15 problems

Let $X$ be a complex variety, let $T^*X$ be its cotangent bundle, and let $\Lambda\subset T^*X$ be a conical Lagrangian variety, such as the conormal variety to a stratification of…

Lagrangianity conjecture. $SS(\mathcal{F})$ is an analytic Lagrangian subspace of $T^*X$, meaning that it is an analytic closed subset and is Lagrangian on its regular locus. In pa…

Microlocal endomorphism conjecture.

Let $X$ be a smooth ambient space, let $f$ define the derived zero locus $\boldsymbol{Z}(f)$, and let $V^{\vee}$ be the ambient dual vector space. The source gives a closed immersi…

Let $X$ be a smooth ambient space and let $Z(f)\subset X$ be the zero locus of $f$. Model chains on $Z(f)$ using currents on $X$, and call a current smooth when it is represented b…

Let $X$ be a smooth space, let $\boldsymbol{Z}(f)$ be the derived zero locus associated to $f$, let $d4aa^f_{\Lambda}$ denote the microlocal homology object associated to…

Let $M$ be a real manifold, let $\pi_M:\mathfrak{X}_M\to M$ be the induced family of curves, and let $s\in M$. Write … where $\widetilde{\mathcal{N}}_{\Pi_M}$ is the universal nilp…

Generalization conjecture. This first equality should generalize to more general Legendrian knots and also to higher-dimensional Legendrian boundaries, for the appropriate notion o…

Pareschi–Popa adjoint-module conjecture. Every summand $\mathscr M\hookrightarrow\mathscr{A}\hspace*{-0.15em}d_\Theta$ is either a skyscraper sheaf or has support $A$.

Let $\lambda$ be an infinitesimal parameter, let $\Xi_\lambda({}^LG)$ be the relevant set of parameter–representation pairs, let $M(\phi,\rho)$ be the standard module, let…

Let $F$ be a local field, let $G$ be a quasi-split connected reductive linear algebraic group over $F$, let $\lambda\in\Lambda({}^LG)$ be an infinitesimal parameter, and let…

Let $G$ be a quasi-split connected reductive algebraic group over a $p$-adic field, and let Arthur's packet map be the map described in the preceding discussion. Geometric realizat…

Microlocalization conjecture. (a) $\eta^*\bmu(\operatorname{IC}(X))$ is constant in any chamber $\fC$. (b) There is a canonical isomorphism

Let $\mathcal{D}^\alpha$ be the microlocal sheaf of algebras, and consider objects of $\mathcal{D}^\alpha\!\operatorname{-mod}$ supported on $\pi^{-1}(\mathfrak{h}/W)$. The support…

Bimodule–microlocal cell conjecture. The bimodule Kazhdan–Lusztig cells coincide with the two-sided microlocal cells.