Working Group on Symplectic Dynamics

The Conley conjecture, recently established by Nancy Hingston, asserts that every Hamiltonian diffeomorphism of a standard symplectic 2n-torus admits infinitely many periodic points. While this conjecture has been extended to more general closed symplectic manifolds, all the known proofs require sophisticated arguments. In this talk, we use generating function techniques in symplectic geometry to give a simple proof of the conjecture for those Hamiltonian diffeomorphisms of the torus that are C^1-close to the identity.