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 doubly symmetric periodic orbits, 2023, with Urs Frauenfelder. To appear in Celestial Mechanics & Dynamcal Astronomy. Arxiv.
2. 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.
3. Pseudo-holomorphic dynamics in the restricted three-body problem, 2022. Math. Proc. Camb. Philos. Soc. Published version. Arxiv.
4. Bourgeois contact structures: tightness, fillability and applications, 2022, with Jonathan Bowden, and Fabio Gironella. Inventiones Mathematicae. Published version. Arxiv.
5. Global hypersurfaces of section for the spatial restricted three-body problem, 2022, with Otto van Koert. Nonlinearity. Published version. Arxiv.
6. 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.
7. 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.
8. Algebraic and Giroux torsion in higher-dimensional contact manifolds, 2018 (accepted 2023). To appear in Algebraic & Geometric Topology. Arxiv.
9. SFT computations and intersection theory in higher-dimensional contact manifolds, 2018 (accepted 2021), J. Inst. Math. Jussieu, Cambridge University Press. Published version. Arxiv.
10. Planarity in higher-dimensional contact manifolds, 2020, with Bahar Acu. Int. Math. Res. Not. (IMRN). Published version. Arxiv.
11. 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. Floer theory of Anosov flows in dimension three, 2022, with Kai Cieliebak, Oleg Lazarev, Thomas Massoni. Submitted. Arxiv.
2. Non-standard contact spheres and applications, 2022, with Jonathan Bowden, Fabio Gironella, Zhengyi Zhou. Arxiv.
3. On Floer-type numerical invariants, GIT quotients, and orbit bifurcations of real-life planetary systems, 2022, with Urs Frauenfelder, Dayung Koh. Submitted. Arxiv.
4. A landscape of contact manifolds via rational SFT, 2020, with Zhengyi Zhou. Submitted. Arxiv.
5. 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).
• Jackman Connor (Postdoc).

Invited Talks

• From smooth to C^0 symplectic geometry: topological aspects and dynamical implications, CIRM, Luminy, France, July 3-7, 2023.
• Escuela “Foliaciones y Flujos de Anosov en dimensión 3”, IMERL, Montevideo, Uruguay, Nov 15.
• Osaka Metropolitan University Geometry Seminar, Osaka, Japan, Nov 4, 2022.
• Symplectic Geometry seminar, Stanford University, Palo Alto, California, USA, Sept 8, 2022.
• Satellite ICM Geometry and Topology sectional workshop (short communication), University of Copenhagen, Copenhagen, Denmark, July 10, 2022.
• STRUCTURES, cluster of excellence, Universität Heidelberg, Heidelberg, Germany, July 8, 2022. Poster.
• Mercator Workshop 2022, Universität Heidelberg, Heidelberg, Germany, June 23, 2022.
• Gravitación y física matemática, Cinvestav, Ciudad de Mexico, Mexico, Apr 28, 2022.
• UCLA Topology seminar, UCLA, Los Angeles, California, USA, Jan 21, 2022.
• MIT Geometry and Topology Seminar, Massachusetts Institute of Technology (MIT), Boston, USA, Nov 22, 2021.
• IAS/PU joint symplectic seminar, Princeton University, Princeton, NJ, USA, Nov 4, 2021.
• Contact and symplectic geometry seminar, UC Berkeley, Berkeley, California, USA, Oct 29, 2021.
• Members’ Colloquium, Institute for Advanced Study, Princeton, NJ, USA, Oct 25, 2021.
• Short postdoc talk, Institute for Advanced Study, Princeton, NJ, USA, Sept 28, 2021. YouTube.
• IAS/PU, Montreal, Paris & Tel-Aviv Symplectic Geometry Seminar, June 18 2021.

