Research Interests:

    C0 symplectic geometry, symplectic dynamics, area-preserving homeomorphisms.
    Here is a, somewhat outdated, brief introductory talk on C0 symplectic geometry and two of the most well-known problems in the field.
    My research is supported by ERC Starting Grant No. 851701 : homeomorphisms in symplectic topology and dynamics (HSD).

   News and events:

   Upcoming events:

   Recent talks:

   Recent events:

  • IHP Trimester on symplectic and contact geometry, April 19th - July 16th, 2021.
  • IHP Conference Advances in symplectic topology, May 17-21, 2021.

   Publications:

  1. Quantitative Heegaard Floer cohomology and the Calabi invariant (with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak, and Ivan Smith). ArXiv 2105:11026. pdf
  2. Proof of the simplicity conjecture (with Dan Cristofaro-Gardiner and Vincent Humilière). ArXiv:2001.01792. pdf
  3. 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
  4. 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
  5. 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
  6. Barcodes and area-preserving homeomorphisms (with Frédéric Le Roux and Claude Viterbo). Geometry & Topology, 25 (2021) 2713–2825. pdf
  7. The action spectrum and C0 symplectic topology (with Lev Buhovsky and Vincent Humilière). Mathematische Annalen, 380(1), 293-316. 2021. pdf
  8. A C0 counter example to the Arnold conjecture (with Lev Buhovsky and Vincent Humilière). Inventiones Mathematicae , 213(2):759–809, 2018 pdf
  9. Towards a dynamical interpretation of spectral invariants on surfaces (with Vincent Humilière and Frédéric Le Roux). Geometry & Topology 20-4 (2016), 2253-2334. pdf
  10. Reduction of symplectic homeomorphisms (with Vincent Humilière and Rémi Leclercq). Annales de l'ENS 49 (2016), no. 3, 633-668. pdf
  11. Spectral killers and Poisson bracket invariants. J. Mod. Dyn. 9 (2015), 51–66. pdf
  12. Coisotropic rigidity and C0-symplectic topology (with Vincent Humilière and Rémi Leclercq). Duke Mathematical Journal 164 (2015), n°4, 767-799. pdf
  13. New Energy-Capacity-like inequalities and uniqueness of continuous Hamiltonians (with Vincent Humilière and Rémi Leclercq). Commentarii Mathematici Helvetici 90 (2015), 1-21. pdf
  14. Unboundedness of the Lagrangian Hofer distance in the Euclidean ball. Electron. Res. Announc. Math. Sci. 21 (2014), 1–7. pdf
  15. The displaced disks problem via symplectic topology. C. R. Math. Acad. Sci. Paris 351 (2013), no. 21-22, 841–843. pdf
  16. C0-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants. Int. Math. Res. Not. IMRN 2013, no. 21, 4920–4960. pdf
  17. A note on C0 rigidity of Hamiltonian isotopies. J. Symplectic Geom. 11 (2013), no. 3, 489–496. pdf
  18. Uniqueness of generating Hamiltonians for topological Hamiltonian flows. J. Symplectic Geom. 11 (2013), no. 1, 37–52. pdf
  19. Descent and C0-rigidity of spectral invariants on monotone symplectic manifolds. J. Topol. Anal. 4 (2012), no. 4, 481–498. pdf
  20. 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.
  2. Erman Cinelli.

   Students:

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

  4. © IMJ-PRG 2014