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Daniel Peralta-Salas

Institution: CSIC

Position: Científico Titular

Phone: +34 912999 746


Personal Webpage


Biographical Review

Daniel Peralta-Salas (Madrid, 1978) is a permanent member of the ICMAT. His research lines concern the connections and interplay between dynamical systems, partial differential equations and differential geometry. This includes different topics in fluid mechanics, spectral theory and conservative dynamics.

He has published over 80 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.

He has been an invited speaker in more than 60 conferences and courses in national and international congresses, and is a member of the editorial boards of the international journals "Revista Matematica Iberoamericana" (EMS), “Qualitative Theory of Dynamical Systems" (Birkhaüser) and “Journal of Geometric Mechanics” (AIMS).

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 Dirichlet 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).

His main honors and distinctions include:

- ERC Starting Grant (2014-2019), to work on the invariant manifolds that emerge from solutions to PDE.

- The Barcelona Dynamical Systems Prize (joint with Alberto Enciso). Awarded by the Societat Catalana de Matemàtiques (2015).

- Plenary Speaker, European Congress of Mathematics (July 2016, Berlin, Germany). He was the second spanish mathematician that gives a plenary lecture at the ECM since its foundation in 1992.

- The Floer Lectures, Floer Center of Geometry (June 2019, Bochum, Germany).

- The MINT Distinguished Lectures, Mathematical Institute at Tel Aviv (January 2020, Tel Aviv, Israel).

Research Interests

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