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 in space mission design.

Publications

  1. Symplectic methods in the numerical search of orbits in real-life planetary systems, 2023, with Urs Frauenfelder, Dayung Koh. SIAM Journal of Applied Dynamical Systems. Published version. Arxiv.
  2. On doubly symmetric periodic orbits, 2023, with Urs Frauenfelder. Celestial Mechanics & Dynamical Astronomy. Published version. Arxiv.
  3. On GIT quotients of the symplectic group, stability and bifurcations of periodic orbits, 2023, with Urs Frauenfelder. J. Symplectic Geom. 21 (2023), no. 4, 723–773. Published version. Arxiv.
  4. Pseudo-holomorphic dynamics in the restricted three-body problem, 2022. Math. Proc. Camb. Philos. Soc. Published version. Arxiv.
  5. Bourgeois contact structures: tightness, fillability and applications, 2022, with Jonathan Bowden, and Fabio Gironella. Inventiones Mathematicae. Published version. Arxiv.
  6. Global hypersurfaces of section for the spatial restricted three-body problem, 2022, with Otto van Koert. Nonlinearity. Published version. Arxiv.
  7. 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.
  8. 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.
  9. Algebraic and Giroux torsion in higher-dimensional contact manifolds, 2018 (accepted 2023). To appear in Algebraic & Geometric Topology. Arxiv.
  10. SFT computations and intersection theory in higher-dimensional contact manifolds, 2018 (accepted 2021), J. Inst. Math. Jussieu, Cambridge University Press. Published version. Arxiv.
  11. Planarity in higher-dimensional contact manifolds, 2020, with Bahar Acu. Int. Math. Res. Not. (IMRN). Published version. Arxiv.
  12. 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.

Conference Proceedings

  1. Symplectic methods in space mission design, 2023, with Cengiz Aydin, Urs Frauenfelder, Dayung Koh, to appear in the Proceedings of the 2023 AAS/AIAA Astrodynamics Specialist Conference.

Preprints

  1. RSFT functors for strong cobordisms and applications, 2023, with Zhengyi Zhou. Submitted. Arxiv.
  2. Floer theory of Anosov flows in dimension three, 2022, with Kai Cieliebak, Oleg Lazarev, Thomas Massoni. Submitted. Arxiv.
  3. Tight contact structures without symplectic fillings are everywhere, 2022, with Jonathan Bowden, Fabio Gironella, Zhengyi Zhou. Submitted. Arxiv. Quanta Article.
  4. A landscape of contact manifolds via rational SFT, 2020, with Zhengyi Zhou. Submitted. Arxiv.
  5. Pseudo-holomorphic dynamics in the three-body problem: fillability and convexity, 2023. Submitted. Arxiv.
  6. Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension, 2023, with Francesco Ruscelli. Submitted. Arxiv.
  7. Symplectic geometry and space mission design, with Cengiz Aydin, Urs Frauenfelder, Otto van Koert, Dayung Koh. Submitted. Arxiv.
  8. 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).

In preparation

  • Symplectic structures from almost symplectic structures, with Fabi Gironella, Fran Presas, Lauran Toussaint.

Books

  1. Symplectic geometry of the three-body problem, 2024. Draft available in 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 a survey; version 3 is a book). See the Teaching section for the recordings, available on YouTube.

Supervision

  • Arthur Limoge (PhD student).
  • Francesco Ruscelli (PhD student).
  • Jackman Connor (postdoc).
  • Favio Piran (PhD student, co-supervision).
  • Cengiz Aydin (postdoc).
  • Bhanu Kumar (postdoc).
  • Josua Kugler (masters).

Thesis Commitees

  • Cengiz Aydin, PhD thesis, Université de Neuchâtel. April 29, 2023. With Felix Schlenk (thesis director), and Urs Frauenfelder.

Invited Talks

Friends Talk, IAS, March 10, 2023.
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.
  • Topology seminar, Morningstar Center of Mathematics, Beijing, China, March 27, 2024.
  • Geometry & Topology seminar, UCLA, California, USA, March 15, 2024.
  • Lecture series (3), 44th Winter school Geometry and Physics, Srni, Czech Republic, Jan 13-20, 2024.
  • Hamburg Colloquium, Hamburg Universität, Germany, Jan 9, 2024.
  • CP7 seminar, Heidelberg universität, Germany, Dec 13, 2023.
  • Strasbourg Day, Université Strasbourg, France, Nov 16, 2023.
  • Enceladus team (NASA), JPL, Pasadena, California, Oct 27 2023.
  • Symplectic Field Theory X, HU Berlin, Berlin, Germany, Aug 28 – Sept 1, 2023.
  • Founders Day Q&A, with David Nirenberg (IAS Director), IAS, Princeton NJ, USA, May 19 2023.
  • Space mission design seminar, JPL-NASA, Pasadena, California, USA, May 11, 2023.

Seminars/workshops Organized

  • Symplectic geometry and Anosov flows, Heidelberg, Germany. Main organizer, together with Peter Albers (Heidelberg), Jonathan Bowden (Regensburg).
  • Symplectic Dynamics in Montevideo, Uruguay. Main organizer, together with Alejandro Passeggi (UDELAR), Rafael Potrie (UDELAR), Vinicius Ramos (IMPA).
  • Schoental Workshop, Schoental, Germany. Invited as an expert and mentor.
  • Discussion Seminar on Symplectic topology, IAS, Princeton, USA.
  • 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