At the moment, I am interested in the interplay between low-dimensional topological properties of orbits of Hamiltonian systems, Hofer geometry and Floer Homology. Essentially, my results are corollaries of the well known but extremely useful fact that 2+2=4.
Here is the slide I wrote for a lightning talk in Budapest about a result of mine.
Methods I apply include Generating Functions homology, Hamiltonian and Lagrangian Floer homology, together with their filtered structures.
Publications & Preprints
- Hamiltonian Braids via Generating Functions, arXiv:2410.06495, published in Mathematische Zeitschrift, Volume 311 (2025).
- Hofer Energy and Link Preserving Diffeomorphisms in Higher Genus, joint with Ibrahim Trifa, arXiv:2404.01052, published in the Journal of Modern Dynamics, Volume 21 (2025) Number 3.
- Link Floer Homology and a Hofer Pseudometric on Braids, arxiv:2301.08105, published in Journal of Symplectic Geometry, Volume 23 (2025) Number 3.
Unpublished
Where I will be
- Symplectic Topology - A conference in honor of Kai Cieliebak, Universität Augsburg, Augsburg, Germany, 24/08/2026-28/08/2026.
- Symplectic Topology, Hamiltonian Dynamics, and Persistence Structures. A conference in honour of Octav Cornea, FIM - ETH, Zurich, Switzerland, 15/06/2026-19/06/2026.
Where I was
- Workshop on Geometry, Topology, and Machine Learning (GTML 2025), MPI für Mathematik in den Naturwissenschaften Leipzig, Leipzig, Germany, 10/11/2025-14/11/2025.
- Laudenbach 80, Université de Nantes, Nantes, France, 13/10/2025-15/10/2025.
- Workshop: Billiards and quantitative symplectic geometry, Heidelberg University, Heidelberg, Germany, 14/07/2025-18/06/2025.
- Symplectic Dynamics and Topology, Cetraro, Italy, 16/06/2025-20/06/2025.
- Geometry and Mathematical Physics, University of Tokyo, Tokyo, Tokyo, Japan, 20/11/2024-22/11/2024.
- Geometry and Topology 2024, Kyushu University, Fukuoka, Japan, 16/10/2024-18/10/2024.
- Symplectic Dynamics in Aachen, RWTH Aachen, Aachen, Germany, 16/09/2024-20/09/2024.
- From Hamiltonian Dynamics to Symplectic Topology and Beyond. A 2024
celebration of Claude Viterbo and his mathematics, Institut Henri Poincaré, Paris, France, 03/06/2024-07/06/2024.
- Floer Homotopy Theory Spring School, Grand-Varennes, Serbonnes, France, 29/04/2024-03/05/2024 (co-organised with Amanda Hirschi).
- Symplectic Dynamics in Montevideo, UDELAR, Montevideo, Uruguay, 05/09/2024-09/02/2024.
- SFT X - Workshop on Symplectic Field Theory X, Humboldt Universität zu Berlin, Berlin, Germany, 26/08/2023-01/09/2023.
- From smooth to C⁰ symplectic geometry: topological aspects and dynamical implications, CIRM, Marseille, France, 03/07/2023-07/07/2023.
- LP-60: Geometry and Dynamics. A Conference in Honour of Leonid Polterovich, ETH, Zürich, Switzerland, 26/06/2023-30/06/2023.
- Persistence Homology in Symplectic and Contact Topology, Institut National Universitaire Champollion, Albi, France, 12/06/2023-16/06/2023.
- Symplectic Dynamics-INdAM Meeting, Instituto Nazionale di Alta Matematica, Rome, Italy, 22/05/2023-26/05/2023.
- Winter school in singularities and low dimensional topology, Rényi Institute, Budapest, Hungary, 23/01/2023-27/01/2023.
- Two days in Symplectic Dynamics, ENS de Lyon, France, 29/09/2022-30/09/2022.
- Giroux60, IHP, Paris, France, 04/07/2022-08/07/2022.
- Frontiers of Quantitative Symplectic and Contact Geometry, Institut Mittag-Leffler, Djursholm, Sweden, 27/06/2022-01/07/2022.
- Braids in Low Dimensional Topology, ICERM, Providence, RI, 25/04/2022-29/04/2022.
- Braids in Symplectic and Algebraic Geometry, ICERM, Providence, RI, 21/03/2022-25/03/2022.
- Hyperbolic and Symplectic Dynamics, Rurh-Universität Bochum, Germany, 20/09/2021-24/09/2021.
- Symplectic 2021, Institut Henri Poincaré, Paris, France, 19/04/2021-21/05/2021.