The first part of the course constitutes an introduction to symplectic geometry :
symplectic manifold, Darboux theorem, Marsden-Weinstein theorem. In the second part, I'll talk about Deformation Quantization theory. I'll present Boris Fedosov's
construction of a star product on every symplectic manifold, and I'll give the classification of these structures in terms of the second order de Rham's cohomology of the manifold at hand. This result constitutes an introduction to Kontsevitch's formality.
The course will be accessible to people who have a knowledge in basic notions of differential geometry (differentiable manifold, tangent bundle, tangent vector fields, differential form). Depending on the audience, I'll precisely recall these notions if necessary.
- Teacher: Bieliavsky Pierre