Poisson brackets and symplectic invariants
  We introduce new invariants associated to collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these invariants involves various flavors of Floer theory. We present applications to approximation theory on symplectic manifolds and to Hamiltonian dynamics. 
Lev Buhovsky, Michael Entov and Leonid Polterovich
math.SG math.DS