7 problems

Simultaneous Waring identifiability conjecture. The polynomial vector admits a unique simultaneous Waring decomposition with

Exhaustive classification conjecture. The complete list of diagonal ternary positive $(p,\ell)$-universal quadratic forms is the one displayed in the source, namely the forms liste…

Finiteness conjecture. There are only finitely many primes $p$ and integers $\ell$ with $1\leq\ell<p$ for which a diagonal ternary positive $(p,\ell)$-universal quadratic form exis…

Kaplansky's conjecture. Each of these ternary quadratic forms represents every positive odd integer; that is, for every positive odd integer $n$, the equation $Q(x,y,z)=n$ is solva…

Spinor-genus preservation conjecture. Suppose that $G_1$ and $G_2$ have exactly the same number, namely some power $2^j$, of spinor genera. Then the genus-correspondence respects s…

Spinor-genus correspondence conjecture. Suppose that $G_1$ and $G_2$ each have exactly two spinor genera. Then $G_1$ has spinor exceptional integers if and only if $G_2$ has spinor…

Let $P_{3,6}$ be the cone of nonnegative ternary sextic forms, let $\Delta_{3,6}$ be its relevant cone of forms under consideration, and let $E(P_{3,6})$ denote the set of extremal…