Nikolay Martynchuk (Moscow Center for Fundamental and Applied Mathematics and FAU Erlangen-Nuremberg)
On applications of Morse theory to Hamiltonian systems
Morse theory is a powerful tool for studying the topology of smooth manifolds. This theory and generalisations thereof have numerous applications in differential and symplectic geometry and the theory of dynamical systems. The Bott periodicity theorem, Smale's proof of the generalised Poincaré conjecture, and the Floer theory are some of the most striking examples.
In this talk, we shall focus on applications of Morse theory to autonomous Hamiltonian systems. In particular, we address the general question of the topology change of energy levels in such systems and discuss applications to problems arising in the theory of integrable systems and celestial mechanics.
This talk is based on a joint work with A. Knauf (FA University Erlangen-Nürnberg).