15 problems

Smooth-to-holonomic equivalence conjecture. The inclusion

Sheaf quantization and Fukaya category conjectures. For each Lagrangian brane $\bm L$ in $X$, there is an almost quasi-isomorphism

Complex-constructible wrapping conjecture. For every object $\mathcal E$ of $\Sh_{\mathbb C\text{-}c}(M)$, there exists an inductive system $\{\mathcal E_i\}$ in…

Let $\bm L$ be a Lagrangian brane, let $CF_{\mathrm{SQ}}(\bm L,\bm L)$ be the colimit curved dga constructed from sheaf quantizations, and let $CF(\bm L,\bm L)$ be the correspondin…

Let $X$ be a symplectic manifold, let $\bm L$ be a Lagrangian brane, and let $c_{\bm L}>0$ be as in the classification theorem. A sheaf quantization of $\bm L$ in $(X,u<c_{\bm L})$…

Paracyclic lift conjecture. This simplicial $\infty$-category can be lifted to a paracyclic $\infty$-category.

Waldhausen S-construction conjecture. The relative Waldhausen $S$-construction of $m_\Lambda^l$ is the simplicial $\infty$-category

Extension conjecture. The construction $\operatorname{\mathfrak{w} sh}_\Lambda$ should extend from the zero section to the cotangent bundle $T^\ast M$.

Let $Q$ be a $d$-dimensional $\operatorname{Spin}^c$ manifold, let $\Lambda\subset T^*Q$ be a conic Lagrangian, and let $U\subset Q$ be open. Write…

Wrapped microlocal sheaves conjecture. There is a cosheaf of … , on $$ such that

Let $M$ be a free abelian group of rank $n$, let $N$ be its dual, and let $\Sigma$ be a smooth complete fan in $N_\bR:=N\otimes_\bZ\bR$. Let $X_\Sigma$ be the associated smooth tori…

Let $X$ be a complex manifold, let $\Lambda\subset T^*X$ be a conic Lagrangian support, and let $\mathcal{P\!er}_\Lambda(R)$ denote the stack of microlocal perverse sheaves with co…

Let $(\Sigma,\Gamma_\Sigma)$ be a punctured Riemann surface together with its skeleton, and let $\mathrm{CPM}(-)$ be the sheaf of dg categories on $\Gamma_\Sigma$ whose local restr…

Nadler–Tanaka's stratified constructible-sheaf conjecture. There is a canonical equivalence of stable $\infty$-categories

Suppose $\triangle$ is vertex-simplicial and $\triangle^\vee$ is facet-simplicial. Let $Z^\vee_\infty$ be the large volume limit and let $\Lambda^\infty$ be the associated Legendri…