Course Description:
This course is an introduction to symplectic geometry. Though this is the second part of a two quarter sequence, the class is somewhat independent of 257A. The first quarter covered mostly the topology of symplectic manifolds, and this quarter we plan to focus on their
geometry. The topics covered include:
- Hamiltonian systems and flows;
- Symplectic and Hamiltonian group actions
- Moment maps and Hamiltonian systems with symmetries
- Symplectic reduction, topology of symplectic quotients
- Convexity and fixed points of Hamiltonian group actions
- Duistermaat-Heckmann theorem, equivariant cohomology
- Morse theory and Floer theories: Hamiltonian Floer theory and Lagrangian Floer theory basic setup;
- applications: discussion of the Weinstein conjecture and Arnold conjectures.
This is meant to be mostly an introductory course to the subject, and
there are no formal prerequisites for this class, although a good
background in topology, geometry and analysis/PDEs is desirable.