4 problems

Generic means conjecture. For a generic set of points $x_1,\ldots,x_n$ in $\bar{X}$, $\bar{\bar{X}}$, $\bar{Z}$, or $\bar{\bar{Z}}$, means exist and are unique.

Polyhedral-complex conjecture. If geodesic triangles in orthant spaces $\mathcal{F}_\Omega$ are always closed, then each geodesic polytope $T$ is a polyhedral complex with cells…

Non-closedness conjecture. The convex envelope of three points is not closed, except in very special cases, with the question arising typically in $\mathbb{CP}^2$.

Let $\mathcal{T}_n$ be the space of trees on $n$ leaves. For $T,T'\in\mathcal{T}_n$, let $d_{TBR}(T,T')$ denote the minimum number of tree-bisection-regrafting moves needed to tran…