4 problems

Let $B$ be a $k$-row reduced bumpless pipe dream such that row $k$ has no blanks (“weighty tiles”). Let $\phi(B)$ be the RC graph corresponding to $B$ under the natural bijection b…

RBPD limit-shape and arctic-curve conjecture. As $n\to\infty$, the height function converges to a deterministic limit shape consisting of four frozen regions adjacent to the domain…

Connectivity conjecture. For every $n$, the set of reduced bumpless pipe dreams of size $n$ is connected under the $2\times2$ flips that preserve reducedness.

Let $\omega$ be a permutation, and let $P\in\operatorname{Pipes}(\omega)$. If $P$ is non-reduced, replace the redundant crossings with bump tiles. Up-elbow bound conjecture. Pipe…