7 problems

Let $\operatorname{FHilb_n^{dg}}(\mathbb{C})$ be the dg flag Hilbert scheme parametrizing full flags of ideals containing an ideal of codimension $n$ in $\mathbb{C}[x,y]$, with suc…

Let $a_1,\ldots,a_m,b\geq0$ and set $\bm{a}=(a_1,\ldots,a_m)$. A one-sided twisted complex of threaded digons is a chain of complexes obtained by increasing the number of crossings…

Flag Hilbert scheme deformation conjecture. There is an $A_\infty$-deformation $(\mathcal{A}_\infty(FHilb_n),\tilde{\otimes})$ of $(\mathrm{DG}(FHilb_n),\otimes)$ such that

Flattening conjecture. The flattening of ${\mathcal{V}}$ is a complex ${\mathcal{E}}$ satisfying the requirements of Gorsky–Negut–Rasmussen's conjecture.

Let $P_T$ be the categorified Jones--Wenzl projector indexed by a standard Young tableau $T$ of size $n$, and let $\mathring{\mathrm{FHilb}}_T(\mathbb{C})$ be the corresponding aff…

Let $n$ be a positive integer, let $w\in S_n$ be a permutation, and let $E$ be the ring from Definition of the source. Let $x_1,\ldots,x_n$ be formal indeterminates, and let…

Let $n$ be a positive integer, let $T$ be a Young tableau, and let $P_T\in K^-(\mathbb{S}\mathbf{Bim}_n)$ be a complex categorifying the corresponding $q$-Young symmetrizer. Write…