31 problems

Beem–Rastelli conjecture. The Higgs branch of the 4d SCFT should coincide with the associated variety of the corresponding 2d CFT.

Associated-variety conjecture. For any integral dominant $\lambda\in\frak h^*$ with degree of atypicality $k$,

Let $\fg$ be simple of simply-laced type, let $k\in\BQ$ satisfy $k+\check{\operatorname{\mathbbm{h}}}=m/u$ in lowest terms with $m\geq1$ and $\operatorname{gcd}(m,u)=1$, and let…

Let $\fg$ be simple of simply-laced type and let $k\in\BQ$ satisfy $k+\check{\operatorname{\mathbbm{h}}}=m/u$ in lowest terms with $m\geq1$. Let $\check{\fg}^{(u)}$ be the metaplec…

Let $\fg$ be a simple simply-laced Lie algebra, let $k\in\BQ$ satisfy $k+\check{\operatorname{\mathbbm{h}}}=m\geq1$, and let $L_k(\fg)$ be the simple affine vertex algebra. Let…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{E_7(a_5)}$ be the nilpotent orbit of Bala–Carter type $E_7(a_5)$ in $E_7$. Associated-variety…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{F_4(a_3)}$ be the nilpotent orbit of Bala–Carter type $F_4(a_3)$ in $F_4$. Level $-6$ $F_4$ co…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{E_6(a_1)}$ be the nilpotent orbit of Bala–Carter type $E_6(a_1)$ in $E_6$. Associated-variety…

Let $W$ be a vertex algebra that is a finite extension of a vertex algebra $L$, and let $X_W$ and $X_L$ denote their associated Poisson varieties. Dominance conjecture. The morphis…

Let $\fg$ be a simple Lie algebra of simply-laced type, let $\check \fg$ be its Langlands dual, and let…

Subregular reduction conjecture.

Let a three-dimensional abelian gauge theory be equipped with the A-twist and additional boundary free fermions, and let $V^A$ be the resulting boundary VOA. Write $X_{V^A}$ for it…

Let $k=-3+\frac{2}{2m+1}$ with $m\geqslant 0$, let $V^k(sl_3)$ be the universal affine vertex operator algebra, and let $\mathcal I_k$ be its maximal ideal. Let $\mathcal V(I_k)$ d…

Let $V$ be a simple quasi-lisse conformal vertex algebra, and let $X_V$ denote its associated variety. Arakawa–Moreau's conjecture. … The paper explains that the theorem proved the…

Let $L_{-3}(F_4)$ be the simple affine vertex algebra at level $-3$ associated with the exceptional Lie algebra $F_4$, and let $X_{L_{-3}(F_4)}$ denote its associated variety. The…

Let $(Q,\mathbf v,\mathbf w)$ specify a type A linear quiver gauge theory, let $\CV_{\partial}$ be its H-twisted boundary vertex algebra, and let $X_{\CV_{\partial}}$ denote its as…

Let $4\mathcal{A}4$ be a two-dimensional chiral algebra, let $4\operatorname{Vac}_{\mathrm{TI}}(\mathcal{A})4$ denote its space of translation-invariant vacua, and let…

Let $L_{-2}(G_2)$ be the simple vertex algebra at level $-2$, and let $X_{L_{-2}(G_2)}$ denote its associated variety. Let $\mathbb{O}_{\mathrm{subreg}}$ be the subregular nilpoten…

Type A irreducibility conjecture. For every $w\in W$, the associated variety $V(L_w)$ is irreducible.

Let ${\mathcal V}$ be a simple, strongly finitely generated VOA that is $\mathbb N$-graded by conformal weight, with ${\mathcal V}[0]\cong\mathbb C$. Let $G$ be a finite group of a…

Isomorphism conjecture. The induced map $\hat{\psi}$ is an isomorphism.

Let $\lambda=[\lambda_1,\ldots,\lambda_n]$ be a partition, let $m_1(\lambda)$ denote the multiplicity of its parts equal to $1$, and let $\mathcal{F}_j(\lambda)$ be the family of d…

Let $f$ be a nilpotent element selected by the preceding conditions: the relevant Coulomb-branch operator count is non-negative and as small as possible, and $f$ is maximal among t…

Let $\mathcal{O}$ be a special nilpotent orbit, let $\mathscr{C}$ be the corresponding double cell, and let $\mathscr{C}/ {\small \stackrel{R}{\sim}}$ be the set of right cells con…

Let $L_w$ be the simple highest weight module of highest weight $-w\rho-\rho$ for an element $w$ of the Weyl group, and let $V(L_w)$ denote its associated variety. Irreducibility c…