Title: Towards the strong Arnold conjecture

Abstract:
We discuss the relative and absolute versions of the stable Arnold conjecture,
which improve the relative and absolute versions of the homological Arnold
conjecture and are closely related to the strong Arnold conjecture.  In the
relative setting, we show that the number of Reeb chords on a Legendrian
submanifold, which admits an exact Lagrangian filling satisfying some
technical conditions, is bounded from below by the stable Morse number of the
filling.  In the absolute setting, given a closed symplectically aspherical
manifold, we show that the number of fixed points of a generic Hamiltonian
diffeomorphism on it is bounded from below by the stable Morse number of this
manifold. This is joint work with Georgios Dimitroglou Rizell.