41 problems

Polterovich's conjecture. There exists a constant $C_M$, depending only on the symplectic manifold $(M,\omega)$, such that for every finite open cover $\mathcal{U}=\{U_i\}$ of $M$,

Givental's conjecture. The Floer $\mathcal{D}$-module and the quantum cohomology $\mathcal{D}$-module are the same; equivalently, $F=G$, with the components of $F$ giving appropria…

Let $c,c'$ be matching paths, let $\Lambda_c$ and $\Lambda_{c'}$ be the associated eventually Lagrangian submanifolds, and let $\mathcal A,\mathcal A'$ be directed $A_\infty$-categ…

Floer-theoretic identification conjecture. The Floer-theoretic coset is the same as the nearby Lagrangian torsion:

Nullhomotopy-dependence conjecture. The classes $\tau_{2k}(L,\gamma_t^i)$, for $i=1,2$, differ by $p_k(E)$.

Let $M$ be a del Pezzo surface of degree $1$, $5$, or $7$, and let $D$ be a generic smooth representative of $M$'s anticanonical divisor. A stable $\mathbb{R}$-polarization of $X$…

Let $\mathcal{S}$ be an abstract wrapped Floer setup, let $\mathcal{F}^{\text{pre}}_{\mathcal{S}}$ be its pre-wrapped Fukaya $A_\infty$-category, let $\widetilde{C}$ be the set of…

Let $(M,\omega)$ be a compact symplectic manifold, and let $\gamma$ be the Floer-theoretic pseudometric on the universal cover of $\mathrm{Ham}(M)$. Assume that $\omega$ vanishes o…

Arnold's conjecture for non-degenerate Hamiltonians.

Let $L\subset M$ be a Maslov $0$ Lagrangian torus, and let $C^*(L,M)$ be its Floer complex with differential satisfying … Here $\tau(L)$ denotes the relevant boundary-depth invaria…

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…

Spherical framed Floer spectrum identification conjecture. There is a homotopy equivalence of ring spectra

Degenerate Arnol'd conjecture. The intersection satisfies

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…

Assume the setting of the Lie monoid action conjecture in Floer theory, with the actions Hamiltonian. Let $\mathcal{W}(T^*G)$ and $\mathcal{W}(T^*H)$ denote the wrapped Fukaya cate…

Shelukhin's Hofer-Zehnder conjecture. If

Let $M=H_g^1\cup_{\Sigma_g}H_g^2$ be a Heegaard decomposition of a homology $3$-sphere, and let $I(M)$ denote its instanton Floer homology. For the trivial $SU(2)$ bundles on the h…

Let $f \in \mathbb{C}\{z_0,\dots,z_n\}$ be a convergent power series such that $f(\mathbf{0})=0$ that defines an isolated hypersurface singularity at the origin. For every integer…

Let $L$ be an oriented link with non-zero determinant. Let $SWF(L)$ be the link Floer stable homotopy object, let $\frak{s}_L$ be the spin structure determined by the orientation o…

Let $K$ be a knot, let $\#_nK$ denote the connected sum of $n$ copies of $K$, and let $\underline{\delta}_R$, $\bar{\delta}_R$, and $\delta(K)$ be the invariants used in the paper.…

Oscillation-energy conjecture. If $\varphi$ is a contactomorphism of an arbitrary compact contact manifold $Y$, then the implication above holds.

Let $(X,\omega)$ be a symplectic manifold, and let $L$ and $L'$ be Lagrangian submanifolds of $X$. Assume that $X$ is either closed or a Liouville manifold, and that $L$ is connect…

Qin's u-part Floer cohomology conjecture. There is an isomorphism

Let $\Lambda$ be a sutured Legendrian with boundary components $\partial_0\Lambda$ and $\partial_1\Lambda$ in $(\Gamma,\lambda_\Gamma)$. Let…