Research Interests:

   News and events:

   Job opening:

• Postdoc position supported by ERC Starting Grant HSD. Deadline Dec. 20, 2022. Please apply on Mathjobs.

   Seminars:

• Symplectix,
• Géométrie et topologie,
• Working seminar on symplectic topology.

   Upcoming talks and events:

• Talk at Séminaire de Systèmes Dynamiques, IMJ-PRG, Nov. 25, 2022.
• Talk at Geometry Seminar, IST Lisbon, Nov. 29, 2022.
• AIM workshop on symmetric products, Dec. 5-9, 2022.
• Mini-course at Workshop on global dynamics beyond uniform hyperbolicity, Banach Center, Będlewo, Apr. 23-May 5, 2023.
• Conference in honor of Alan Weinstein, IHP, Paris, June 19-23, 2023.
• Talk at LP:60 Conference, ETH-Zürich, June 26-30, 2023.
• Conference on C⁰ symplectic geometry and symplectic dynamics CIRM, Luminy, July 3-7, 2023.
• Oberwolfach workshop Dynamische Systeme, July 9-15, 2023.

   Recent talks:

• Two days in Symplectic Dynamics at ENS Lyon, Sep. 29-Sep.30, 2022.
• Workshop on Low-Dimensional Topology and Homeomorphism Groups at Brin Math Research Center, UMD, Sep. 6-Sep. 10, 2022.
• Frontiers of quantitative symplectic and contact geometry at Mittag-Leffler, June 27-July 1, 2022.
• Mini-Workshop on Symplectic Geometry at Utrecht University, June 24, 2022.

   Recent events:

• Giroux 60 — Convexity in contact and symplectic topology at IHP, July 4-8, 2022.
• IHP Trimester on symplectic and contact geometry, April 19th - July 16th, 2021.
• IHP Conference Advances in symplectic topology, May 17-21, 2021.

   Publications:

1. The strong closing lemma and Hamiltonian pseudo-rotations (with Erman Cineli). ArXiv:2210.00771. pdf
2. A Hölder-type inequality for the C⁰ distance and Anosov-Katok pseudo-rotations (with Dusan Joksimovic). ArXiv:2207.11813. pdf
3. Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces (with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak, and Ivan Smith). ArXiv:2206.10749. pdf
4. Quantitative Heegaard Floer cohomology and the Calabi invariant (with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak, and Ivan Smith). To appear in Forum of Mathematics, Pi. pdf
• Video.
5. PFH spectral invariants on the two-sphere and the large scale geometry of Hofer's metric (with Dan Cristofaro-Gardiner and Vincent Humilière). To appear in J. Eur. Math. Soc. (JEMS).pdf
• Video.
6. Proof of the simplicity conjecture (with Dan Cristofaro-Gardiner and Vincent Humilière). ArXiv:2001.01792. pdf
• An article on our work.
• Video.
7. The Anosov-Katok method and pseudo-rotations in symplectic dynamics (with Frédéric Le Roux). To appear in Journal of Fixed Point Theory and Applications, special issue in honour of Claude Viterbo. pdf
8. An Arnold-type principle for non-smooth objects (with Lev Buhovsky and Vincent Humilière). To appear in Journal of Fixed Point Theory and Applications, special issue in honour of Claude Viterbo. pdf
9. Barcodes and area-preserving homeomorphisms (with Frédéric Le Roux and Claude Viterbo). Geometry & Topology, 25 (2021) 2713–2825. pdf
10. The action spectrum and C⁰ symplectic topology (with Lev Buhovsky and Vincent Humilière). Mathematische Annalen, 380(1), 293-316. 2021. pdf
• Video.
11. A C⁰ counter example to the Arnold conjecture (with Lev Buhovsky and Vincent Humilière). Inventiones Mathematicae , 213(2):759–809, 2018 pdf
• This paper has featured in an INSMI news article.
• Video.
12. Towards a dynamical interpretation of spectral invariants on surfaces (with Vincent Humilière and Frédéric Le Roux). Geometry & Topology 20-4 (2016), 2253-2334. pdf
13. Reduction of symplectic homeomorphisms (with Vincent Humilière and Rémi Leclercq). Annales de l'ENS 49 (2016), no. 3, 633-668. pdf
14. Spectral killers and Poisson bracket invariants. J. Mod. Dyn. 9 (2015), 51–66. pdf
15. Coisotropic rigidity and C⁰-symplectic topology (with Vincent Humilière and Rémi Leclercq). Duke Mathematical Journal 164 (2015), n°4, 767-799. pdf
16. New Energy-Capacity-like inequalities and uniqueness of continuous Hamiltonians (with Vincent Humilière and Rémi Leclercq). Commentarii Mathematici Helvetici 90 (2015), 1-21. pdf
17. Unboundedness of the Lagrangian Hofer distance in the Euclidean ball. Electron. Res. Announc. Math. Sci. 21 (2014), 1–7. pdf
18. The displaced disks problem via symplectic topology. C. R. Math. Acad. Sci. Paris 351 (2013), no. 21-22, 841–843. pdf
19. C⁰-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants. Int. Math. Res. Not. IMRN 2013, no. 21, 4920–4960. pdf
    • Video.
20. A note on C0 rigidity of Hamiltonian isotopies. J. Symplectic Geom. 11 (2013), no. 3, 489–496. pdf
21. Uniqueness of generating Hamiltonians for topological Hamiltonian flows. J. Symplectic Geom. 11 (2013), no. 1, 37–52. pdf
22. Descent and C0-rigidity of spectral invariants on monotone symplectic manifolds. J. Topol. Anal. 4 (2012), no. 4, 481–498. pdf
23. L²-singular dichotomy for orbital measures of classical simple Lie algebras. (with Kathryn Hare and Sanjiv K. Gupta) Math. Z. 262 (2009), no. 1, 91–124. pdf
   My papers are also available at Mathscinet and at Zentralblatt. Here, you can find my CV.

   Other writings:

1. HDR thesis.
2. Oberwolfach reports: 2017, 2019.

  Postdocs:

1. Dusan Joksimovic, Jan. 21-Dec. 22.
2. Erman Cinelli, Sep. 22-Aug. 23.
3. Vukašin Stojisavljević, Apr. 22-Mar. 23.

   Students:

1. Master's (M2), Ibrahim Trifa, ``Floer Homology, Spectral Invariants and Quasimorphisms," Sorbonne Université, 2022.
2. PhD, Yusuke Kawamoto, ENS-Paris (co-supervision with Claude Viterbo) 2018-2021.
   • Article on C⁰ continuous and Hofer Lipshitz quasimorphisms.
   • Article on C⁰ continuity of the spectral norm.
3. Master's (M2), Yusuke Kawamoto, ``Symplectic topology and persistence modules," ENS-Paris, 2018.
4. Master's (M1), Ella Blair,`` Foliations on 3--manifolds: The Thurston--Wood thoerem," Sorbonne Université, 2018.

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