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Monday, March 7, 2016

**Abstract:** Weinstein's classical splitting theorem gives a local description, around any given point, of a Poisson manifold as a product of a symplectic factor and a transversal Poisson manifold, singular at the point. Similar splitting theorems are known in other settings, such as for foliations, Lie algebroids and generalized complex structures. I will describe a new approach to proving such theorems, that leads to various generalizations, including equivariant versions of the results. This is based on joint work with E. Meinrenken and H. Lima.