My work from the last two decades has mainly been at the interface of symplectic topology, and in particular Hamiltonian and Lagrangian Floer theory, and dynamical systems. I have worked extensively on various versions of the problem of existence and non-existence of periodic orbits: the Hamiltonian Seifert conjecture, the Conley conjecture, multiplicity of periodic orbits of Reeb flows in higher dimensions, the existence and multiplicity of periodic orbits of a charge in a magnetic field and several others. More recently, I have been focusing on connections between Floer theory and dynamics beyond periodic orbits, including dynamics of Hamiltonian pseudorotations in all dimensions and topological entropy.
I have also worked in Poisson geometry and studied Hamiltonian actions of compact groups.
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