8 problems

Let $G$ be a quasi-split reductive group over $E$, let $\check{G}$ be its Langlands dual group, and assume $\ell\nmid\lvert\pi_0(Z(G))\rvert$. Let $W_E$ be the Weil group and let…

Let $G$ be a quasi-split reductive group over $E$, let $\operatorname{Bun}_G$ be its moduli stack of $G$-bundles, and let $\operatorname{Bun}_G^b$ denote the stratum indexed by…

Fix a quasi-split reductive group $G$ over a local field $E$, and let $W_E$ be its Weil group. Let $\check{G}$ be the Langlands dual group, and let…

Categorical local Langlands conjecture. There is an equivalence

Categorical local Langlands correspondence. For each standard Levi subgroup $M$ of $G$, there is a fully faithful functor

Let $\mathbb{E}$ be either $\overline{\mathbb{Q}}_\ell$ or $\overline{\mathbb{F}}_\ell$, and regard the indicated compactly induced representations as sheaves on…

Fargues–Scholze's categorical Langlands conjecture. There is a canonical isomorphism between these two $\infty$-categories.

Module-category conjecture. The 2-category of surface operators at $t=0$ can be described in terms of module categories over the monoidal category of boundary line operators for th…