Séminaires : Séminaire Géométrie et Topologie

Given a Lagrangian submanifold L of a symplectic manifold M, an important goal of symplectic topology is understanding its Hamiltonian orbit. Essentially, Hamiltonian diffeomorphisms of M are special diffeomorphisms that preserve its symplectic form, and the Hamiltonian orbit of L is the collection of all Lagrangian submanifolds in M that are the image of L under such a diffeomorphism. When M is equipped with a metric, this Hamiltonian orbit becomes a metric space through the classical Hausdorff distance, and understanding its topological and metric properties are central goals of C^0 symplectic topology. In this talk, I will explain how—in the presence of a certain rationality condition on L—we can begin to understand a Hausdorff neighbourhood of L in its Hamiltonian orbit. This is based on joint work with R. Leclercq, M. Atallah, and E. Shelukhin.