Symplectic rational connectedness conjecture

Let $X$ be a smooth projective rationally connected variety. A Gromov–Witten invariant with two point insertions is an invariant of the form

$$\langle [pt], [pt], A_1, \ldots, A_n, I \rangle^X_{0, \beta},$$

where $A_i \in H^*(X,\mathbb{Q})$ and, if $n\geq 1$, $I$ is the pull-back of a cohomology class from $\overline{M}_{0,n+2}$ via the forgetful map

$$\overline{M}_{0,n+2}(X,\beta)\to\overline{M}_{0,n+2}.$$

Symplectic rational connectedness conjecture. There is a non-zero Gromov–Witten invariant of this form. This conjecture proposes a symplectic analogue of rational connectedness, and motivates the notion of a symplectic rationally connected manifold. Its status is not resolved in the source.