3 problems

Strong polarization conjecture. The inequality above holds for every set of $n$ vectors in $\mathbb{S}^{d-1}$.

Let $\mathcal{C}$ be a 2-CY category associated to a finite-type Coxeter system of rank $r$, and let $\tau$ be a generic stability condition on $\mathcal{C}$. Write $\Sigma_\tau$ f…

Generator-count conjecture. Assuming superintegrability, the number of ring generators is $2r-3$ for the first structure and $r-1$ for the second structure.