Skip to main content

Daniel Peralta-Salas

Institution: CSIC

Position: Científico Titular

Office: 206

Phone: +34 912999 746


Personal Webpage


Biographical Review

Daniel Peralta is a permanent member of the ICMAT. His research lines concern the connections and interplay between dynamical systems, partial differential equations and differential geometry. He has published over 70 papers in high profile mathematical journals such as: Annals of Mathematics, Acta Mathematica, Duke Mathematical Journal, Annales Scientifiques de l'École Normale Supérieure, Journal of Differential Geometry, American Journal of Mathematics, Advances in Mathematics and Communications in Mathematical Physics.

Among his best results, we highlight the proofs, in joint work with Alberto Enciso, of Arnold's conjecture in hydrodynamics (Annals of Mathematics 2012), Lord Kelvin conjecture on the existence of knotted steady vortex tubes (Acta Mathematica 2015), and the solution to Yau's problem on nodal sets of Laplace eigenfunctions (Journal of Differential Geometry 2015). These results had a huge impact in national and international press media. He also developed, in joint work with Alberto Enciso and María Ángeles García Ferrero, the global approximation theory for parabolic PDE (Duke Mathematical Journal 2019).

In 2013 he was awarded with a Starting Grant from the European Research Council (1.260.000 €) to work on the invariant manifolds that emerge from solutions to PDE. He has been an invited speaker in more than 50 conferences and courses in national and international congresses. We highlight the plenary conference at the European Congress of Mathematics held in Berlin in July 2016, being the second spanish mathematician that gives a plenary lecture at the ECM since its foundation in 1992, and the invitation to give the Floer Lectures in June 2019 at the Floer Center of Geometry (Germany). In 2015 he was recognized, jointly with Alberto Enciso, with the Barcelona Dynamical Systems Prize awarded by the Societat Catalana de Matemàtiques. He is a member of the editorial boards of the international journals “Qualitative Theory of Dynamical Systems” (Birkhaüser) and “Journal of Geometric Mechanics” (AIMS).

Research Interests

Dynamical Systems; Partial Differential Equations; Differential Geometry; Mathematical-Physics.