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This is a call for expressions of interest to join the research project COMPLEXFLUIDS and our research team at the Laboratory of Geometry and Dynamics of the UPC.
What we seek:
We look for highly motivated students on the topics of Differential Geometry, Topology, Dynamical Systems and PDE's with an outstanding CV. We are especially interested in double-degree students with profiles in Mathematics and Physics or Mathematics and Computer Science. Students must be enrolled at the master in Advanced Mathematics and Mathematical Engineering (MAMME).
What we plan to offer:
In the next 2 academic years, we plan to offer 3 contracts under the INIREC program https://rdi.upc.edu/ca/uaslr/vols-dedicar-te-a-la-recerca/beques-inirec for a duration of 3 months with a possible extension to 6 months with the highest stipend per month. These grants will be focused on the project COMPLEXFLUIDS and the project ICREA Academia of Eva Miranda. The contracts will be cofinanced by the FBBVA project COMPLEXFLUIDS and the ICREA Academia Project. The candidates must be enrolled at the master in Advanced Mathematics and Mathematical Engineering (MAMME) and pursue their theses under the supervision of Eva Miranda (potential co-supervisions with Robert Cardona, Angel González Prieto at UCM, Daniel Peralta-Salas at ICMAT and Francisco Torres de Lizaur at Universidad de Sevilla are also envisaged/encouraged).
Only in very exceptional cases, the supervision of undergraduate thesis with a strong research component in this scheme could be considered. Then, the stipend would be adjusted to the category.
Timeline:
The contracts can start in the second semester of the 22-23 academic year or in the second semester of the 23-24 academic year.
The topic:
The master thesis will be centered on the many facets of the complexity of fluids (topological, dynamical, computational and geometrical).
The eligible topics are the following:
1- Embedding theorems as Euler and Navier-Stokes flows. Geometrical aspects of embedding theorems in Fluids:
Lie theory, quantization and representation theory.
2- Computational and logical complexity. Undecidability and Turing completeness in hydrodynamics.
Computational and logical complexity and on the dynamical complexity of fluids. The computational complexity of Euler and Navier-Stokes equations.
3- Dynamical complexity of fluids: Chaos and fluids. Topological complexity in fluids and connections with computability. Stability analysis à la Friedlander-Vishik.
To know more:
About our projects: https://www.fbbva.es/noticias/ayudas-fundacion-bbva-35-proyectos-de-investigacion/
About our work:
https://www.pnas.org/doi/10.1073/pnas.2026818118
https://link.springer.com/article/10.1007/s00222-021-01089-3
https://www.pourlascience.fr/sd/mathematiques/les-indecidables-trajectoires-d-un-fluide-22023.php
https://arxiv.org/abs/2107.09471
What's next?
If you are interested please send an email with a cv, a motivation letter and your transcripts to Professor Eva Miranda (eva.miranda@upc.edu)
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