• Geometri och topologiseminariet, working group, Uppsala Universitet, Uppsala, Sweden, May 5, 2021.
• Floer Theory and Hamiltonian Dynamics of Non-Compact Hypersurfaces, online conference, ETH Zürich, Jan 18-22, 2021.
• IML seminars, “Knots, Strings, Symplectic Geometry and dualities”, Mittag-Leffler Institute, Stockholm, Sweden, Oct 08, 2020.
• Geometry Oberseminar, Augsburg Universität, ZOOM talk, Augsburg, Germany, May 4, 2020.
• BGHK Joint Seminar on Symplectic and Contact Geometry, Universität Heidelberg, Heidelberg, Germany, Oct 25, 2019.
• Columbia Symplectic Geometry, Gauge Theory, and Categorification Seminar, Columbia University, New York, Oct 18, 2019.
• Topology and Symplectic Geometry Seminar, Stony Brook University, Stony Brook, Oct 17, 2019.
• MIT Geometry and Topology Seminar, Massachusetts Institute of Technology (MIT), Boston, Oct 14, 2019.
• Gauge-Topology-Symplectic seminar, Harvard University, Boston, Oct 11, 2019.
• PU/IAS Symplectic Geometry Seminar, Institute for Advanced Study (IAS), Princeton, Oct 7, 2019.
• Topology seminar, Monash University, Melbourne, Australia, Sept 19, 2019.
• International Conference in Symplectic Topology, IMPA, Rio de Janeiro, Brazil, Aug 26-30, 2019.
• Talk series in Dynamical Systems seminar, IMERL, Montevideo, Uruguay, Aug 9, Aug 16, 2019.
• Oberseminar Dynamische Systeme, Ruhr-Universität Bochum, Bochum, Germany, June 18 2019.
• Geometry-Topology seminar, Middle East Technical University, Ankara, Turkey, 18 March 2019.
• Topology seminar, Tokyo Institute of Technology, Tokyo, Japan, Feb 23 2019.
• Oberseminar Dynamische Systeme, Ruhr-Universität Bochum, Bochum, Germany, Jan 29 2019.
• Talk mini-series in Symplektische Geometrieseminar, Augsburg Universität, Augsburg, Germany, Nov 19, Nov 26, Dec 3, 2018.
• Geometric structures on 3 and 4 manifolds, IUC, Dubrovnik, Croatia, June 11-15 2018.
• 25th Gökova Geometry-Topology conference, Gökova, Turkey, May 28-June 2 2018.
• Talk series in Arbeitsgruppe Symplektische Geometrieseminar, Humboldt Universität zu Berlin, Berlin, Germany, May 7, May 14, May 22, 2018 .
• Symplectix, Institut Herni Poincaré, Paris, France, March 9 2018.
• Séminaire de Systèmes dynamiques, Analyse et Géométrie, Université d’Avignon, Avignon, France, March 6 2018.
• MATH AmSud – SIDIHAM, Montevideo Workshop on Hamiltonian Dynamics and Celestial Mechanics, IMERL, Montevideo, Uruguay, Dec 17-21 2017.
• Talk series in Arbeitsgruppe Symplektische Geometrieseminar, Humboldt Universität zu Berlin, Berlin, Germany, June 12, June 19, 2017.
• Kylerec workshop, Truckee, California, USA, May 19-25 2017.
• Dynamical Systems seminar, IMERL, Montevideo, Uruguay, 2017.
• Arbeitsgruppe Symplektische Geometrieseminar, Humboldt Universität zu Berlin, Berlin, Germany, Dec 12 2016.
• Imperial College Junior Geometry Seminar, Imperial College London, London, UK, Nov 27 2015.
• A Symplectic Cut, King’s College London, London, UK, Nov 3 2015.
• Dynamical Systems seminar, IMERL, Montevideo, Uruguay, July 31 2015.
• UCL Symplectic Working Group seminar, University College London, London, UK, Nov 26 2014.
• UCL Junior Geometry Seminar, University College London, London, UK, 9 Dec 2014.

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

• Algebraic & Geometric Topology.
• International Mathematics Research Notices. (2 articles)
• Advances in Mathematics.
• Geometry & Topology.
• Journal of Fixed Point Theory and Applications.
• Celestial Mechanics and Dynamical Astronomy.
• Journal of Symplectic Geometry.

