The existence of codimension one foliations on compact manifolds has a nice history, starting with Reeb's foliation on $S^3$ that marked the birth of Foliation Theory, then on general 3-manifolds, then Lawson's foliations on $S^5$ and then on all odd-dimensional sphere, up to the general characterization of Thurston via the Euler characteristic. The analogous question for symplectic foliations is far from being understood- it is only rather recently that Lawson's foliation on $S^5$ was turned onto a symplectic one, by Mitsumatsu, but the construction is rather involved.
On the other hand, the confoliations of Eliashberg-Thurston revealed very close relationship (via actual deformations) between foliations foliations and contact structure. That theory is well developed only in dimension 3 and that is due, I believe (at least in part), to not noticing that when moving to higher dimensions one should be looking not only at foliations, but at symplectic ones. As a side remark: also Mitsumatsu's construction exploits the geometry of contact forms and adapted open book decompositons.
The aim of the talk will be to present a new, we believe much simpler and more conceptual, approach to Lawson's foliation on $S^5$, based on log-symplectic geometry/stable generalized geometry instead of contact geometry. That is joint work with my colleague Gil Cavalcanti.
