MAT 1341S Topics in Differential Geometry: Poisson Geometry

Classes: M 10-12, W 11-12 BA 6180

This course is an introduction to Poisson geometry and related subjects.

• Poisson brackets and Poisson bivector fields
• Symplectic foliation
• Weinstein splitting theorem
• Lie algebroids and Lie groupoids
• Symplectic groupoids
• Dirac structures
• Poisson Lie groups and Poisson actions

The course mark will be based on attendence, as well as a short essay (two to four pages) on a topic related to Poisson geometry or Dirac geometry. For example, it could be a synopsis of some paper, or some encyclopedia-style summary of some topic. It should be `reasonable', but should not be a time sink.

Some possible topics:

• deformation quantization
• Schouten brackets, Gerstenhaber brackets
• Poisson groupoids
• Poisson homology and cohomology
• history of Poisson geometry
• Lie bialgebroids
• Cluster algebras and Poisson geometry
• the super-geometric approach to Lie and Courant algebroids
• the Poisson sigma model
• Dirac structures and the classical dynamical Yang-Baxter equation
• Bi-Hamiltonian systems
• a topic of your choice!

Course notes will be posted here.

Our main references are:

• E. Meinrenken: Poisson Geometry from a Dirac perspective. Available at the arXiv.

• Dufour-Zung: Poisson Structures and Their Normal Forms, Birkhaeuser Verlag. Electronic copy available from UofT library.

• Fernandes-Marcut: Poisson Geometry. Available here.

• Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke Poisson structures, Springer. Electronic copy available from UofT library.