My main interest is the study of different properties of the solutions to PDEs related with Fluid Dynamics. More precisely, I am familiarized with the following concepts:
Changes in the topology of the set of integral lines of the solutions to PDEs.
Well-posedness for incompressible MHD equations (ideal density dependent, viscous and (non-)resistive, etc.).
Linear and nonlinear spectral (in)stabiliy around steady states.
Some objects/techniques I am familiarized with: energy estimates, Littlewood-Paley theory and Besov spaces, heat-semigroup estimates, Beltrami fields, Elsässer variables, perturbation analysis, fixed point arguments, normal forms and spectral theory.
I also have a strong background and interest in Operator Theory and, in particular, in the boundedness of Singular Integral Operators (SIO). I developed my Bachelor and Master theses on this topic.
I have attended the specialized program in Applied Artificial Intelligence and its Mathematical Foundations offered by the EHU (Bizkaia, Spain). I developed my Final Degree thesis on the statistics behind Survival Analysis, also applying the theory to a real medical dataset.