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Here is a, somewhat outdated, brief introductory talk on C0 symplectic geometry and two of the most well-known problems in the field.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:
Seminars:
Upcoming talks and events:
- Séminaire Bourbaki by E. Ghys on my work with D. Cristofaro-Gardiner and V. Humilière, IHP Apr 1, 2023.
- 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:
- AIM workshop on symmetric products, Dec. 5-9, 2022.
- Talk at Geometry Seminar, IST Lisbon, Nov. 29, 2022.
- Talk at Séminaire de Systèmes Dynamiques, IMJ-PRG, Nov. 25, 2022.
- 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:
Publications:
- The strong closing lemma and Hamiltonian pseudo-rotations (with Erman Cineli).
ArXiv:2210.00771. pdf
- A Hölder-type inequality for the C0 distance and Anosov-Katok pseudo-rotations (with Dusan Joksimovic).
ArXiv:2207.11813. pdf
- 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
- 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
- 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
- This article is to be presented at a Bourbaki seminar by E. Ghys.
- Video.
- Proof of the simplicity conjecture (with Dan Cristofaro-Gardiner and Vincent Humilière). ArXiv:2001.01792. pdf
- This article is to be presented at a Bourbaki seminar by E. Ghys.
- An article on our work.
- Video.
- 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
- 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
- Barcodes and area-preserving homeomorphisms (with Frédéric Le Roux and Claude Viterbo). Geometry & Topology, 25 (2021) 2713–2825. pdf
- The action spectrum and C0 symplectic topology (with Lev Buhovsky and Vincent Humilière). Mathematische Annalen, 380(1), 293-316. 2021. pdf
- A C0 counter example to the Arnold conjecture (with Lev Buhovsky and Vincent Humilière). Inventiones Mathematicae , 213(2):759–809, 2018 pdf
- Towards a dynamical interpretation of spectral invariants on surfaces (with Vincent Humilière and Frédéric Le Roux). Geometry & Topology 20-4 (2016), 2253-2334. pdf
- Reduction of symplectic homeomorphisms (with Vincent Humilière and Rémi Leclercq). Annales de l'ENS 49 (2016), no. 3, 633-668. pdf
- Spectral killers and Poisson bracket invariants. J. Mod. Dyn. 9 (2015), 51–66. pdf
- Coisotropic rigidity and C0-symplectic topology (with Vincent Humilière and Rémi Leclercq). Duke Mathematical Journal 164 (2015), n°4, 767-799. pdf
- New Energy-Capacity-like inequalities and uniqueness of continuous Hamiltonians (with Vincent Humilière and Rémi Leclercq). Commentarii Mathematici Helvetici 90 (2015), 1-21. pdf
- Unboundedness of the Lagrangian Hofer distance in the Euclidean ball. Electron. Res. Announc. Math. Sci. 21 (2014), 1–7. pdf
- The displaced disks problem via symplectic topology. C. R. Math. Acad. Sci. Paris 351 (2013), no. 21-22, 841–843. pdf
- C0-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants. Int. Math. Res. Not. IMRN 2013, no. 21, 4920–4960. pdf
- A note on C0 rigidity of Hamiltonian isotopies. J. Symplectic Geom. 11 (2013), no. 3, 489–496. pdf
- Uniqueness of generating Hamiltonians for topological Hamiltonian flows. J. Symplectic Geom. 11 (2013), no. 1, 37–52. pdf
- Descent and C0-rigidity of spectral invariants on monotone symplectic manifolds. J. Topol. Anal. 4 (2012), no. 4, 481–498. pdf
- 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:
- HDR thesis.
- Oberwolfach reports: 2017, 2019.
Postdocs:
- Dusan Joksimovic, Jan. 21-Dec. 22.
- Erman Cinelli, Sep. 22-Aug. 23.
- Vukašin Stojisavljević, Apr. 22-Mar. 23.
Students:
- Master's (M2), Ibrahim Trifa, ``Floer Homology, Spectral
Invariants and Quasimorphisms," Sorbonne Université, 2022.
- 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.
- Master's (M2), Yusuke Kawamoto, ``Symplectic topology and persistence modules," ENS-Paris, 2018.
- Master's (M1), Ella Blair,`` Foliations on 3--manifolds: The Thurston--Wood thoerem," Sorbonne Université, 2018.