7 problems

Let $\mathbb{K}$ be a finite field, let $d\geq 2$ be an integer, and let … Here $\operatorname{PR}_{\mathbb{K}}(f)$ is the partition rank and $\operatorname{AR}_{\mathbb{K}}(f)$ is…

Let $\mathbb{K}$ be a field, let $d\geq 2$ be an integer, and let … Here $\operatorname{PR}_{\mathbb{K}}(f)$ denotes the partition rank of $f$, and $\overline{\mathbb{K}}$ is an al…

Lovett–Adiprasito–Kazhdan–Ziegler conjecture. There exists a constant $C_d$ such that for any finite field and multilinear form $f$ we have

Let $G$ be a vector space over $\mathbb{F}_p$, and let $\alpha\colon G^k\tomathbb{F}_p$ be an $r$-approximately symmetric multilinear form, meaning that the partition rank of…

Symmetrization conjecture. If

Constant-factor equivalence conjecture. For every $k ge 2$ there is a constant $C=C(k)$ such that, for every finite field $F$ and every $k$-tensor $T$ over $F$,

Mao's conjectured inequalities. Computation evidence suggests that