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I am currently an Ikerbasque Research Professor and Group Leader of Applied Analysis at the Basque Center for Applied Mathematics (BCAM), Bilbao, and a Senior Researcher at the Simion Stoilow Institute of Mathematics of the Romanian Academy.

I am a mathematician working on the analytical study of nonlinear partial differential equations and variational problems arising from physically motivated models.

My research includes liquid crystals and complex materials, Newtonian and non-Newtonian fluids, fluidstructure interaction, homogenisation and multiscale problems, phase transitions, and variational methods for nonlinear PDEs. More recent directions include variational formulations for incompressible fluids and probabilistic and neural-network methods for PDEs.

Current research directions

• Complex materials  liquid crystals, defects, phase transitions and mathematical material design.

• Fluids and fluid-structure interaction,  Newtonian and non-Newtonian fluids, rigid particles, singular limits and multiscale systems.

• Variational and multiscale PDE  calculus of variations, homogenisation, nonlinear PDE and variational formulations of incompressible fluid equations.