35 problems

The E2-degeneration conjecture. The spectral sequence degenerates at the $E_2$ page.

The critical-eigenspace conjecture. There is an isomorphism

The filtration conjecture. One has

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

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 $D$ 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 $X$ 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…

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 $P \in X$ 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 $W$ 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…

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 $(M,\a9\omega)$ 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 $M_\mathcal{R}$ 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…

Let $\mathcal{R}$ be a simple eigenray diagram, let $M_{\mathcal{R}}$ be the associated symplectic manifold, and let $\mathcal{Y}_{\mathcal{R}}$ be its proposed non-Archimedean mir…

Let $\mathcal{R}$ be a simple eigenray diagram, let $M_{\mathcal{R}}$ be the associated symplectic manifold, and let $\mathcal{Y}_{\mathcal{R}}$ be its proposed non-Archimedean mir…

Let $\mathcal{R}$ be a simple eigenray diagram, let $M_{\mathcal{R}}$ be the associated symplectic manifold, let $\mathcal{Y}_{\mathcal{R}}$ be the analytification of the scheme co…

Assume the log Calabi–Yau condition, so that $\lambda_i=2$ for every divisor component, and assume the minimal Chern number of $M$ is at least $2$. For each $i$, let $B_i$ be the c…

In Tonkonog's setup, let $\mathcal{BS}\in SH^0(X;\Bbbk)$ be the class obtained by counting holomorphic caps, and write $\beta=\beta_1+\beta_2+\cdots$ for the filtration components…