9 problems

Counting-function symmetry conjecture. For every $\kappa\in\mathbb{F}_q^*$, one has

Let ${\mathcal P}$ be a rank $d$ polar space, and let $Y$ be a family of lines with characteristic vector $\chi_Y \in \langle \bm{j}\rangle + V_{10} + V_{11}$. Consider the example…

Non-regularity conjecture. The polar space associated to this induced form is non-regular.

Embedding conjecture. Every regular polar space admits a tight embedding.

Let $\Delta_i$ denote the graph associated with the $i$-dimensional subspaces of the finite polar space, and let $\kappa_i$, $\chi_i$, and $\xi_i$ be its corresponding graph parame…

Let $\mathbb{F}_0$ be a proper subfield of a field $\mathbb{F}$, and let $Q^+_{n-1}(2n-1,\mathbb{F})$ denote the polar Grassmannian of maximal singular subspaces of the hyperbolic…

Polar graph classification conjecture. Let $k\geq 2$. Then there exists $n_{q,k}$ such that every Boolean degree $1$ function $f$ on $C_q(n,k,e)$ with $n\geq n_{q,k}$ is trivial, t…

Let $Y$ be a maximum-size $(d,t)$-EKR set of generators in a polar space of rank $d$ and type parameter $e$, meaning that any two members of $Y$ meet in dimension at least $d-t$. A…

Let ${\goth M}:=\VerSpace(k,\PolarSpace(\varpi))$, and let ${\mathscr H}$ be a hyperplane of \VerSpace(k,\text{\boldmathgoth P}) determined by a polarity $\varkappa$. The inter…