5 problems

Infinite equalizer conjecture. There is an upper bound, depending only on $n$, for the number of $\operatorname{Eq}(\phi,\psi)$-orbits of the regular points of…

Let $G$ be a one-ended group acting geometrically on a CAT(0) space $X$, and let $\partial X$ denote its boundary. Assume that $\partial X$ has no finite cut and that a circle of T…

Let $G$ be a one-ended group acting geometrically on a CAT(0) space $X$, and let $\partial X$ denote its boundary. Assume that $\partial X$ has no finite cut. No-short-separating-a…

Non-rigidity conjecture. The group $G$ will be a non-rigid CAT(0) group with uncountably many boundaries.

Boundary maximality conjecture. Such a boundary is maximal, that is, a Poisson–Furstenberg boundary for $G$.