4 problems

Let $\mathbb{X}$ be a family of projective point sets and let $I(\mathbb{X})$ denote its vanishing ideal. Vaz Pinto's conjecture. The ideal $I(\mathbb{X})$ is Gorenstein if and onl…

Ballinger et al.'s conjecture. Ballinger et al. conjecture that the construction obtained from such a matrix $S$ gives the optimal code in every dimension.

A maximal quaternionic simplex is a simplex in $\mathbb{H}\mathbb{P}^{d-1}$ attaining the maximal size permitted by the relevant simplex bound. The only known example is the simple…

Universal-optimality conjecture. The $16$-line configuration in $\mathbb{R}^5$ is universally optimal and is the unique optimal $16$-point code in $\mathbb{R}\mathbb{P}^4$.