20 problems

The paper considers partition functions arising from framed quiver moduli and their relationship with gauge-theoretic generating functions. Nekrasov's conjecture. These partition f…

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 $Q$ be a quiver and let $\theta$ be a stability condition such that the corresponding quiver moduli space carries a universal bundle $\mathcal{U}$. An object is partial tilting…

Let $\iota^{\emph{gr},\emph{stab}}_{\boldsymbol{x},{\boldsymbol{m}}}$ be the map in the diagram relating the graded stable geometric construction to the corresponding algebraic spa…

Let $\pi$ be the map appearing in the diagram relating the geometric and algebraic realizations of the vector space…

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…

Let $S$ be a del Pezzo surface, let $\sigma$ be a geometric stability condition, and let $\textsf{v}\in K(S)$. Say that $\mathcal M^{\sigma-\operatorname{ss}}_\textsf{v}$ admits a…

Let $S$ be a del Pezzo surface, let $\textsf{v}\in K(S)$), and let $\sigma$ be a geometric stability condition. The stability condition defines the moduli stack…

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.

Type D one-loop Hodge equality conjecture. For $e,k\geq 1$,

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…

Stack-invariant reconstruction conjecture. A bona-fide Poincaré–Laurent polynomial $Q(\mathcal{M};y)$ may be reconstructed from the stack invariants $G_{\rm Higgs}$.

The paper considers localization data arising from the construction above. Realizability conjecture. Every localization datum can be obtained by this construction. The authors note…

Let $G$ be a finite subgroup of $\operatorname{SL}(3,\mathbb C)$, let $(Q,R)$ be its McKay quiver with relations, let $\Theta$ be the space of stability conditions, and let…

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…

Let $Q$ be a quiver, let $\Theta$ be a stability parameter, let $n$ be a framing dimension vector, and let $M_{d,n}^{\Theta}(Q)$ be an arbitrary smooth model for the moduli problem…

Let $Q$ be a quiver with stability parameter $\Theta$, and let $d$ be a dimension vector that is coprime for $\Theta$. Consider the moduli space $M_d^{\rm st}(Q)$ of stable represe…