## 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

Prerequisites: Topology I (Manifolds). Basic knowledge of symplectic geometry would be helpful.

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.