4 problems

Involution pipe-dream conjecture. If $y\in I_\infty^{(n)}$, then

Let $I_n(B)$ be the ideal associated with the matrix $B$ in the construction of the Rees algebra, and let $\mathcal{P}$ denote the non-linear part of the defining ideal of that Ree…

Cha's primary decomposition conjecture. The canonical homomorphisms $\mathcal{T}^p_\Delta\to\mathcal{T}_\Delta$ induce an isomorphism

Let $s>n$ and let $\mathcal H=\{H_1,\ldots,H_s\}$ be properly meeting hyperplanes in ${\bf P}^n$, defined by linear forms $L_i$. Let $N+1=s$, let $\mathcal H'$ be the coordinate hy…