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.
Official language of the school: English
Administrative and scientific coordinators
Course 1: "The Length Spectrum of a Riemannian Manifold", Otto VAN KOERT (Seoul National University, South Korea)
Course 2: "The Laplace Spectrum of a Riemannian Manifold", Felix SCHLENK (Université de Neuchâtel, Switzerland)
Course 3: "Symplectic Geometry", Esmaeel ASADI (IASBS, Iran)
Course 4: "Small Eigenvalue of Negatively Curves Surfaces", Asma HASSANNEZHAD (Bristol University, UK)
Course 5: "From the Laplace Spectrum to the Length Spectrum and Back", Urs FRAUENFELDER (Universität Augsburg, Germany)
Course 6: "The Role of the Action Spectrum in Symplectic Dynamics and Geometry", Urs FRAUENFELDER (Universität Augsburg, Germany)
Website of the school
How to participate