60 problems

Brylinski's conjecture. Every $k$-de Rham cohomology class contains a symplectic harmonic representative.

Let $D$ be a Liouville domain whose boundary $partial D$ has no contractible Reeb orbits. The intrinsic symplectic cochains $SC^*(D)$ and the $S^1$-equivariant symplectic cochains…

Let $P \in X$ be a compound Du Val singularity, let $\Uv$ be its Milnor fiber, and let $\SH^i(\Uv)$ denote its symplectic cohomology in degree $i$. Evans–Lekili conjecture. The sin…

Let $M$ and $M^{\vee}$ be open Calabi–Yau manifolds that are mirror to each other in the sense of homological mirror symmetry. A ring isomorphism is an isomorphism preserving the p…

Let $M$ be an exact symplectic manifold satisfying Assumption, and let … be the natural open–closed string map from symplectic cohomology to the Hochschild cohomology of the Fukaya…

Mod-$p$ vanishing conjecture. Assume $p$ is chosen so that holds. Then

Relative Etingof–Lee $p$-curvature conjecture. The connection satisfies

Let $(M,\omega)$ be a closed symplectic manifold and let $K\subset M$ be a compact subset with non-empty interior, in the sense specified by the paper's section on symplectic-detec…

Let $(M,bomega)$ be a closed symplectic manifold and let $K_0\subset M$ be a compact subset. The relative symplectic cohomology $SH_M(K;\Lambda_{\geq0})$ is defined for compact sub…

Let $X$ be a symplectic manifold, let $V\subset X$ be a symplectic crossing divisor carrying the symplectic form, and let $D\subset X\setminus V$. The intrinsic symplectic cochains…

Let $X$ be a Liouville domain with stable tangent bundle classified by $X \to BU$, and let $\Phi \to BU$ be a based space over $BU$. Suppose the classifying map $X \to BU$ factors…

Let $c_{-}^{\alpha}(\varphi_t)$ and $c_{+}^{\alpha}(\varphi_t)$ be the order measurements of a contact isotopy, and let $c_{\alpha}(1;\varphi_t)$ be the spectral invariant of the u…

Calabi–Yau analogue conjecture. All of the results and conjectures in the paper have analogues when $M$ is Calabi–Yau, with no Hypothesis A required.

Relative symplectic cohomology conjecture. There is an isomorphism of graded $R$-modules

Let $Y \to X$ be a small $\bQ$-factorialization of a compound Du Val singularity $P \in X$. Let $\ell$ be the number of irreducible components of the exceptional locus, let $\Uv$ b…

Let $W$ be a convex-at-infinity symplectic manifold. For each contact isotopy $\varphi_t$, let $\mathrm{HF}(\varphi_t)$ denote its Floer cohomology, and let $\mathrm{SH}^{e}(W)$ be…

Let $M$ be a closed graded manifold with a weakly involutive cover $M=\bigcup_{i=1}^N C_i$, and let $Y=\bigcup_{i=1}^N Y_i$ be a smooth rigid analytic space over $\Lambda$ with an…

Let $M_d$ be the complement of $d\geq n+2$ generic hyperplanes in $\mathbb{CP}^n$, and let $\mathit{SC}_{S^1}^*(M_d)$ be its geometric $S^1$-equivariant symplectic cochain…

Cyclic coordinate-function conjecture. If $T^*Q$ admits a cyclic coordinate function, then $Q$ is diffeomorphic to $S^1\times\Sigma_g$, where $g\geq0$, or a spherical space form. T…

Ganatra-Pomerleano's conjecture. If $T^*Q$ admits a coordinate function, then $Q$ is diffeomorphic to $S^1\times\Sigma_g$ for some $g\geq0$. The conjecture is presented as motivate…

Twisted symplectic cohomology vanishing conjecture. A deformation argument should imply

Borman–Sheridan class compatibility conjecture. Under this equivalence, the action of $t$ on $\mathcal{W}_{S^1}(X)_{-1}$ coincides with the action of $\tau$ on…

Let $(M,\a9omega)$ be a closed symplectic manifold and let $K\subset M$ be a compact subset. The subset $K$ is SH-visible when its relative symplectic cohomology satisfies … where…

Let $\pi_\mathcal{R}:M_\mathcal{R}\to B_\mathcal{R}$ be the symplectic fibration, let $L$ be its Lagrangian section, and let $P\subset B$ be a small admissible polygon. Set…

Let $M_\mathcal{R}$ be the symplectic cluster manifold, let $\mathcal{Y}_\mathcal{R}$ be its mirror, and suppose that all node multiplicities in $\mathcal{R}$ are $1$. Write…