One of the fascinating bridges between classical mechanics and quantum physics is expressed in the fact that the length spectrum and the Laplace spectrum of a closed Riemannian manifold determine each other (at least generically). The main goal of this school is to introduce graduate students and young researchers to basic facts on these two spectra, and to the above correspondence.
The length spectrum generalizes to the action spectrum of an autonomous Hamiltonian function. Floer homofogy filtered by the action spectrum can be used to construct so-called action selectors, that are a principal tool in modern symplectic geometry and dynamics.
The second goal is to understand this relevance of the action spectrum in symplectic geometry.
A third, more hypothetical, goal is to see which parts of the two sides can be related.
Langue officielle de l'école : anglais