7 problems

Gaitsgory's conjecture. There is an equivalence of monoidal categories

Let ${\mc C}$ be a smooth projective algebraic curve, let $p_i$ be marked points, let $L_{\lambda_i,{}^Lk}$ be the relevant modules for the affine algebra at level ${}^Lk$, and let…

Let $G$ be the group associated with $\mathfrak{g}$, let $\operatorname{Gr}_G$ be its affine Grassmannian, and let $\operatorname{Whit}^c(\operatorname{Gr}_G)$ denote the Whittaker…

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra, let ${}^L\mathfrak{g}$ be its Langlands dual, and let $\widehat{{}^L\mathfrak{g}}_{{}^Lk}\text{-mod}^0$ be the semisi…

Whittaker and theta-lifting conjecture. (i) $\mathcal K_E$ is a perverse sheaf, each of whose $\mathbb Z/2\mathbb Z$-parity pieces is irreducible, and

Parabolic compatibility conjecture. There is an automorphism $\delta:\operatorname{Bun}_n\widetilde\to\operatorname{Bun}_n$ such that the diagram

Quantum Langlands conjecture. There is an equivalence