The strong Arnold conjecture on symplectic fixed points

The strong Arnold conjecture states that every Hamiltonian symplectomorphism on a closed symplectic manifold $M$ has as many fixed points as the number of critical points of a smooth function on $M$. In my talk I shall survey progress in the strong Arnold conjecture including recent results obtained by Kaoru Ono and myself in 2015 concerning the strong Arnold conjecture on compact nonsimply connected manifolds.