My research interests are centred on the one hand on microlocal and semiclassical analysis (à la Duistermaat-Hörmander, Robert, Helffer, Sjöstrand, etc.) of hamiltonian systems, with a specific focus on integrable and near-integrable systems, and on the other hand on related symplectic geometry topics.

More generally, I am naturally attracted by problems combining geometry and analysis, and building bridges between maths and physics.

Here are the current mathematical topics I am involved in:
  • Singularities of completely integrable systems. Normal forms, symplectic classification.
  • Atiyah and Guillemin-Sternberg's moment polytopes, Delzant theorem.
  • Establishing strong links between symplectic invariants and quantum spectra of commuting microlocal operators (pseudo-differential, or Toeplitz). Quantum versions of monodromy and Chern class of integrable systems.
  • Semiclassical and WKB analysis.
  • Birkhoff normal forms, and quantum reduction.
  • Non self-adjoint operators, pseudo-spectra.
  • Almost integrable systems, KAM theory.
  • Long time behaviour of semiclassical wave packets, revivals.