3 problems

Let $G\le \operatorname{\mathsf{PL}}([0,1])$ be a finitely generated group of piecewise linear homeomorphisms of $[0,1]$. Its standard action is assumed to be conjugate to a…

Distortion conjecture. An element in $\mathrm{Homeo}_{0}(S)$ which satisfies the conclusion of the proposition—that is, is non-spreading—is distorted.

Conjugacy-class conjecture. The closure of the conjugacy class of any pseudo-rotation of the torus of angle $\alpha$ contains the translation of angle $\alpha$. The closure of the…