My work from the last two decades has mainly been in what we now call symplectic dynamics, an area at the interface of symplectic topology 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, invariant sets, and connections between dynamics and the Floer homology persistence modules (e.g., barcode entropy and topological entropy).

I have also worked in Poisson geometry and studied Hamiltonian actions of compact groups.