Research

Mathematical Interests

Broad interests in Contact and Symplectic topology, and interactions: Symplectic Field Theory and related Floer theories (and polyfolds if need calls), holomorphic curves and foliations, approximately and honestly holomorphic geometry, geometric structures in Hamiltonian dynamical systems and celestial mechanics, global analysis, and low-dimensional topology, but all with a biased view towards pushing techniques to higher-dimensions. Further interests in mathematical physics, Quantum Field Theory, String Theory and Quantum Mechanics.

Publications/Preprints/In Progress

  1. Contact geometry in the restricted three-body problem –a survey–, 2021. To Appear in the Journal of Fixed Point Theory and Applications, Claude Viterbo’s 60th birthday edition. Survey based on these lecture notes.
  2. A landscape of contact manifolds via rational SFT, 2020, with Zhengyi Zhou. Preprint. Arxiv.
  3. Global hypersurfaces of section for the spatial restricted three-body problem, 2020, with Otto van Koert. Preprint. Arxiv.
  4. Holomorphic dynamics in the spatial restricted three-body problem, 2020. Submitted. Arxiv.
  5. A generalized Poincaré-Birkhoff theorem, 2020, with Otto van Koert. Submitted. Arxiv.
  6. Bourgeois contact structures: tightness, fillability and applications, 2019, with Jonathan Bowden, and Fabio Gironella. Submitted. Arxiv. (This article strictly contains the manuscript titled “5-dimensional Bourgeois contact structures are tight”, therefore now withdrawn.)
  7. Algebraic and Giroux torsion in higher-dimensional contact manifolds, 2019. Submitted. Arxiv.
  8. SFT computations and intersection theory in higher-dimensional contact manifolds, 2019. J. Inst. Math. Jussieu, Cambridge University Press. DOI: 10.1017/S1474748020000559. Published version. Arxiv.
  9. Holomorphic curves in the presence of holomorphic hypersurface foliations, 2019, with Richard Siefring. Submitted. Arxiv.
  10. Planarity in higher-dimensional contact manifolds, 2018, with Bahar Acu. Int. Math. Res. Not. (IMRN), Oxford University Press. Advance version. Arxiv.
  11. Algebraic Torsion in higher-dimensional contact manifolds, 2018, PhD thesis. Published via Humboldt Universität zu Berlin, open access EDOC server. DOI: 10.18452/19849. 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. See the Teaching section for the recordings, available on YouTube.

Invited Talks

Upcoming

Past

Talk in IMPA, Rio de Janeiro, Aug 26, 2019.
Same talk in IAS, Princeton, USA, Oct 7, 2019
Part of a USA, East Coast, mini-tour.

Seminars Organized

  • 2014, UCL Geometry Seminar.

Journal Refereeing

Academic Visits

  • Mittag-Leffler Institute, Stockholm, Sweden, 1 Sept-11 Dec 2020.
  • Fabio Gironella, Bahar Acu. Joint visit to Oberwolfach Research Institute for Mathematics, Oberwolfach, Germany, 3-9 Nov 2019.
  • Oleg Lazarev, Columbia University, New York, USA, 19-21 Oct, 2019.
  • Kevin Sackel, Simons Center for Geometry and Physics, and Stony Brook University, Stony Brook, USA, 14-18 Oct 2019.
  • Chris Gerig, Harvard University. Yu Pan, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, USA, 10-14 Oct 2019.
  • Zhengyi Zhou. Institute for Advanced Study (IAS), Princeton, New Jersey, USA, 6-10 Oct, 2019.
  • Jonathan Bowden, Fabio Gironella. Visit in Monash University, Melbourne, Australia, 9-25 Sept 2019.
  • Fabio Gironella, Bahar Acu. Joint visit to IMPA, Rio de Janeiro, Brazil, 18 Aug-2 Sept 2019.
  • Oliver Fabert, Vrije Universitet Amsterdam, Amsterdam, Netherlands, 29 April 2019.
  • Fabio Gironella, Chris Wendl. Visit in Humboldt-Universität zu Berlin, Berlin, Germany, 9-12 March 2019.
  • Yoshi Mitsumatsu, Chuo University, Tokyo, Japan. Visit in Tokyo Institute of Technology, Tokyo, Japan, 23 Feb 2019.
  • Otto van Koert, Seoul National University, Seoul, Korea, 12-17, 27-28 Feb 2019.
  • Murat Saglam, Ruhr-Universität Bochum, Bochum, Germany, 29-31 Jan 2019.
  • Nesin Mathematics Village, Selçuk, Izmir, Turkey, 9-15 Sept 2018.
  • Richard Siefring, Ruhr-Universität Bochum, Bochum, Germany. Visit in Münster, Germany, 27 April 2018.
  • Mittag-Leffler Institute, Stockholm, Sweden, 1-19 Sept 2015.

Collaborators

Conferences, Seminars, Summer Schools and Workshops

Past