3 problems

Let $X$ be a symplectic $4$-manifold, let $f$ be a sufficiently high-degree pencil on $X$, and let $\mathcal{I}_f$ denote the integer-valued invariants counting sections of the ass…

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…

Let $G=G(r,k)$ be the Grassmannian, let $P(X_1,\dots,X_r)$ be a polynomial of weighted degree $kd-r(k-r)(g-1)$, and let $N_d(P,g)$ denote the genus-$g$ degree-$d$ Gromov invariant.…