6 problems

Masur–Minsky's conjecture. The diameter of the set of vertex cycles for every train track in every surface is bounded above by $3$.

A train-track on the surface $S$ has vertices that determine simplices in the curve complex, and let $d_{\mathcal C}$ denote distance in the curve complex. The constant $B$ is a bo…

de Carvalho–Hall conjecture. (a) If $q\ne q_w$, then $P$ has pseudo-Anosov braid type. (b) If $P'$ is another periodic orbit with height $q'$ and the same decoration $w$, then

Merging rarity conjecture. Merging outer automorphisms are rare, and most fully singular train track representatives have a proper full fold decomposition.

Existence and genericity conjecture. Every ageometric fully irreducible outer automorphism has a fully singular train track representative, and these representatives generically ha…

Let $S$ be a surface and let $\tau$ be a train track on $S$. A vertex cycle of $\tau$ is the simple closed curve whose counting measure represents an extreme point of the projectiv…