My research
Here you can download a description of the problems and projects I am working on lately.
Below you find the list of my publications, including my doctoral thesis and recent preprints.
Want to know more? Have a look at my papers on the arXiv or at my profile on MathSciNet.
Preprints
- Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems,
with L. Asselle,
submitted, arXiv:2003.09141, 19 pages, 2020. - On the local systolic optimality of Zoll contact forms,
with A. Abbondandolo,
submitted, arXiv:1912.04187, 56 pages, 2019. - On a systolic inequality for closed magnetic geodesics on surfaces,
with J. Kang,
submitted, arXiv:1902.01262, 26 pages, 2019. - On a local systolic inequality for odd-symplectic forms,
with J. Kang,
submitted, arXiv:1902.01261, 2019.
Published papers
- Invariance of symplectic cohomology and twisted cotangent bundles over surfaces,
with A. F. Ritter,
Int. J. Math., 42 pages, to appear. - Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities,
with L. Asselle,
J. Geom. Anal., doi:10.1007/s12220-020-00379-1, 17 pages, to appear. - Minimal boundaries in Tonelli Lagrangian systems,
with L. Asselle and M. Mazzucchelli,
Int. Math. Res. Notices, doi:10.1093/imrn/rnz246, 42 pages, to appear. - A local contact systolic inequality in dimension three,
with J. Kang,
J. Eur. Math. Soc., 43 pages, to appear. - The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere,
with A. Abbondandolo, L. Asselle, M. Mazzucchelli, and I. A. Taimanov,
Adv. Nonlinear Stud. 17, no. 1, 17 - 30, 2017. - On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus,
with L. Asselle,
Math. Z. 286, no. 3 - 4, 843 - 859, 2017. - On closed orbits for twisted autonomous Tonelli Lagrangian flows,
Proceedings of the CIMPA Research School "Hamiltonian and Lagrangian Dynamics"
Publ. Mat. Urug. 16, 41 - 79, 2016. - Magnetic Katok examples on the two-sphere,
Bull. Lond. Math. Soc. 48, no. 5, 855 - 865, 2016. - The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles,
with L. Asselle,
J. Topol. Anal. 8, no. 3, 545 - 570, 2016. - On the existence of periodic orbits for magnetic systems on the two-sphere,
with K. Zehmisch,
J. Mod. Dyn. 9, 141 - 146, 2015. - Infinitely many periodic orbits of non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level,
with L. Asselle,
Calc. Var. Partial Differential Equations 54, no. 2, 1525--1545, 2015. - The contact property for symplectic magnetic fields on the 2-sphere,
Ergodic Theory Dynam.~Systems 36, no. 3, 682--713, 2016. - The contact property for magnetic flows on surfaces,
PhD Thesis University of Cambridge, 2014.