Abstract: 

Two simply-connected smooth 4-manifolds are homeomorphic if and only if their stabilisations (their products with \(S^{^2}\)) are diffeomorphic. The Donaldson 4-6 question ask whether this fact can be lifted to the symplectic category. Concretely, it conjectures that the underlying smooth manifolds of two symplectic manifolds are diffeomorphic if and only if stabilisations are deformation equivalent. I will first describe symplectic structures and the difficulties in distinguishing them. Subsequently, I will explain one example of a smooth 4-manifold admitting two symplectic forms which remain deformation inequivalent after stabilisation, and why two symplectic manifolds, whose stabilisations are deformation equivalent, have the same Gromov-Witten invariants. This is joint work with Luya Wang.