symp-foliations

Since the meeting on Engel structures at AIM in April, I have been extensively working on the geometric construction of Engel structures (not h-principle type but really geometric, so it is just furnishing our fundamental understanding of Engel structures)and I myself feel what I have understood so far must have deep relations with Poisson structures or transverse contact foliations and so on.

As mentioned above, also some perspectives for symplectic or transversely contacgt foliations arising from recent research from Engel structures can be a possible candidate.

One of my interest around the topic of this conrefence is, though it is not on codimension one foliation, but on foliations on symplectic manifold whose leaves are symplectic submanifolds. This topic comes from our joint work with Elmar Vogt which explains the process of `turbulization' of 2-dimensional foliations on 4-manifolds. One main topic might be the notion of 'tightness' of 2-calibrated codimension-1 foliations (i.e., codimension one foliations on odd dimensional manifolds with a closed 2-form which restricts to each leaves as a symplectic structure) which fails in the case of leafwise symplectic foliation. I do understand the issue from the works (of you and Fran with David Martines-Torres) extending Donaldson's asymptotically holomorphic geometry to the codimension one setting and Fran has been working on this. I belileve at least philosophically the study of foliations with symplectic leaves on symplectic manifolds must have deep relationships and it should be extended under the really deep and difficult concept of `integrability' for Poisson structures.