Daniel Peralta-Salas

Daniel Peralta-Salas is a CSIC Research Professor and Chair of the Group 'Differential Geometry and Geometric Mechanics' at the Institute of Mathematical Sciences (ICMAT) in Madrid, Spain. ICMAT is a joint research institute of the Spanish National Research Council (CSIC) and several Madrid universities. He is an active researcher with leadership roles in the ICMAT board and multiple international advisory boards.

• PhD in Mathematics, Universidad Complutense de Madrid, 2006

His research lies at the intersection of dynamical systems, partial differential equations, and differential geometry, with applications in fluid mechanics, plasma physics, quantum mechanics, and mathematical physics. He has developed a unifying theory to study geometrically complex structures in physical models. His work includes proving long-standing conjectures by Arnold, Lord Kelvin, and Michael Berry, and constructing fluid flows that simulate universal Turing machines, thereby demonstrating undecidable dynamics in fluid particle paths.

The most recent articles highlight his ongoing focus on steady Euler flows, topological obstructions in magnetic fields, optimal eigenvalue problems, and Turing universality in fluid dynamics. His publications span geometric analysis, spectral theory, and mathematical physics, often combining deep topological insight with PDE techniques. He has developed novel methods such as global approximation and inverse localization, which have broad implications across mathematical physics.

His scientific awards include:

• ERC Starting Grant (2014–2019)
• Barcelona Dynamical Systems Prize (2015)
• Plenary Speaker, European Congress of Mathematics (2016)
• The Floer Lectures (2019)
• MINT Distinguished Lectures, Tel Aviv (2020)
• Plenary Speaker at major national and international mathematical societies (2021–2024)
• EMS Distinguished Speaker (2023)

Peralta-Salas advises and collaborates extensively with researchers including Alberto Enciso, Robert Cardona, Eva Miranda, and others. His work has been supported by prestigious grants such as the ERC Starting Grant. He has published over 100 papers in top journals including Annals of Mathematics, Acta Mathematica, PNAS, and Physical Review Letters. He is a member of editorial boards for journals such as Revista Matemática Iberoamericana and Journal of Dynamics and Differential Equations, and serves on the scientific advisory board of IMTECH (UPC-Barcelona Tech).

He leads the research group on Differential Geometry and Geometric Mechanics at ICMAT, which focuses on geometric structures in dynamical systems and PDEs. The group explores topics like Beltrami fields, vortex dynamics, and topological aspects of eigenfunctions. Their work is highly collaborative and interdisciplinary, bridging pure mathematics and theoretical physics.