6 problems

Let $\mu$ be the unique normalized invariant measure of a cubic critical homeomorphism of the circle, and let $HD(\mu)$ denote the Hausdorff dimension of its measure-theoretical su…

A hyperbolic-like action of a group on the circle is an action by orientation-preserving circle homeomorphisms in which every non-trivial element has exactly two fixed points, one…

Let $G\leq \operatorname{Homeo}_+(S^1)$ be a subgroup such that every non-trivial element has at most two fixed points, and whose action on $S^1$ is minimal. Assume that the action…

Let $G\leq \operatorname{Diff}_+^\omega(\mathbf{S}^1)$ be a finitely generated locally discrete group. A locally discrete group's structure conjecture predicts both that the action…

Period-set characterization conjecture. There exist sets $E_c,E_d\subset\mathbb N$, each a finite union of tails of the orderings $\leso{2}$ and $\leso{3}$, such that

Let $\Gamma$ be a higher-rank lattice acting continuously on the circle $S^1$. The circle-action conjecture. Every such action should be finite. This is part of the low-dimensional…