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

  1. On GIT quotients of the symplectic group, stability and bifurcations of periodic orbits, 2021 (accepted 2023), with Urs Frauenfelder. To appear in the Journal of Symplectic Geometry. Arxiv.
  2. Pseudo-holomorphic dynamics in the restricted three-body problem, 2022. Math. Proc. Camb. Philos. Soc. Published version. Arxiv.
  3. Bourgeois contact structures: tightness, fillability and applications, 2022, with Jonathan Bowden, and Fabio Gironella. Inventiones Mathematicae. Published version. Arxiv.
  4. Global hypersurfaces of section for the spatial restricted three-body problem, 2022, with Otto van Koert. Nonlinearity. Published version. Arxiv.
  5. 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.
  6. 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.
  7. Algebraic and Giroux torsion in higher-dimensional contact manifolds, 2018 (accepted 2023). To appear in Algebraic & Geometric Topology. Arxiv.
  8. SFT computations and intersection theory in higher-dimensional contact manifolds, 2018 (accepted 2021), J. Inst. Math. Jussieu, Cambridge University Press. Published version. Arxiv.
  9. Planarity in higher-dimensional contact manifolds, 2020, with Bahar Acu. Int. Math. Res. Not. (IMRN). Published version. Arxiv.
  10. 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.

Preprints

  1. On doubly symmetric periodic orbits, 2023, with Urs Frauenfelder. Submitted. Arxiv.
  2. Floer theory of Anosov flows in dimension three, 2022, with Kai Cieliebak, Oleg Lazarev, Thomas Massoni. Submitted. Arxiv.
  3. Non-standard contact spheres and applications, 2022, with Jonathan Bowden, Fabio Gironella, Zhengyi Zhou. Arxiv.
  4. On Floer-type numerical invariants, GIT quotients, and orbit bifurcations of real-life planetary systems, 2022, with Urs Frauenfelder, Dayung Koh. Submitted. Arxiv.
  5. A landscape of contact manifolds via rational SFT, 2020, with Zhengyi Zhou. Submitted. Arxiv.
  6. Holomorphic curves in the presence of holomorphic hypersurface foliations, 2019, with Richard Siefring. Preprint. Arxiv. (This preprint serves as a brief introduction and explanation, to the wider community, of Richard Siefring’s intersection theory in higher dimension, which is work in progress).

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