Symplectic groupoids appear as global counterparts to Poisson manifolds, in a manner similar to how Lie groups are global counterparts of Lie algebras. Moreover, they provide complete symplectic realizations, which are useful for relating Hamiltonian dynamics on the Poisson manifold (degenerate) and on the Symplectic groupoid (non-degenerate). We'll discuss the definition of symplectic groupoids, some concrete examples, and their properties.
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).
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