Fixed Points of Small Hamiltonian diffeomorphisms and the Flux Conjectures

The C0 flux conjecture predicts that a symplectic diffeomorphism that can be C0

 approximated by a Hamiltonian diffeomorphism is itself Hamiltonian. We describe how the flux conjecture relates to new instances of the strong Arnol’d conjecture and make progress towards the C0 flux conjecture. This is joint work in progress with Egor Shelukhin.