Introduction
I went to school at Colegio Maristas La Inmaculada in Granada (Spain) and then studied for both my undergraduate and doctoral degrees in Mathematics at the Universidad de Granada (Spain). I held assistant and associate professor positions at the Universidad de Granada 1992-1998 and 2000-2003. My postdoctoral years were at the University of Texas at Austin (USA) where I taught part-time as lecturer during 1998-2000. My first professorial position was as an ICREA Research Professorship at the Universitat Autònoma de Barcelona (Spain) during the period 2003-2012. Before joining Queen’s in April 2020, I was a Chair in Applied and Numerical Analysis at Imperial College London from 2012 to 2020.
Teaching
I teach the entire breadth of the core courses in applied mathematics at Queen’s, together with option topics in Calculus of Variations and Manifolds. I also typically supervise three or four graduate (DPhil) students and two or three post-doctoral researchers. I will be teaching a Part C course at the Mathematical Institute on advanced material in Optimal Transport and applications to Partial Differential Equations.
Research
My research field is Partial Differential Equations (PDE). They constitute the basic language in which most of the laws in physics or engineering can be written and one of the most important mathematical tools for modelling in life and socio-economical sciences. The modelling based on PDEs, their mathematical analysis, the numerical schemes, and their simulation in applications are my general topics of research. My expertise comprises long-time asymptotics, qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations in the modelling of collective behavior of many-body systems such as gas molecules in rarefied gases, sand beads in granular media, charge particle transport in semiconductors, synchronization of neurons in computational neuroscience or cell movement by chemotaxis or adhesion forces. I was awarded an ERC Advanced Grant in 2020 for funding my research in related topics.
The video below is of an online talk aimed at a non-specialist audience given by José for the Queen’s College Symposium in November, 2020 entitled: ‘Aggregation-Diffusion and Kinetic PDEs for collective behaviour: applications in the sciences’.
Publications
Please see José’s profile page on the Mathematical Institute website for a list of his publications.