symp-foliations

The topic related to the workshop that I am recently interested in is the study of “Poisson transversals” in Poisson geometry. These submanifolds play in Poisson geometry the role of symplectic submanifolds in symplectic geometry. A Poisson transversal is a submanifold in Poisson manifold that intersects the symplectic leaves transversally and symplectically. So far I managed to extend some of the simple results from the symplectic setting (in collaboration with Pedro Frejlich).

My student Florian Zeiser is working on the question of existence of compact Poisson transversals. He's trying to extend Donaldson's proof of existence of compact symplectic submanifolds. This was already done successfully by David Martinez Torres for codimension-one “calibrated” symplectic foliations. Florian is trying to extend this result to higher codimension (but still for “calibrated” symplectic foliations).