10 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…

Let $d\geq 3$ be an integer, let $F$ be a generic ternary degree $d$ form, and let $\mathbb{X}(d+1)$ denote a star configuration of $d+1$ points in the projective plane. Existence…

For each integer $d\ge2$, let $p(3,2d)$ denote the least integer $r$ such that every nonnegative ternary form of degree $2d$ is a sum of at most $r$ squares of forms. Ternary Pytha…

Let $f$ be a ternary form of degree $d$, and let $\mathcal{R}_d$ be the semialgebraic set of forms in $\mathbb{R}[x,y,z]_d$ whose real rank equals the generic complex rank $R(d)$.…

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…

Let $\Delta_{3,6}$ denote the cone of psd ternary sextic forms, and let an extremal form be an extremal element of this cone. A form has a zero at which it attains the relevant max…