Academic Visits

• Franca Hoffmann, Caltech, Pasadena, California, USA, Jan 2-6 2023.
• Hyunki Min, UCLA, Los Angeles, California, USA, Jan 3 2023.
• Michael Hutchings, UC Berkeley, Berkeley, California, USA, 28 Oct-2 Nov 2021.
• Jonathan Bowden, Fabio Gironella. Visit in Regensburg Universität, Regensburg, Germany, 5-9 July 2021.
• Franca Hoffmann, visit in Hausdorff Center for Mathematics, Bonn, Germany, 2-5 July 2021. 
• 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

• Kai Cieliebak, Augsburg Universität, Augsburg, Germany.
• Otto van Koert, Seoul National University, Seoul, Korea.
• Umberto Hrynewicz, Aachen Universität, Aachen, Germany.
• Urs Frauenfelder, Augsburg Universität, Augsburg, Germany.
• Jonathan Bowden, Regensburg Universität, Regensburg, Germany.
• Richard Siefring, Bochum Universität, Bochum, Germany.
• Dayung Koh, NASA Jet Propulsory Laboratory (JPL), Pasadena, California, USA.
• Fabio Gironella, Humboldt Universität zu Berlin, Berlin, Germany.
• Bahar Acu, ETH Zürich, Zürich, Switzerland.
• Zhengyi Zhou, IAS, Princeton, USA.
• Oleg Lazarev, Columbia University, New York, USA.
• Thomas Massoni, Princeton University, Princeton, USA.

