Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures (cf. Open Problem 1 in McDuff & Salamon). Given a formal symplectic manifold, i.e. a closed manifold $M$ with a non-degenerate 2-form and a non-degenerate second cohomology class, we investigate when its natural stabilization to $M$ $ \times$ $T^2 $ can be realized by a symplectic form.
We show that this can be done whenever the formal symplectic manifold admits a positive symplectic divisor. It follows that if a formal symplectic 4-manifold, which either satisfies that its positive/negative second betti numbers are both at least 2, or that is simply connected, then $ M$ $ \times$ $T^2 $ is symplectic.
This is joint work with Fabio Gironella, Fran Presas, Lauran Touissant.