Poisson manifolds can sometimes have complex behavior, such as a complicated underlying foliation, and symplectic forms varying from leaf to leaf, among other features. One possible way to deal with these difficulties is to realise the Poisson manifold as some kind of "quotient" of a symplectic manifold - a much simpler (i.e. non-degenerate) Poisson manifold. We'll discuss the definition of symplectic realizations, some concrete examples, and constructions.

We'll follow the book:

Crainic, M.; Fernandes, R. L.; Mărcuţ, I., Lectures on Poisson geometry. Graduate Studies in Mathematics 217. American Mathematical Society (AMS) (2021).