9 problems

Let $G$ be a group, let $\Shv(G)^{\on{q-mon}}$ denote the quasi-monodromic sheaf category, and write $G\mmod$ for the category of categorical representations of $G$. Let … be the i…

Let $G$ be a Chevalley group over $\mathbb{F}_q$ and let $\check G$ be its Langlands dual Chevalley group. Define the category of potent representations of $G(\mathbb{F}_q)$ as the…

Let $G\circlearrowright M$ be a polarized hyperspherical $G$-variety with $M=T^*X$, and let $\check G\circlearrowright\check M$ be its Langlands-dual polarized hyperspherical varie…

Let $G$ be a reductive group, and let $G\operatorname{-cat}^{pot}$ denote its 2-category of potent categorical representations. A 2-category is 2-dualizable and 2-orientable when i…

Let $G$ be a reductive group and let $\check G$ be its Langlands dual group. Denote by $\mathcal{H}_G^{dR}$ and $\mathcal{H}_{\check G}^{dR}$ the de Rham potent Hecke monads, and b…

Let $G=GL_n(\a0\mathcal{K})$ and let $P$ be its mirabolic subgroup, with unipotent subgroup $U$ and character $\theta$ as above. Let $\a0\mathcal{C}$ be an irreducible cuspidal cat…

ULA module characterization conjecture. This functor induces an equivalence onto

Ngô's very central image conjecture. The Ngô functor defines a fully faithful braided monoidal functor on abelian categories, whose essential image is $\mathcal M(G)^G_{vc}$. Moreo…

Let $R$ be the integral coefficient ring, let $\overline R$ be the corresponding coefficient ring for the construction with $e$ replaced by $e+1$, and let $O^{\nu,\Delta}_{\mu,R}$…