Course: Symplectic Geometry.

Lecture: Tuesdays and Thursdays 8:00 - 9:30, seminar room 5, ground floor, Mathematics Department.

Office Hours: Wednesdays 4-5 pm, room 05a.

Exercise Sessions with Marc Kegel: Thursdays 4-5:30 pm, Übungsraum 1.

Homeworks are posted here.

Exam: Tuesday, February 14th, 9:00 am, Hörsaal, Mathematischen Institut.

Course description:

The course is intended for Master students. It is required to have a good background in differential geometry and algebraic topology. Symplectic geometry is a study of manifolds equipped with a non-degenerate closed 2-form. These manifolds are always even dimensional and equipped with an almost complex structure. The motivation for studying such structures comes from physics: a prototype of a symplectic manifold is the phase space of a particle moving in the three dimensional space. Symplectic geometry has strong connections with algebraic geometry, mathematical physics and combinatorics. The goal of this course is to give an overview on main concepts of symplectic geometry. We will analyze the properties of such manifolds, discuss various important examples and ways of constructing new symplectic manifolds from old ones (symplectic reduction, symplectic cutting), and study Hamiltonian group actions.It is mandatory to register also for the exercise session for "Symplectic Geometry".

The lecture will follow closely the book:

Ana Cannas da Silva "Lectures on Symplectic Geometry", Lecture Notes in Mathematics, Springer-Verlag.

Suggested additional reading:

McDuff, Salamon "Intorduction to Symplectic Topology", Oxford Mathematical Monographs.