My main research interest is dynamical systems, which is a vibrant and diverse field that evolves around certain central ideas. Currently, I am interested in the following list of topics, all connected to the central idea of variational methods in Hamiltonian systems:
Arnold diffusion (instability in Hamiltonian systems);
Weak KAM theory and viscosity solutions of Hamilton-Jacobi equations;
Normal form and averaging theory.
I also work in smooth dynamics and thermodynamic formalism.