Institution: CSIC
Position: Investigador Científico
Office: 206
Phone: +34 912999 746
Email: dperalta@icmat.es
About:
Daniel Peralta-Salas (Madrid) is a senior scientific researcher at the ICMAT and Chair of the Group “Differential Geometry and Geometric Mechanics”. 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, conservative dynamics and geometric analysis.
He has published over 100 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, Journal of the European Mathematical Society and Advances in Mathematics.
He has been an invited speaker in more than 100 conferences, seminars and courses in national and international events, is a member of the editorial boards of the international journals Revista Matematica Iberoamericana (EMS), Journal of Dynamics and Differential Equations (Springer), Qualitative Theory of Dynamical Systems (Birkhaüser) and Geometric Mechanics (World Scientific), and member of the scientific advisory board of IMTECH (Institute of Mathematics of UPC-Barcelona Tech.).
Among his best results, we highlight:
- A new theory to study geometrically complex structures in the equations that model physical phenomena. His main landmarks, in collaboration with A. Enciso, include the proof of a 1965 Arnold's conjecture in hydrodynamics (Annals of Mathematics 2012), of the centennial Lord Kelvin conjecture on the existence of steady knotted vortex tubes (Acta Mathematica 2015) and the proof of Michael Berry's conjecture in quantum mechanics (Journal of the European Mathematical Society 2018).
- First theoretical construction of a 3D steady fluid flow that can simulate a universal Turing machine, in collaboration with R. Cardona, E. Miranda and F. Presas. This implies the existence of undecidable fluid particle paths, a long standing open problem posed by C. Moore in 1991 (Proc. Natl. Acad. Sci. USA 2021 and J. Math. Pures Appl. 2022).
- Analytical construction of a new family of solutions to the equations of electromagnetism whose electric and magnetic lines encode all torus knots and links, which persist for all time, in collaboration with H. Kedia, I. Bialynicki-Birula and W. Irvine. The existence of these structures was an elusive open problem since 1990 (Physical Review Letters 2013, featured on cover).
His main honors and distinctions include:
- ERC Starting Grant (2014-2019), to work on the invariant manifolds that emerge from solutions to PDEs.
- The Barcelona Dynamical Systems Prize. 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).
- Plenary Speaker, Biannual Congress of the Spanish Applied Mathematical Society, CEDYA-CMA (June 2021, Gijón, Spain).
- Plenary Speaker, Biannual Congress of the Royal Spanish Mathematical Society, RSME (January 2022, Ciudad Real, Spain).
- Colloquium Lecture for the meeting (season 2022-2023) of the Edinburgh Mathematical Society, University of Dundee (November 2022, Dundee, UK).
- EMS Distinguished Speaker, Nordic Congress of Mathematicians (July 2023, Aalborg, Denmark).
