19 problems

Stabilized Lagrangian isotopy conjecture. If $L_1$ and $L_2$ are smoothly ribbon isotopic, then after stabilizing both cobordisms, they become Lagrangian isotopic.

Let $\mathcal K$ denote the symplectic bielliptic surface, and let $\operatorname{Cob}^{trop}(\mathcal K)$ be the subgroup of the Lagrangian cobordism group…

Functoriality conjecture. There is an $L_\infty$ morphism from the $L_\infty$ algebra $((\mathcal{A}^+)^{\operatorname{comm}},\{\ell_k^+\})$ of $\Lambda^+$ to the $L_\infty$ algebr…

Let $L_0$ and $L_1$ be Lagrangian isotopic submanifolds, and let $K:L_1\rightsquigarrow L_0$ be a Lagrangian cobordism. Let $d(L_0,L_1)$ denote the minimal flux distance, defined b…

Let $\Lambda_{-}$ and $\Lambda_{+}$ be the Legendrian knots described in the satellite construction, and let $P\subset J^1S^1$ be the Legendrian clasp tangle used to form their sat…

Duality compatibility conjecture. For $j=1,\ldots,s-1$, the quasi-isomorphisms

Biran–Cornea identification conjecture. The categories $T^s$ of Biran and Cornea are the discrete colored planar operads associated to the $s$-dot constructions of…

Paracyclic compatibility conjecture. The map is compatible with the paracyclic action on the $s$-dot construction.

Compatibility conjecture. The filtration of the vertical-collar theorem defines a map of colored planar $\infty$-operads to the colored planar $\infty$-operad obtained from the $s$…

Let $(W;L_0,L_1)$ be an exact Lagrangian cobordism, and let a Lagrangian suspension denote the suspension associated to a Hamiltonian isotopy. Biran and Cornea's conjecture. Any ex…

Nadler–Tanaka's wrapped-Fukaya conjecture. The continuation-map functor induces an equivalence of stable $\infty$-categories

Nadler–Tanaka's cosheaf conjecture. The functor

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

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

Nadler–Tanaka's cotangent-bundle conjecture. The object $T_x^*X\in\Lag_X(T^*X)$ is a generator; every object is a finite colimit of objects $T_x^*X[k]$, $k\in\mathbb Z$; and

Nadler–Tanaka's endomorphism-spectrum conjecture. The spectrum $\cE$ is connective and

Nadler–Tanaka's point-generation conjecture. The object $pt\in\Lag_{pt}(pt)$ is a generator, every object of $\Lag_{pt}(pt)$ is a finite colimit of objects $pt[k]$ for…

Let $cLambda$ be a Legendrian knot in $cmathbb{R}^{3}$, and let $L_{cLambda}$ be an exact Lagrangian filling with $cemptysetcprec^{ex}_{L_{cLambda}}cLambda$. The notation…

Let $\mathcal{K}0$ and $\mathcal{K}1$ be Legendrian knots in $(Y,xi)$, and suppose that $\mathcal{K}0prec{\Sigma}\mathcal{K}1$ is a Lagrangian cobordism of arbitrary genus. Write…