7 problems

Let $\Gamma$ be a countable group acting minimally and topologically freely on a space $X$ by … , and let $\Gamma\ltimes X$ be the associated transformation groupoid. Write…

Let $d$ be a positive integer, let $X$ be the Cantor set, and let $\mathbf{Z}^d$ act freely and minimally on $X$. An AT algebra is an algebra isomorphic to a direct limit … of C-al…

Topological almost finiteness conjecture. Continuous free Cantor minimal actions are always topologically almost finite.

Maximal-subgroup classification conjecture. Exactly one of the following holds:

AH conjecture. The index map $I$ should be surjective, and its kernel should be a quotient of

Let $(C,T)$ be a minimal dynamical system on a Cantor set $C$, and let $\rho$ be a metric on $C$ equivalent to its original metric. The (LRS) property means that $T$ is locally rad…

Let ${\mathcal G}_{{\mathcal F}}$ be a pseudogroup acting minimally on a Cantor space ${\mathfrak{X}}$. The action is equicontinuous-or-expansive dichotomy conjecture. either equic…