11 problems

Let $f\colon \widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ be a post-critically finite rational map that is not a flexible Lattès map. A simple closed curve on…

Let $f:S^1\to\mathbb{CP}^1$ be a CaTherine wheel arising from an expanding Thurston map. Uniform quasiconformality conjecture. There exists a finite constant $K$ such that $f$ is a…

Let $B$ be a non-exceptional Hurwitz biset, and let $B^*$ denote its associated semigroup of elements. An element of $B^*$ is unobstructed if it has no Thurston obstruction. Conver…

Let $f\colon (\widehat{\mathbb{C}},P)\to(\widehat{\mathbb{C}},P)$ be a rational Thurston map with a hyperbolic orbifold. Let $\overline{\mathscr{C}_P}$ be the set of isotopy classe…

Let $(F,Q)$ be a marked expanding Thurston map, where $F$ is an expanding Thurston map of the sphere and $Q$ is the marked set. An $F$-invariant graph is a graph preserved by $F$.…

Higher-dimensional extension conjecture. Theorem on X-rays holds with respect to any fixed point $\star$ of $F$.

Let $f\colon S^2\to S^2$ be a Thurston map with a hyperbolic orbifold that is realized by a rational map. Let $P_f$ denote its postcritical set, and let pullbacks be considered up…

Let $f$ be a rational Thurston map, and consider the pullback relation on nontrivial curves associated to $f$. A finite global attractor conjecture asserts that, if $f$ is not a fl…

Exceptional Hurwitz structure set conjecture. The Hurwitz structure set of every primitive NET map with constant pullback map is either an MC2 or MC4 Hurwitz structure set, or it i…

Extended half-space algorithm conjecture. The extended half-space algorithm decides, in finite time, whether or not $f$ is equivalent to a rational function.

Cellular Markov partition conjecture. Every expanding Thurston map admits a cellular Markov partition.