27 problems

Let $W$ be a Weinstein manifold and let $L$ be its Lagrangian skeleton. Denote by $\mathcal{W}(W)$ the wrapped Fukaya category of $W$ and by $\operatorname{MSh}(L)$ the microlocal…

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 $M$ be a manifold and let $\Lambda\subseteq S^*M$ be a compact subanalytic Legendrian. Consider the cyclic trace objects…

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 $\bm L$ be a self-intersecting immersed Lagrangian brane, let $L_{\mathrm{SI}}\coloneqq L\times_XL$ be its self-intersection locus, and let $_{,}$ be the local system associate…

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 $(X,u<c_{\bm L})$…

Let $X$ be a Liouville manifold, and let the microlocal category constructed in the paper be denoted by … be the Novikov ring. The Novikov Fukaya equivalence conjecture. Our catego…

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

Swappability conjecture. The Legendrian stops in Example $$ are swappable.

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…

Let $\Lambda$ be a Legendrian knot in $\mathbb R^3$ and let $\mathbbm k$ be a field. For each integer $n\geq 1$, let $\mathcal{R}ep_n(\Lambda,\mathbbm k)$ be the $A_\infty$ categor…

Let $W$ be a Weinstein manifold and let $\Lambda\subset\partial W^c$ be a closed singular Legendrian. Let $W'$ be the Weinstein sector corresponding to the Weinstein pair…

Let $W$ be a Weinstein manifold and let $\Lambda\subset\partial W^c$ be a closed singular Legendrian. Let $W'$ be the Weinstein sector corresponding to the Weinstein pair…

In the case of Lagrangian knots in the Euclidean threefold with its standard contact structure, augmentations are algebraic objects associated with the knot, while microlocal sheav…

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, not necessarily complete fan in $N_\bR$. Let $X_\Sigma$ be the associated smooth tor…

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

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 $\Phi$ be the functor cited in the paper, and let the Coxeter structures be those defined in the paper's Sections 5.1 and 5.2. Microlocal Coxeter-structure conjecture. The func…

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 microlocal sheaf conjecture. There is a canonical equivalence of stable $\infty$-categories

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