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
Proof of the simplicity conjecture (with Dan Cristofaro-Gardiner and Vincent Humilière). ArXiv:2001.01792. pdf
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.
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:
- Postdoc position supported by ERC Starting Grant HSD. Deadline Dec. 20, 2022. Please apply on Mathjobs.
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.
- The strong closing lemma and Hamiltonian pseudo-rotations (with Erman Cineli).
- A Hölder-type inequality for the C0 distance and Anosov-Katok pseudo-rotations (with Dusan Joksimovic).
- Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces (with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak, and Ivan Smith).
- 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
- HDR thesis.
- Oberwolfach reports: 2017, 2019.
- Dusan Joksimovic, Jan. 21-Dec. 22.
- Erman Cinelli, Sep. 22-Aug. 23.
- Vukašin Stojisavljević, Apr. 22-Mar. 23.
- 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.