Research

Mathematical Interests

Broad interests in Contact and Symplectic topology, and interactions: Symplectic Field Theory and related Floer theories, holomorphic curves and foliations, geometric structures in Hamiltonian dynamical systems and celestial mechanics, global analysis, all with a biased view towards pushing techniques to higher dimensions. Further interests in mathematical physics, and practical applications.

Publications/Preprints/In Progress

  1. Bourgeois contact structures: tightness, fillability and applications, 2022, with Jonathan Bowden, and Fabio Gironella. Inventiones Mathematicae. Published version. Arxiv.
  2. Global hypersurfaces of section for the spatial restricted three-body problem, 2022, with Otto van Koert. Nonlinearity. Published version. Arxiv.
  3. Contact geometry in the restricted three-body problem: a survey, 2022, Journal of Fixed Point Theory and Applications, Claude Viterbo’s 60th birthday edition. Survey based on lecture notes for a mini-course. Published version. Arxiv.
  4. A generalized Poincaré-Birkhoff theorem, 2022, with Otto van Koert. Journal of Fixed Point Theory and Applications, Claude Viterbo’s 60th birthday edition. Published version. Arxiv.
  5. SFT computations and intersection theory in higher-dimensional contact manifolds, 2021, J. Inst. Math. Jussieu, Cambridge University Press. Published version. Arxiv.
  6. Planarity in higher-dimensional contact manifolds, 2020, with Bahar Acu. Int. Math. Res. Not. (IMRN). Published version. Arxiv.
  7. On the Fukaya category of 4-dimensional non-Weinstein Liouville domains, with Kai Cieliebak, Oleg Lazarev, Thomas Massoni. In progress.
  8. On Floer-type numerical invariants, GIT quotients, and orbit bifurcations of real-life planetary systems, 2022, with Urs Frauenfelder, Dayung Koh. Submitted. Arxiv.
  9. On GIT quotients of the symplectic group, stability and bifurcations of symmetric orbits, 2021, with Urs Frauenfelder. Submitted. Arxiv.
  10. A landscape of contact manifolds via rational SFT, 2020, with Zhengyi Zhou. Submitted. Arxiv.
  11. Pseudo-holomorphic dynamics in the restricted three-body problem, 2020. Submitted. Arxiv.
  12. Algebraic and Giroux torsion in higher-dimensional contact manifolds, 2019. Submitted. Arxiv.
  13. Holomorphic curves in the presence of holomorphic hypersurface foliations, 2019, with Richard Siefring. Preprint. Arxiv.
  14. Algebraic Torsion in higher-dimensional contact manifolds, 2018, PhD thesis. Humboldt Universität zu Berlin, open access EDOC server. DOI: 10.18452/19849. Published version. Arxiv.

Other documents

  1. “Contact geometry in the spatial restricted three-body problem”, Lecture notes for online mini-course. Available on the Arxiv (version 1; version 2 is now a survey). See the Teaching section for the recordings, available on YouTube.

Supervision

  • Arthur Limoge (PhD student, since September 2022).

Invited Talks

Nov 5, 2021, IAS. Joint PU/IAS symplectic seminar. A discussion on the idea of the shadow of the spatial three-body problem.
Oct 26, Members’ Colloquium, IAS. Informal overview.
Symplectic Zoominar talk, IAS, June 18, 2021.
Talk in IMPA, Rio de Janeiro, Aug 26, 2019.

Seminars Organized

  • Symplectic Zoominar (CRM-Montréal, Princeton/IAS, Tel Aviv, and Paris), together with Octav Cornea (Montréal), Helmut Hofer (IAS), Vincent Humilière (Paris), Leonid Polterovich (Tel Aviv), Egor Shelukhin (Montréal), Shira Tanny (IAS), Sara Tukachinsky (Tel Aviv), Claude Viterbo (Paris).
  • PU/IAS Symplectic Geometry Seminar (joint Princeton University/IAS), together with Yusuf Bariş Kartal (Princeton), Julian Chaidez (Princeton), John Pardon (Princeton), Emmy Murphy (Princeton), Helmut Hofer (IAS), and Ipsita Datta (IAS).
  • 2014, UCL Geometry Seminar.

Journal Refereeing

Academic Visits

Collaborators

Conferences, Seminars, Summer Schools and Workshops