He is a research professor at the Spanish National Research Council (CSIC) and a corresponding academic at the Royal Academy of Sciences. His research focuses on partial differential equations, which is the area of mathematics commonly used to model physical phenomena.

In his work, he uses and develops tools at the frontier of analysis and geometry. He has obtained results that have attracted significant international attention, such as the resolution (in joint work with Daniel Peralta) of conjectures about knotted vorticity structures in equilibrium fluids that date back to Lord Kelvin in 1875 and Vladimir Arnold in 1965. He has published some 90 research papers on fluid mechanics, spectral theory, dynamical systems and mathematical physics. His research has been funded by European Research Council projects and has led him to win several awards, including the 2014 Princess of Girona Award.