Conférencier: Simone Gutt, Université Libre de Bruxelles 

Smooth almost complex structures on manifolds (in particular on symplectic manifolds) have various integrability properties. We have been interested in defining relevant properties which a non-integrable almost complex structure may have, in terms of its Nijenhuis tensor. In particular, we define the notions of minimally or maximally non-integrable almost complex structures and the notion of the transverse complex structure defined by an almost complex structure. We review some Dolbeault-type cohomologies associated to an almost complex structure.

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