13 problems

Quantum geometric Langlands Eisenstein-induction conjecture. The $\mathrm{GL}_r$-eigenobject attached to $(E,\nabla)$ on $\operatorname{Bun}_{\mathrm{GL}_r}$ is Eisenstein-induced…

Let $G$ be a reductive group with maximal torus $T$, coweight lattice $X_{*}(T)$, dominant coweights $X_{*}(T)_{+}$, Langlands dual group $\check{G}$, and principal equivariant aff…

Let $G$ be a reductive group, let $\check{G}$ be its Langlands dual group, and let $\kappa$ be a Kac–Moody level for $G$. Denote by $\check{\kappa}$ the dual level for $\check{G}$,…

Let $k$ be generic, let $\tilde{\mathfrak g}$ be the Lie algebra related to $\mathfrak g$, and let … be a kernel vertex operator algebra, where the shifted levels satisfy the relat…

Let $V$ be a vertex algebra associated with a four-dimensional quantum field theory, and let quantum geometric Langlands kernel vertex operator algebras act by a convolution operat…

Let two $mathcal W$-(super)algebras have levels related by a Feigin--Frenkel-type relation. Let a kernel vertex operator algebra be a vertex operator algebra used to connect these…

Let $G$ be a reductive group, let $\check{G}$ be its Langlands dual group, and let $\kappa$ be a nondegenerate level for $G$ with dual level $\check{\kappa}$ for $\check{G}$. Write…

Gaiotto–Creutzig conjecture. The object $A^n[\mathfrak g,\psi]$ can be given the structure of a simple vertex operator superalgebra.

Quantum geometric Langlands correspondence is a correspondence between categories associated with a reductive group and its Langlands dual, and a Fourier–Mukai transform is expecte…

Let $G$ be a complex reductive group, let $X$ be a smooth complex projective curve, and let $G^{\vee}$ be its Langlands dual group. Let $\mathfrak{det}$ denote the determinant line…

Let $x_1,\ldots,x_n$ be points on a global curve, and let $W^c(G)_{x_i}$ and $KL^{check\kappa}(G)_{x_i}$ be the corresponding local categories. Let $Poinc$ and $Loc$ be the functor…

Let $X$ be a global curve, let $G$ and $G$ be Langlands-dual groups, and let $Bun_G$ and $Bun_{G}$ be their stacks of principal bundles on $X$. For twisting parameters $c$ and…

Let $G$ be a reductive group with Langlands dual group $G$, and let $kappa$ and $check\kappa$ be invariant forms on their Lie algebras such that, for the mutually dual Cartan subal…