7 problems

Symplectic invariance and Taubes correspondence conjecture. Once $f$ is of sufficiently high degree, $\mathcal{I}_{(X,f)}$ should be independent of $f$ and define a symplectic inva…

For each degree $d$, let $\mathbf{T}_{d}^{a}$ denote the count associated with the ellipsoidal superpotential for $\CP^2$ with parameter $a>1$. Monotonicity conjecture. The count…

Let $d$ be an integer and let $p/q>1$ be a reduced fraction. The count $\mathbf{T}_{d}^{p/q}$ is the index-zero finite-energy holomorphic-plane count associated with degree $d$ cur…

Let $(X,J)$ be a closed almost complex $4$-manifold. Suppose there exists a closed $2$-form $\phi$ such that, for every $x\in X$, there is a closed connected pseudoholomorphic curv…

Eliashberg–Hofer conjecture. The differential satisfies $d^2=0$, and the homology $H_*(C_*,d)$ is independent of the contact form $\alpha$ for $\xi$ and of the complex structure…

Let the assumptions of Lemma(c) hold, and consider the inequality in Remark. Equality conjecture. Under these assumptions, the inequality is an equality. This proposed equality wou…

Let $(M,\omega)$ be a closed symplectic manifold of real dimension at least four, and let ${\mathcal J}_{\operatorname{reg}}$ denote a subset of the space of smooth $\omega$-tame a…