8 problems

Let ${\mathfrak{g}}$ be of finite type and let ${\boldsymbol{\psi}}$ be a reachable highest $\ell$-weight. Write ${\boldsymbol{\psi}}$ in terms of vectors ${\mathbf{l}}=(l_{i,s})$…

Let $Q$, ${\mathbf{d}}$, and $\theta$ satisfy the assumptions of the theorem on partial tilting bundles, and let $\mathcal{U}$ be the universal representation on…

General Grassmannian reconstruction conjecture. For any $1\leq r<n$, the morphism

Vanishing-cycle W-algebra action conjecture. There is a $W_\kappa({\mathfrak gl}_r)$-action on this direct sum identifying it with the $W$-vacuum module.

Orientifold primitive-cohomology conjecture. The surjection

Orientifold Hodge equality conjecture. The canonical surjection

Let $Q$ be a quiver, let ${\bf d}$ be a dimension type for which stable representations exist, and let $M_{\bf d}^{\rm sst}(Q)$ denote the corresponding moduli space of stable repr…

Douglas's conjecture. There exists a continuous function $f:[m_1,m_2]\subset\mathbb{R}\to\mathbb{R}$ such that, for every $r\in[m_1,m_2]$ and every $\varepsilon>0$, there are…