6 problems

Hypothesis (O) conjecture. An embedding satisfies Hypothesis $(O)$, or equivalently the stronger condition that every pair of points of $\mathscr{O}$ at mutual distance $4$ is oppo…

Ovoidal embedding conjecture. Every symmetric embedding is ovoidal.

Pseudo-isometric embedding conjecture. Every pseudo-isometric embedding is strongly polarised.

Uniqueness conjecture. This is the only example of size $s+1$ in any projective plane of order $s$ with that property and such that no flag of the plane is opposite all of its memb…

Let $\Gamma$ be a finite thick generalised hexagon or octagon, and let a collineation be an automorphism preserving points and lines. Say that a collineation maps all lines (or all…

A finite thick generalised octagon is a finite generalised $8$-gon in which every line is incident with at least three points and every point is incident with at least three lines.…