I obtained my PhD in Applied Mathematics from Universitat Politècnica de Catalunya under the supervision of Tere M. Seara. I have held postdoctoral positions in the Pennsylvania State University, the Fields Institute (Toronto), the University of Maryland, the Institute for Advanced Study (Princeton) and Université de Paris 7 – Denis Diderot (with a Marie Curie Fellowship). I am currently a Juan de la Cierva researcher in the Universitat Politècnica de Catalunya.
My research is (mostly) focused on the analysis of invariant objects and unstable behaviors in Hamiltonian systems of finite or infinite dimension (including Partial Differential Equations) and its applications to Celestial Mechanics.
- Hamiltonian Systems
- Hamiltonian Partial Differential Equations
- Celestial Mechanics
- Exponentially small phenomena
- Jacques Féjoz, Marcel Guardia, Vadim Kaloshin, Pablo Roldan, Diffusion along mean motion resonance in the restricted planar three-body problem. To appear in the Journal of the European Mathematical Society
- Marcel Guardia, Pau Martin, Tere M. Seara, Oscillatory motions for the restricted planar circular three body problem. Inventiones Mathematicae, published online, DOI 10.1007/s00222-015-0591-y
- Marcel Guardia, Vadim Kaloshin, Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society, 17 (1): 71–149 (2015)
- Inma Baldomá, Marcel Guardia, Ernest Fontich, Tere M. Seara, Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results. Journal of Differential Equations, 253 (12): 3304-3439 (2012)
- Marcel Guardia, Tere M. Seara, Marco Antonio Teixeira, Generic bifurcations of low codimension of planar Filippov Systems. Journal of Differential Equations, 250 (4): 1967-2023 (2011)