Seminar on Symplectic Geometry
Prof. Dr. Umberto Hryniewicz, Dr. Matthias Meiwes
The meetings take place on Wednesday, from 10:30 to 12:00, via Zoom.
Symplectic manifolds are the phase spaces of Hamiltonian systems. The goal of this seminar is to cover basic facts on symplectic geometry and Hamiltonian systems. Topics range from simple examples from classical mechanics, to more advanced topics like, for instance, the analysis of the Action functional and the geometry of the group of Hamiltonian diffeomorphisms.
- Symplectic linear algebra.
- Maslov index.
- Hamiltonian systems and calculus of variations.
- Basic facts about symplectic manifolds.
- Symplectic diffeomorphisms, Flux homomorphism, Hamiltonian diffeomorphisms, Calabi homomorphism.
- Symplectic capacities and non-squeezing.
- Basics on Hofer geometry.
- Basic facts about contact manifolds.
Plan of the talks
- MCDUFF, D. and SALAMON, D. - Introduction to Symplectic Topology, Chapter 2 and 3 Oxford Graduate Texts in Mathematics 27, Oxford University Press, Oxford, 2017.
Hamiltonian dynamics and Symplectic Capacities:
- HOFER, H. and ZEHNDER, E. - Symplectic Invariants and Hamiltonian Dynamics Chapter 1 and 2 Modern Birkhäuser Classics, Birkhäuser Boston, Boston 2011.