5 problems

Dimension conjecture. The dimension of the two-point variety is

Let $f\in \operatorname{Sym}^{2d}V$ be generic of SOS-rank $k\leq n$, and let … For a decomposition of $f$ into $k$ squares, write $A\in\mathbb C^k\otimes\mathbb C^N$ for the coeff…

Let $F$ be a frame for $\mathbb{F}^n$, and let $G$ be one of its dual frames. Write $Gr(F,G)$ for their cross Gramian and let $\mu(Gr(F,G))$ denote its maximum off-diagonal magnitu…

Inverse-eigenvector product conjecture. There exists an inverse eigenvector $\alpha$ such that

Gram-matrix parity conjecture. One has