4 problems

Radicality conjecture. The ideal $I_{\Delta}$ is radical if and only if

Primality and perfection conjecture. If $\Delta$ is any simplicial complex, then

Collapsing conjecture. Suppose that

Bounded Markov complexity conjecture. If $\{1,2,\ldots,j\}$ is an independent subset of the underlying graph of $\Delta$, then the preceding bounded-format conclusion holds. This w…