University of Toronto's Symplectic Geometry Seminar

Abstract: This will be the first talk in a series of two. I will present an elementary introduction to Lie algebroids and groupoids, via examples, stressing their role in Poisson geometry. Lie algebroids are natural generalizations of Lie algebras and often arise in connection with singular geometric structures (such as a Poisson structure). Lie groupoids are the corresponding global objects and often play an important role as an intermediate object linking classical and noncommutative geometries. In Poisson geometry, symplectic groupoids provide a natural framework for the study of moment maps and hamiltonian spaces. (The second talk, next week, will discuss Lie group-valued moment maps in this framework.)