My work in symplectic topology and Hamiltonian dynamical systems focuses on two problems. The first one is the existence problem for periodic orbits of Hamiltonian dynamical systems and, in particular, of systems describing the motion of a charge in a magnetic field on a manifold. The second problem, known as the Hamiltonian Seifert conjecture , is that of constructing Hamiltonian dynamical systems without periodic orbits on one or more regular energy levels. A result of this type is an example of a Hamiltonian system on R2n, 2n> 6, with a compact non-singular energy level having no periodic orbits.
In the field of Poisson geometry I am interested in the explicit calculation of certain invariants (Poisson cohomology) of Poisson manifolds or, more generally, in the just emerging area of "Poisson topology" and also in the study of moment maps for Poisson Lie groups.
Many properties of Hamiltonian actions of compact groups have topological rather than symplectic origins. My research on Hamiltonian group actions focuses on developing a topological framework suitable for the investigation of these actions.