Introduction to Poisson geometry
Professor: Henrique Bursztyn
- Aulas: Seg/Qua 13:30 - 15:00, sala 347
- Syllabus: The course offers an introduction to Poisson geometry. Topics to be discussed include:
- Poisson brackets and bivectors. Examples (linear, log-symplectic, Poisson Lie groups/homogeneous spaces, etc).
- Local structure: Weinstein's splitting, transversal structure, linearization problem.
- Symplectic foliation.
- Some Poisson invariants: Poisson cohomology, modular class.
- Symplectic realization and dual pairs.
- Interlude: Lie algebroids and Lie groupoids.
- Symplectic groupoids, integrability problem.
- Poisson Lie group(oids)s. Courant algebroids and Manin triples.
- Elements of Dirac geometry: pullbacks, pushforwards, gauge equivalences.
- Submanifolds in Poisson geometry.
- Bibliography:
- M. Crainic, R. Fernandes, I. Marcut: Lectures on Poisson geometry. GMS 217, AMS.
- A. Cannas da Silva, A. Weinstein: Geometric models for noncommutative algebras. Berkeley lecture notes, AMS.
- J.-P. Dufour, N.T. Zung: Poisson structures and their normal forms. Progress in Math., Birkhauser.
Other textbooks will be suggested during the course.
- The course evaluation will be based on problem sets and a project.
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