symp-foliations

(Ioan Marcut) Strong symplectic foliations of codimension-1 admit strong symplectic divisors as a consequence of Donaldson theory. What about foliations of higher codimension? (It is worth pointing out that in codimension-1 one obtains a non-singular foliation because of the symplectic analogue of Bertini's theorem: singular divisors generically appear in real families of dimension at least 2.) What about weak symplectic foliations, to which Donaldson theory does not apply?

(M. Bertelson) The kernel of a closed 2-form of constant rank is a transversally symplectic foliation. Is there a notion of duality between tangentially symplectic foliations and transversally symplectic foliations? In particular, given a transversally symplectic foliation, can one find a foliation transverse to it (which is then strong symplectic)? It is not even known whether an h-principle holds for transversally symplectic foliations on open manifolds. There is some progress regarding Seiberg-Witten for transversally symplectic foliations due to Kordyukov, Lejmi and Weber.

(Y. Mitsumatsu) This relates to the previous question: what can be said about symplectic manifold foliated by symplectic submanifolds?

(Y. Mitsumatsu) What about relations with other classes of foliations with tangent/transverse structure? What about the relation between transversely contact foliations with Engel structures?