Research output per year
Research output per year
Personal profile
Research
Hi!
I am a mathematician working at the interface of Differential Geometry, Dynamical Systems and the Calculus of Variations.
In particular, I study the relationship between Symplectic Geometry and Hamiltonian Systems on manifolds. On the one hand, periodic orbits of Hamiltonian systems yield geometric invariants such as symplectic capacities and symplectic homology. On the other hand, using symplectic tools we can understand concrete Hamiltonian systems coming from physics, such as those describing the motion of charged particles in a magnetic field.
You find more information on my personal website with some videos of my talks.
Teaching
I always look forward to supervising new students for Bachelor and Master projects.
Here are some projects I supervised:
- The illumination and the blocking problem for polygonal billiards (Bachelor)
- The twist condition for strong magnetic fields on the two-sphere (Master)
Here are some projects that I would like to supervise:
- Bertrand's Theorem on central forces and Mercury's relativistic precession (Bachelor)
- Integrable magnetic flows on the two-torus (Master)
I can also suggest other topics and if you have an idea for a further project that is also very welcome!
Ancillary activities
No ancillary activities
Ancillary activities are updated daily
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Collaborations and top research areas from the last five years
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Research output
- 23 Article
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The Hopf–Rinow theorem and the Mañé critical value for magnetic geodesics on odd-dimensional spheres
Albers, P., Benedetti, G. & Maier, L., Aug 2025, In: Journal of Geometry and Physics. 214, p. 1-21 21 p., 105521.Research output: Contribution to Journal › Article › Academic › peer-review
Open AccessFile6 Downloads (Pure) -
Symplectic capacities of domains close to the ball and Banach–Mazur geodesics in the space of contact forms
Abbondandolo, A., Benedetti, G. & Edtmair, O., 1 Jun 2025, In: Duke mathematical journal. 174, 8, p. 1567-1646 80 p.Research output: Contribution to Journal › Article › Academic › peer-review
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Lorentz--Finsler metrics on symplectic and contact transformation groups
Benedetti, G., Abbondandolo, A. & Polterovich, L., 7 Mar 2025, (E-pub ahead of print) In: Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. p. 1-104 104 p.Research output: Contribution to Journal › Article › Academic › peer-review
Open AccessFile23 Downloads (Pure) -
An Observation About Conformal Points on Surfaces
Benedetti, G. & Albers, P., Dec 2024, In: Arnold Mathematical Journal. 10, 4, p. 473-485 13 p.Research output: Contribution to Journal › Article › Academic › peer-review
Open Access -
Symplectic capacities of disc cotangent bundles of flat tori
Benedetti, G., Bimmermann, J. & Zehmisch, K., Dec 2024, In: Proceedings of the American Mathematical Society. 152, 12, p. 5367-5372 6 p.Research output: Contribution to Journal › Article › Academic › peer-review
Open AccessFile20 Downloads (Pure)