17 problems

Let $V$ be a symplectic vector space, let $X'\subset \P(V)$ be an irreducible Legendrian subvariety, let $g\in\mathfrak{sp}(V)$ be a nilpotent endomorphism, and let $m$ be an integ…

Let $X\subset \P^{2n-1}$ be an irreducible indecomposable Legendrian subvariety, and let $G<\P\operatorname{GL}_{2n}$ be a connected subgroup preserving $X$. Automorphism conjectur…

Let $(M,g)$ be a globally hyperbolic $(3+1)$-dimensional spacetime with a Cauchy surface diffeomorphic to a subset of $\mathbb{R}^3$, and let $N$ be its manifold of light rays. For…

Let $Y$ be the ambient space and let $\Lambda_n$ be the specified Legendrian stop. Write $\mathcal L^{\mathrm{emb}}_{\Lambda_n}(Y)$ for the moduli space of stops with embedded Lagr…

Let $\lambda$ be a Legendrian link such that $\mathcal{M}_1(\lambda)$ has a cluster structure. Let $L_1$ and $L_2$ be exact Lagrangian fillings of $\lambda$, and let…

Let $\rho$ be the twisting monodromy, let $\rho^k$ denote its $k$-fold iterate, and let $\Sigma_{\rho^k}(\lambda(2,n))$ be the corresponding twist-spun Legendrian. Let $f(k)$ be th…

Let $\mathbb{S}^5\subset\mathbb{C}^3$ be the unit sphere, and let $\Sigma_H\subset\mathbb{S}^5$ be the hexagonal Legendrian minimal torus. For a Legendrian surface…

Let $W$ be a stopped Weinstein manifold and let $\Lambda$ be a singular Legendrian submanifold in its boundary. Its Chekanov–Eliashberg dg-algebra is the dg-algebra associated to…

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

Let an annulus-type surface be an embedded surface whose underlying domain is an annulus. Assume it is minimal and Lagrangian in the unit ball, with Legendrian capillary boundary o…

Let $L\subset(\mathbb{C}P^2,\omega_{\operatorname{FS}})$ be an embedded monotone Lagrangian two-torus, and let $\Lambda$ be the Legendrian lift of its canonical threefold Bohr–Somm…

Let $n\geq 1$, let $\mathbbm{k}$ be a field, and let $\Lambda\subset\mathbb{R}^3$ be a Legendrian link. The representation–sheaf conjecture. The $A_\infty$ category…

Causal Legendrian-linking conjecture. Assume that one cannot put a $Y^x_{\ell}$ Riemann metric on the Cauchy surface $M$. Then two events $x,y\in X$ are causally related if and onl…

Legendrian knots are Legendrian submanifolds in the contactization of a one-dimensional base, and their Legendrian contact homology is encoded by a differential graded algebra gene…

Legendrian Gronwall conjecture. Every Legendrian 3-web admits at most one distinct local linearization in $\mathbb{P}^3$, except when it is locally equivalent to the dual 3-web of…

Let $\varphi_1,\varphi_2:(\mathbb{R}^2,0)\to(\mathbb{R}^3,0)$ be two $C^\infty$ map-germs of pedal unfolding type. Let $\Phi_1,\Phi_2:(\mathbb{R}^2,0)\to(\mathbb{R}^3,0)$ be two no…

Conjecture on linearly normal Legendrian varieties. $X$ is one of the subadjoint varieties.