7 problems

Let $\mathcal{S}$ be a finite flag-transitive generalized quadrangle. A generalized quadrangle is classical when it is one of the standard generalized quadrangles arising from a cl…

Let $\mathbb F$ be an algebraically closed field of characteristic zero, and let $f_2,f_3\in\mathbb F[p_1,l_1]$. Kronenthal–Lazebnik's conjecture. Every graph…

Let $q$ be a prime power, and let a BIBD consist of $q$ copies of a non-Desarguesian affine plane of order $q$. A non-triangular local resolution system is a local resolution syste…

Kantor's conjecture. If $\mathcal{Q}$ is a finite flag-transitive generalized quadrangle and $\mathcal{Q}$ is not a classical generalized quadrangle, then, up to duality,…

Let $\mathcal{Q}$ be a generalized quadrangle of order $s>1$, and suppose a group of automorphisms acts regularly on both the point set and the line set of $\mathcal{Q}$. Nonexiste…

Linearity conjecture. Every translation generalized quadrangle has a projective representation; equivalently, the kernel $k$ is a division ring.

Let $\Gamma^x$ be an infinite translation generalized quadrangle with translation group $T$. Let $z$ be an affine point, meaning a point not collinear with $x$, and let $\{U\}_z$ b…