Marcel Guàrdia (PhD in Applied Mathematics, Universitat Politècnica de Catalunya, 2010) is Associate Professor (Professor Agregat) at Universitat Politècnica de Catalunya. He has 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.

Marcel Guàrdia has published 15 papers including articles at Inventiones Mathematicae, Journal of the European Mathematical Society, Advances in Mathematics and Communications in Mathematical Physics. In 2015, he received the first Barcelona Dynamical Systems Prize. In 2017 he obtained an ERC Starting grant.

Research interests

Marcel Guardia's research is focused on the dynamics of Hamiltonian systems. In particular on the analysis of the unstable and chaotic motions these systems may possess. He has worked in Celestial Mechanics, where he has studied different type of behaviors such oscillatory motions, drift along resonances, stochastic behavior, non-integrability, Smale horseshoes, etc.

He also works in Hamiltonian Partial Differential Equations (PDEs) such as the nonlinear Schrödinger equation, which can be seen as infinite dimensional Hamiltonian systems. In these models he studies transfer of energy behaviors and also different homoclinic phenomena (solitons, breathers).

Keywords

Hamiltonian Systems, Celestial Mechanics, Hamiltonian Partial Differential Equations, Arnol'd diffusion, Exponentially small phenomena