Conferences, Seminars, Summer Schools and Workshops

• ICM Geometry and Topology sectional workshop, University of Copenhagen, Copenhagen, Denmark, July 6-16, 2022.
• Convexity in contact and symplectic topology, in honour of Giroux 60th birthday, Institut Henri Poincaré, Paris, France, 4-8 July 2022.
• 12th School on Analysis and Geometry in Metric Spaces, Levico Terme, Italy, 27-29 June 2022.
• Mercator Workshop 2022, Universität Heidelberg, Heidelberg, Germany, June 23, 2022.
• Mathematical Physics aspects of localization, Les Diablerets, Switzerland, March 28 – April 1, 2022.
• Simons Collaboration on Localization of Waves Annual Meeting 2022, Simons Foundation, New York City, February 17-18, 2022.
• Workshop on the h-principle and beyond, IAS, Princeton NJ, USA, 1-5 Nov 2021.
• The unity of mathematics: A conference in honour of Sir Michael Atiyah, Isaac Newton Institute (INI), Cambridge, UK, 21-23 Sept 2021.
• Floer Theory and Hamiltonian Dynamics of Non-Compact Hypersurfaces, online conference, ETH Zürich, Jan 18-22 2021.
• Knots, Strings, Symplectic Geometry and Dualities, Mittag-Leffler Institute, Stockholm, Sweden. Sept 1-Dec 11 2020.
• International Conference in Symplectic Topology, IMPA, Rio de Janeiro, Brazil. August 26-30 2019.
• Séminaire de Mathématiques Supérieures 2019: Current trends in Symplectic Topology, Université de Montréal, Montréal, Canada, July 1-13 2019.
• CAST 2019: XIII Workshop on Symplectic Geometry, Contact Geometry, and Interactions, Humboldt Universität zu Berlin, Berlin, Germany, March 7-9 2019.
• Fukaya 60: Geometry and Everything, University of Kyoto, Kyoto, Japan, Feb 17-22 2019.
• Geometric Dynamics Days, Schloß Rauischholzhausen, JLU Gießen, Germany, Nov 23-25 2018.
• Workshop on Symplectic Field Theory IX: Polyfolds for SFT, Augsburg Universität, Augsburg, Germany, Aug 25-31 2018.
• Geometric structures on 3 and 4 manifolds, IUC, Dubrovnik, Croatia, June 11-15 2018.
• 25th Gökova Geometry-Topology conference, Gökova, Turkey, May 28-June 2 2018.
• Berlin-Hamburg Symplectic seminar, Humboldt Universität zu Berlin, Berlin, Germany, Jan 15 2018.
• CAST 2018: XII Workshop on Symplectic Geometry, Contact Geometry,
  and Interactions, Uppsala Universitet, Uppsala, Sweden, Jan 11-13 2018.
• 6to Coloquio Uruguayo de Matemática, Facultad de Ingeniería, Montevideo, Uruguay, Dec 20-22 2017.
• MATH AmSud – SIDIHAM, Montevideo Workshop on Hamiltonian Dynamics and Celestial Mechanics, IMERL, Montevideo, Uruguay, Dec 17-21 2017.
• Workshop on topological aspects of symplectic foliations, Université de Lyon 1, Lyon, France, 4-8 Sept 2017.
• Symplectic Geometry – Celebrating the work of Simon Donaldson, Isaac Newton Institute (INI), Cambridge, UK, 14-18 Aug 2017.
• Berlin-Hamburg Symplectic seminar, Humboldt Universität zu Berlin, Berlin, Germany, June 26 2017.
• 24th Gökova Geometry-Topology Conference, Gökova, Turkey, May 29-June 3 2017.
• Kylerec Workshop 2017, Standford University, Truckee, California, USA, May 19-25 2017.
• Spring School in Convex Symplectic Geometry, Ruhr-Universität Bochum,
  Bochum, Germany, Feb 20-24 2017.
• CAST 2017: XI workshop on Contact and Symplectic topology, University of
  Nantes, Nantes, France, 26-28 Jan 2017.
• Berlin-Hamburg Symplectic seminar, University of Hamburg, Hamburg, Germany, Oct 28 2016.
• Workshop on Symplectic Field Theory VIII, Humboldt Universität zu
  Berlin, Berlin, Germany, Aug 8-12 2016.
• Symplectic topology, sheaves and mirror symmetry, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, June 27-July 8 2016.
• LMS-CMI Research School: Developments in Contact and Symplectic Topology, University of Glasgow, Glasgow, Scotland, UK, June 20-24 2016.
• ECSTATIC 2 topology conference, Imperial College London, London,
  UK, June 13-14 2016.
• Analysis in the Large – Calculus of Variations, Dynamics, Geometry…
  In honour of Helmut Hofer, ETH Zürich, Zürich, Switzerland, June 6-10 2016.
• Topological and Quantitative Aspects of Symplectic Manifolds: A Conference in Honor of Dusa McDuff’s 70th Birthday, Columbia University, New York, USA, March 17-20 2016.
• CAST 2016: X Workshop on Symplectic Geometry, Contact Geometry, and
  Interactions, Augsburg Universität, Augsburg, Germany, Feb 25-27 2016.
• 5to Coloquio Uruguayo de Matemática, Facultad de Ingeniería, Montevideo, Uruguay, Dec 21-23 2015.
• Workshop in Symplectic topology and Geometry, Uppsala Universitet,
  Uppsala, Sweden, Sept 21-25 2015.
• Mittag-Leffler scientific program: Symplectic geometry and topology workshop, Mittag-Leffler Institut, Stockholm, Sweden, Sept 1-19 2015.
• Summer school on moduli problems in Symplectic Geometry, Institut des hautes études scientifiques (IHÉS), Bures-sur-Yvette, France, July 6-17 2015.
• Symplectix, Henri Poincaré Institute, Paris, France, May 22 2015.
• Nantes-Orsay seminar, Université Paris-Sud, Orsay, Paris, France, April 10 2015.
• CAST 2015: IX Workshop on Symplectic, Contact Geometry, and Interactions,
  École normale supérieure de Lyon (ENS), Lyon, France, Jan 29-31 2015.
• Clay Research Conference and Workshops: Symplectic Topology, Clay Mathematics Institute, University of Oxford, Oxford, UK, Sept 29-Oct 3 2014.
• Workshop on Contact Geometry in dimension three and higher, University College London (UCL), London, UK, July 28-Aug 1 2014.
• 3er Coloquio Uruguayo de Matemática, Facultad de Ingeniería, Montevideo, Uruguay, Dec 20-22 2011.
• XXI Encuentro Rioplatense de Algebra y Geometría Algebraica, Facultad de Ciencias, Montevideo, Uruguay, Dec 5-9 2011.
• 2do Coloquio Uruguayo de Matemática, Facultad de Ingeniería, Montevideo, Uruguay, Dec 21-23 2009.