2 problems

Quadraticity–quadratic Gröbner basis conjecture. The algebra $\operatorname{A}(X_{n,d}^G)$ is quadratic if and only if $\operatorname{I}(X_{n,d}^G)$ has a quadratic Gröbner basis.

The three-dimensional restriction conjecture. The algebra $\operatorname{A}(X_{n,d}^G)$ is quadratic if and only if, for all $i<j<k$, the algebra…