Research Interests:
My field of research is symplectic and contact geometry and topology. This domain lies at the intersection of geometric analysis, complex geometry, low-dimensional topology, differential geometry and Hamiltonian dynamics.
Publications:
Preprints:
The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities, Preprint arXiv:2412.09555 (joint with Vinicius G. B. Ramos)
Cube normalized symplectic capacities, Preprint arXiv:2208.13666 (joint with Miguel Pereira and Vinicius G. B. Ramos)
Published or accepted papers:
Characterizing symplectic capacities on ellipsoids, accepted for publication in Revista Matemática Iberoamericana (joint with Vinicius G. B. Ramos).
Coarse distance from dynamically convex to convex, IMRN, Volume 2025, 12 (2025) (joint with Julien Dardennes, Vinicius G. B. Ramos and Jun Zhang)
Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology, Revista Matemática Iberoamericana, 40(2024), no.4, 1505--1527 (joint with Michel Cahen and Simone Gutt)
Algorithmic Symplectic Packing, Experimental Mathematics, 33(2024), no.2, 175--192 (joint with Greta Fischer and Michael Jünger)
Symplectic non-convexity of toric domains, Communications in Contemporary Mathematics, Vol. 26, 4 (2023) (joint with Julien Dardennes and Jun Zhang)
Examples around the strong Viterbo conjecture, Journal of Fixed Point Theory and Applications, Volume 24, 41 (2022) (joint with Michael Hutchings and Vinicius G. B. Ramos)
Two closed orbits for non-degenerate Reeb flows, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 170 (2021), no 3, 625--660 (joint with Miguel Abreu, Jungsoo Kang and Leonardo Macarini)
Symplectically knotted codimension-zero embeddings of domains in $\mathbb{R}^4$, Duke Mathematical Journal 168 (2019), no. 12, 2299--2363 (with Mike Usher)
Symplectic capacities from positive $S^1$-equivariant symplectic homology, Algebraic & Geometric Topology, 18 (2018) 3537--3600 (with Michael Hutchings).
Periodic Reeb orbits on prequantization bundles, Journal of Modern Dynamics, Volume 12, 2018, pp. 123--150 (with Peter Albers and Doris Hein).
The positive equivariant symplectic homology as an invariant for some contact manifolds, Journal of Symplectic Geometry, Vol. 15, No. 4 (2017), 1019--1069.
On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$, Annales de l'institut Fourier, 66 no.6 (2016), p. 2485--2505 (with Jungsoo Kang).
Generalized Conley-Zehnder index, Annales de la faculté des sciences de Toulouse, 23, No. 4, 907--932 (2014).
Normal Forms for Symplectic Matrices, Portugalia Mathematicae 71, No. 2, 109--139 (2014).
Roots in 2-spherical apartments, Advances in Geometry 12, No. 2, 229--238 (2012) (with Bernhard Mühlherr).
Other:
Symplect'hearing the contact horizon and contacting the symplectic inner beauty, Habilitation à Diriger des Recherches, July 2021.
Lecture Notes on $S^1$-equivariant symplectic homology, 2018.
On the minimal number of periodic Reeb orbits on a contact manifold, Memoir which won the "Concours annuel 2016 de l'Académie Royale de Belgique'' (with Miguel Abreu, Jungsoo Kang and Leonardo Macarini).
On the minimal number of periodic Reeb orbits on a contact manifold, PhD thesis, June 2014.
The Conley-Zehnder index for a path of symplectic matrices, preprint arXiv:1201.3728 (Expository paper)
Dynamique de Reeb et homologie de contact, Master thesis (in french), June 2010