Mathematics

Program:

 

- Introduction to critical point theory (Morse theory, Lusternik-Schnirelmann theory, equivariant methods and Fadell-Rabinowitz index)

- Introduction to symplectic dynamics: Hamiltonian flows, including geodesic flows and, more generally, Reeb flows

- The periodic orbits problems: introduction, and proof of a selection of results (multiplicity of periodic orbits, spectral characterization of Besse and Zoll Reeb flows, etc.).

- From dynamics to symplectic topology: symplectic capacities, and applications (symplectic and contact non-squeezing, local Viterbo conjecture, etc.)