Abstract:

In this talk, I will provide a precise definition of the group of Hamiltonian homeomorphisms which will set the stage of C⁰ Hamiltonian dynamical systems and C⁰ symplectic topology. Then I will explain how to extend various known symplectic invariants, (e.g., displacement energy and spectral invariants) to their C⁰ counterparts. If time permits, I will discuss several foundational open problems related to the group of Hamiltonian homeomorphisms.