6 problems

Let $G$ be a reductive group, let $\check{G}$ be its Langlands dual group, and let $\kappa$ and $\check{\kappa}$ be corresponding quantum parameters. Let…

Let $M$ and $N$ be the parameters of the orthogonal setup, let $\bF$ be the Laurent series field, and let $U_{M,N}(\bF)$ be the unipotent group equipped with the character…

Assume $N>M$ and let $c\neq0$ be a non-rational number. Let $\Gr_{\GL_N}$ denote the affine Grassmannian, $U_{M,N}(\bF)$ the relevant unipotent subgroup with character $\chi_{M,N}$…

Let $\calY$ and $\calY'$ be stacks such that their cotangent dg-stacks are isomorphic as symplectic dg-stacks. Write $\calC_C(\calY)$ and $\calC_H(\calY)$ for the corresponding Cou…

Let $\calT$ be a three-dimensional $N=4$ theory and let $\calT^*$ denote its mirror. Write $\calC_C(\calT)$ and $\calC_H(\calT)$ for the Coulomb and Higgs categories of line operat…

Let $\hat{\mathfrak{g}}_{\kappa}\textup{-mod}^{G(\mathcal{O})}$ be the category of $G(\mathcal{O})$-equivariant modules for the affine Kac–Moody algebra at level $\kappa$, and let…