path, and let $\alpha_i$ and $\alpha_{i+1}$ be consecutive curves on it, with $\alpha_{i+1}$ intersecting…

Intersection-quotient conjecture. Under this condition, the edge-path is a quasi-geodesic.

Let $S$ be the surface under consideration, and let $\mathcal{SC}(S)$ denote the Schmutz Schaller curve graph, with vertices and edges as defined in the paper. Let…

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

Let $S$ be a surface with complexity $\xi(S)$, let $k$ be an integer, and let $\alpha$ and $\beta$ be simple closed curves on $S$. Write $d_{\mathcal{C}}$ for curve graph distance…