Abstract: 

Consider a symplectic manifold $(M,\omega)$, a closed coisotropic submanifold $N$ of $M$, and a Hamiltonian diffeomorphism $\phi$ on $M$. A leafwise fixed point for $\phi$ is a point $x\in N$ that under $\phi$ is mapped to its isotropic leaf. These points generalize fixed points and Lagrangian intersection points. In classical mechanics leafwise fixed points correspond to trajectories that are changed only by a time-shift, when an autonomous mechanical system is perturbed in a time-dependent way.

J. Moser posed the following problem: Find conditions under which leafwise fixed points exist and provide a lower bound on their number. A special case of this problem is V.I. Arnold's conjecture about fixed points of Hamiltonian diffeomorphisms. 

In this talk the speaker will provide solutions to Moser's problem. As an application, the sphere is not symplectically squeezable. This improves M. Gromov's symplectic nonsqueezing result.