7 problems

Let $v otinquotmax$ and $wgeq v$, let $b1asigma=v^{-1}w$ be the resulting permutation decorated by declaring a fixed index $j$ black if $jin v^{-1}[k]$, and set $I=v^{-1}[k]$. Let…

Galashin–Lam's conjecture. There exists a non-algebraic deformation retract

Let $S_M$ be a $km$-dimensional positroid cell of ${\rm Gr}_+(k,n)$. Let $\pi_+$ be the positive amplituhedron map and let $\pi$ denote its complexified rational map on the closure…

Let $\widetilde \Pi^{\circ}_\pi$ be the relevant open positroid variety, and let $\mathbb{P}_\pi$ be the free abelian group of Laurent monomials in the target frozen variables. The…

The source concerns open positroid varieties and the cluster structures determined by relabeled plabic graphs. For a relabeled graph $G^\rho$ and an ordinary plabic graph $H$ with…

Compatibly split positroid conjecture. The only compatibly split irreducible subvarieties of $\mathrm{Gr}(k,n)$ are the closed positroid varieties.

Affine Grothendieck polynomial conjecture. The $K$-theory class of the structure sheaf of $\Pi_f$ is the image of $\tilde{G}_f$ under this identification: