7 problems

Let $\bar{Y}_f$ be the enhanced $y$-ified Khovanov--Rozansky module of the link $L_f$. Let $\widetilde{Q}_{S}^{\vec{x},\vec{y}}$ be the bigraded $\mathbb{C}[\vec{x},\vec{y}]$-modul…

Rhoades–Wilson conjecture. The coefficient of $z^{n-k}$ in the graded Frobenius characteristic satisfies

Let $r\leq n$ be nonnegative integers, put $k=n-r$, and let ${\mathbf a}\in({\mathbb Z}_{\geq0})^r$. Define $V_n^=({\mathbf a})$ as the associated graded quotient for the component…

Let $\lambda\in P^+$, let $\boldsymbol\omega\in\mathcal P_q^+$ be preminimal of order $2$, and let $L(\boldsymbol\omega)$ be the graded limit of $V_q(\boldsymbol\omega)$. Let…

Let $e\mathfrak{L}_{1/p+k,\epsilon=1}(\operatorname{triv})$ be the graded vector space considered in the source, let $\mathfrak{m}$ be its indicated filtration ideal, and let $Z_p$…

The tensor-product realization conjecture. The graded limit $L(\boldsymbol{\pi}_s)$ is isomorphic to the ${\mathfrak g}[t]$-submodule of this tensor product generated by the tensor…

Let $\widehat{D}_k=\sum_{i=1}^n\partial_i^{k+1}x_i$ for $k\geq1$, and define the space of hat-harmonics by … The symmetric group $\mathfrak S_n$ acts by permuting variables, and th…