Topics in Symplectic Geometry

Poisson manifolds, examples, Local structure (Weinstein’s “splitting” theorem, transverse structure, the linearization problem), symplectic foliation; Symplectic realizations and Lie groupoids.
Courant algebroids and Dirac structures. Supergeometric viewpoint: symplectic N-graded manifolds, homological vector fields.
Introduction to “shifted” symplectic structures.

References:
M. Crainic, R. Fernandes, I. Marcut: Lectures on Poisson Geometry, GSM 217, AMS.
H. Bursztyn, A. Cattaneo, R. Mehta, M. Zambon: Graded geometry and generalized reductions. Arxiv: 2306.01508.
D . Roytenberg, On the structure of graded symplectic supermanifolds and Courant algebroids, Contemporary Math 315, 2002.

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