15 problems

Let $\rho$ be an $\mathrm{SL}(2,\mathbb C)$ character and let ${{\mathcal E}(\rho)}$ denote its set of end invariants, viewed as a subset of the projective lamination space…

Tameness Conjecture. The automorphism $f$ can be isotoped so that it preserves the splitting and the induced automorphism $g$ on $H_1$ is train-track generic and has a tame one-dim…

Let $\rho$ be an $\mathrm{SL}(2,\mathbb C)$ character, let $\mathcal E(\rho)$ be its set of end invariants, and let $\mathscr{PL}$ denote the projective lamination space. Cantor-se…

Let $\mathcal L$ be a lamination arising from a group action. A fidelity of $\mathcal L$ is a germ map into a path-connected space whose induced map on fundamental germ groupoids i…

Let $H$ be a handlebody with invariant measured lamination $\boldsymbol{\Lambda}$, and let the growth rate refer to the associated irreducible automorphism. A lamination is tight w…

Tropical parametrization conjecture. The basis $\mathbb{I}_{\mathcal{X}}^q(\mathcal{L}_{\mathfrak{sl}_3}^p(\Sigma,\mathbb{Z}))$ is parametrized by tropical points. Namely, for every…

Let $\mathbb T_q$ be the tautological tree, whose ends determine sequences of $ell$-values and associated $F$-sequences. An end is big when … and it is of type $S$ when its associat…

Let $\mathcal S_q$ be the shift locus in a one-dimensional slice, and let $\mathbb T_q$ be the tautological tree whose ends correspond to components of the complement of…

Let $\mathscr{A}_{{\rm SL}_3,\frak{S}}(\mathbb{Z}^{T})$ be the set of tropical-integer points of the ${\rm SL}_3$ cluster $\mathscr{A}$-space of a generalized marked surface…

Let $(G,\operatorname{\mathcal{L}}_1,\operatorname{\mathcal{L}}_2)$ be a pseudo-fibered triple. Suppose that $G$ is finitely generated, torsion-free, and freely indecomposable. Pse…

Let $(\operatorname{\mathcal{L}},G)$ be a tight pair, where $G$ acts on the circle preserving the lamination system $\operatorname{\mathcal{L}}$. Tight-pair global fixed-point conj…

Let $G$ be a finitely generated torsion-free discrete subgroup of $\operatorname{Homeo_+}(S^1)$. A pants-like $\operatorname{COL}_2$ group has a pants-like collection of two invari…

A compact lamination $(L,\mathcal L)$ embedded in a manifold $M$ is preserved by a diffeomorphism $f$ and is normally $AS$ if there exists $\epsilon>0$ such that the saturated nonw…

Let $(A,\Sigma)$ be a differentiable stratified space $b$-regularly embedded by $p$ into $\mathbb R^n$: for strata $Y<X$, whenever sequences in $X$ and $Y$ converge to a point of…

Let $V$ be an analytic variety in $\mathbb C^n$ and let $X$ be a stratum of an analytic stratification of $V$. For every point $p\in X$, there should exist a neighborhood $U$ of…