7 problems

Let $\mathrm{det}_n$ denote the determinant polynomial of degree $n$, and let $\operatorname{str}(\mathrm{det}_n)$ denote its strength. Lampert–Moshkovitz conjecture. The strength…

For each form $P$, let $\str(P)$ denote the least number of reducible forms whose sum is $P$. Let $\mathrm{det}_n$ be the determinant viewed as a homogeneous polynomial in the rows…

Adiprasito–Kazhdan–Ziegler conjecture. The bound in Theorem $$ should hold with linear bounds; equivalently, the relevant strength and partition-rank quantities over $K$ should be…

Strength–analytic-rank conjecture. Strength is bounded by a constant multiple of analytic rank:

Strength–slice-rank conjecture. The strength and the slice rank of a general form in $\mathcal{S}_d$ are equal.

Polynomial bound conjecture for ${}^\eta\!A$. For all characteristics, the best possible bound for ${}^\eta\!A$ is, for fixed $\eta$ and fixed $d$, at worst

Polynomial strength-bound conjecture. For all characteristics, the best possible bound for $\mathfrak{K}_d(k)$ is at worst