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BBVA project COMPLEX FLUIDS
Upcoming: We will open several INIREC contracts (initiation to research) for undergraduate and master students financed by our BBVA project “Computational, dynamical and geometrical complexity in fluid dynamics (COMPLEXFLUIDS)”.
Research topic: The entry door of our project is motivated by the work of Tao to find a counterexample to the Navier-Stokes conjecture, one of the open problems in the millennium list of the Clay foundation. In the recent exploration of some of the facets of Tao’s program, we have unveiled deep connections to unexplored pathways in hydrodynamics. In particular, we showed the existence of undecidable fluid paths in hydrodynamics (Cardona, Miranda, Peralta-Salas, Presas, PNAS, 2021) and chaos in the incompressible Euler equation on manifolds of high dimension (Torres de Lizaur, Inventiones Mathematicae, 2022). This investigation took us to cumbersome labyrinths connected to the mathematical foundations of computer science and symbolic dynamics. Our research project focuses on the interplay of pure mathematics and theoretical aspects of computer science. The investigation of the several levels of complexity (topological, dynamical, computational or logical) will play a central role in the project. The project unfolds in three working packages: on embeddings, on computational and logical complexity and on dynamical complexity of fluids. The resolution of the Navier-Stokes conjecture in the Clay list is a breakthrough in mathematics. Even if the initial motivation for this project is to disentangle the Navier-Stokes enigma a priori it is not clear that Tao’s approach can succeed; however, understanding the rich connection to computational mathematics and diverse areas of pure mathematics is an extraordinary accomplishment in mathematics, and at the frontier of science.
About the project: “Computational, dynamical and geometrical complexity in fluid dynamics (COMPLEXFLUIDS)”
Principal Researcher: Eva Miranda at UPC.
Team: Robert Cardona Aguilar (UPC); Ángel González Prieto (Universidad Complutense de Madrid); Daniel Peralta Salas (Instituto de Ciencias Matemáticas – CSIC); Francisco Torres de Lizaur (Universidad de Sevilla).
Alumni: Current INIREC students: Josep Fontana McNally.
Fund awarded: 150.000 euros.
The activities organized along the project comprise two workshops on top-edge topics, a colloquium on the limits of computer science and a round table on open problems in mathematics and social impact. With this project, we also aim at sup- porting young researchers that would join us in this endeavor by offering a postdoctoral contract and several grants for initiation of research.
Information about this grant on the media:
https://www.fbbva.es/equipo/ecuaciones-modelizar-comportamiento-fluidos/
Interested? Send me an email with your cv and a motivation letter.
Interested? Send me an email with your cv and a motivation letter.
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