7 problems

Higher transversality conjecture. The involution $\omega$ is also $n$-transverse for every integer $n\ge 3$.

Let $K$ be an algebraically closed field of characteristic $2$, and let $X\subset\mathbb{P}^3_K$ be a normal quartic surface. Write $\mu(4)$ for the maximal number of singular poin…

Let $mathbb F$ be a field of characteristic $2$. Let $n\in\mathbb N$ be odd, $m\in\mathbb N^n$, and set $K=K(n,m)$. Write $K'$ for the derived algebra and $N(K')$ for its relevant…

Let $H(4,(m_1,m_2,m_3,1))$ and $S(3,(m_1,m_2,m_3))$ denote the indicated graded Lie algebras of Cartan type in characteristic $2$. Brough–Eick's exceptional-isomorphism conjecture.…

CTS prolong conjecture. Such prolongs return the initial algebra, as in the generic cases of Yamaguchi's theorem.

Factorization characterization conjecture. The polynomial $P$ is representable if and only if, for some (equivalently any) tuple of squares $\ell\in{\mathbb F}^m$,…

Characteristic-2 nonexistence conjecture. Symmetric determinantal representations for polynomials represented by weakly-skew circuits do not always exist over fields of characteris…