- Integrable Hamiltonian systems, in particular (hyper)semitoric systems and their focus-focus and hyperbolic singularities, and interactions with Hamiltonian S^1-actions.
- Symplectic geometry, Floer theory and its applications to symplectic and contact dynamics (homoclinic points, growth behaviour)
- Hyperkähler Floer theory and associated Hamiltonian PDEs on Hilbert spaces; Bubbling-off analysis.
- Optimal transport and its application to integer partitions and integrable systems.
Morse theory and its application to integrable systems and n-categories.