8 problems

Let $X$ be an irreducible Euclidean building of dimension $\geq 2$, and let $\Gamma<\operatorname{Aut}(X)$ act properly and cocompactly on $X$. The group $\Gamma$ is virtually simp…

Haines's refinement. The assumption that one vertex of $T$ is special can be replaced by

Let a harmonic map be defined from a surface into a Euclidean building, and let its order mean the frequency-function quantity associated with the map. Mese's discreteness conjectu…

Let $X$ be an irreducible, locally finite, exotic Euclidean building and let $\Gamma < \operatorname{Aut}(X)$ be a lattice. Bader–Caprace–Lécureux's conjecture. Then $\Gamma$ is vi…

Let $M$ be a finite-volume Riemannian manifold, let $\widetilde M$ be its universal cover, and let $\widetilde X$ be a thick Euclidean building that is not locally finite. For a ho…

Following Witzel, a Singer cyclic lattice is a group $\Gamma \leq \operatorname{Aut}(\Delta)$ acting simply transitively on the panels of each type of an $\tilde{A}_2$-building…

Incompressible tiling conjecture. Spheres such as $\mathds{S}_0$ are tiled by isometric copies of $A_0$.

Bruhat–Tits boundary conjecture. Then $B$ is the Tits boundary of a locally finite simplicial Bruhat–Tits building.