Poisson manifolds and their associated stacks

Lie groupoids with Morita equivalence are a convenient model for the study of singular manifolds. This talk will explain how one can interpret a symplectic groupoid and symplectic Morita equivalence as a model for a singular Dirac manifold. To that end, we will define a site (a category with a topology) whose objects are Dirac manifolds, DMan, and explain how to associate a stack over DMan to any symplectic groupoid. Furthermore, we will relate isomorphisms of such stacks with symplectic Morita equivalences.Non UBCUnreviewedAuthor affiliation: IllinoisGraduat