Henrique Bursztyn, MSRI and Université Libre de Bruxelles
Dirac Geometry

Dirac manifolds were introduced by Weinstein and Courant to provide a geometric framework for the study of mechanical systems with constraints. Examples of Dirac structures on manifolds include (pre-)symplectic forms, Poisson structures and foliations. In this talk, I will describe the basic features of the geometry of Dirac manifolds, pointing out their role in Poisson geometry and explaining their connection with the world of Lie algebroids and groupoids.