5 problems

Let $X$ be a locally compact CAT(0) space with a geometric group action $\Gamma\curvearrowright X$. An $n$-flat is an isometrically embedded copy of Euclidean $n$-space, where…

Lytchak's Regular Point Conjecture. The Tits boundary $\partial_T X$ contains a regular point.

Let $X$ be a proper, geodesically complete $\operatorname{CAT}(0)$ space under a geometric action. A rank one axis is an axis in $X$ that does not bound a flat half-plane. Rank Rig…

Let $X$ be a proper CAT(0) space with a proper cocompact action of a discrete group $\Gamma$. A flat $F\subset X$ is $\Gamma$-periodic if some subgroup $\Gamma_0\leq\Gamma$ preserv…

Let $D$ be a bounded contractible domain in a Euclidean space of arbitrary dimension, and consider reflecting Brownian motions in $D$ together with co-adapted couplings. A coupling…