Cohomologous Symplectic Forms with Different Gromov Widths

For closed symplectic manifolds, the Gromov width is among the most fundamental symplectic capacities: it measures the size of the largest embedded symplectic ball and is sensitive to the perturbation of the symplectic forms. A natural question, posed as Problem 46 in McDuff-Salamon's problem list, asks whether there are cohomologous symplectic forms with different Gromov widths. In this talk, I will explain how to obtain such examples in dimension 6 from dimension 4, by adapting Ruan's early example of deformation inequivalent symplectic forms.