E-mail
robert.cardona@ub.edu
Position
Lecturer
Research interests
Geometry
Area
Algebra Geometry Number Theory And Topology
Group
Algebra Geometry Number Theory And Topology
Cardona, Robert
Biosketch
Robert Cardona is an assistant professor at the Universitat de Barcelona. He earned his Ph.D. in Mathematics at the Universitat Politècnica de Catalunya in 2021 and was awarded the Vicent Caselles prize from the Royal Spanish Mathematical Society. His research interests are mostly geometry, topology, and dynamical systems—his work centers on contact/symplectic topology, Hamiltonian dynamics, geometric hydrodynamics, and their interaction.
Webage: https://sites.google.com/view/robertcardona/robert-cardonas-homepage
Other Research Interests
Symplectic topology, contact topology, Topological Hydrodynamics, Hamiltonian dynamics, Differential Topology
Projects
- SymHyCo - Interactions between symplectic topology, hydrodynamics, and conservative flows. Ministerio de Ciencia e Innovación (starting 2025). Principal investigator.
- Geometria i Topologia UB - 2021SGR00697 - member of the group.
- COMPLEX FLUIDS - Computational, dynamical and geometrical complexity in fluid dynamics. Proyectos de Investigación Fundación BBVA - member of the group.
Selected publications
- Contact type solutions and non-mixing of the 3D Euler equations. R. Cardona, F. Torres de Lizaur. Preprint arXiv:2312.03514 (2023).
- Stability is not open or generic in symplectic four-manifolds. R. Cardona. Preprint arXiv:2305.13158 (2023).
- An h-principle for embeddings transverse to a contact structure. R. Cardona, F. Presas. Journal of Topology, 17: e12326 (2024).
- Periodic orbits and Birkhoff sections of stable Hamiltonian structures. R. Cardona, A. Rechtman. Preprint arXiv:2206.14732 (2022).
- Computability and Beltrami fields in Euclidean space. R. Cardona, E. Miranda, D. Peralta-Salas. Journal de Mathématiques Pures et Appliquées, 169 (2023), 50-81.
- Constructing Turing complete Euler flows in dimension 3. R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Proceedings of the National Academy of Sciences,118.19 (2021).
- Steady Euler flows and Beltrami fields in high dimensions. R. Cardona. Ergodic Theory and Dynamical Systems, 41.12 (2020), 3610-3633.
- Universality of Euler flows and flexibility of Reeb embeddings. R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Advances in Mathematics, 428 (2023), 109142