MAT 1341S Topics in Differential Geometry: Poisson Geometry
M 10-12, W 11-12 BA 6180
This course is an introduction to Poisson geometry and related subjects.
Prerequisites: Topology I (Manifolds). Basic knowledge of symplectic geometry would be helpful.
- 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
Our main references are:
- E. Meinrenken: Poisson Geometry from a Dirac perspective.
Available at the
Poisson Structures and Their Normal Forms,
Birkhaeuser Verlag. Electronic copy available from UofT library.
- Fernandes-Marcut: Poisson Geometry. Available
- Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
Poisson structures, Springer. Electronic copy available from UofT library.