Symplectic geometry, Gromov-Witten invariants, Hamiltonian groups actions, low dimensional topology
My main interest is in symplectic topology and geometric topology. Currently, my research focuses on the homotopy theoretic, geometric, and algebraic properties of symplectomorphism groups. Symplectic geometry was initially developped as the mathematical framework of classical physics. It evolved into an independent field of research, very topological in nature, at the crossroads of differential topology, algebraic geometry, dynamics, and gauge theory. Nowadays most of the new developments involve Gromov's theory of $J$-holomorphic curves, Hofer geometry, Donaldson's theory of topological Lefschetz fibrations, and Floer homology theory.