His domains of expertise in Applied Mathematics include Partial Differential Equations, Control Theory and Numerical Analysis. These subjects interrelate with the final to model, analyse, computer simulate, and finally contribute to the control and design of the most diverse natural phenomena and all fields of R + D + i. Thirty two PhD students got the degree under his advice and they now occupy positions in centres throughout the world: Brazil, Chile, China, Mexico, Romania, Spain, etc. He has developed intensive international work having led co-operation programmes with various Latin American countries, as well as with Portugal, the Maghreb, China and Iran, amongst others. He has been guest speaker in many International Conferences worldwide, with highlights including the Second
European Congress of Mathematics, Budapest, 1996, ECCOMAS 2004 in
Jyväskylä (Finland) the SMAI2005 Congress in Evian (France), FoCM2005 in Santander, ENUMATH2005 in Santiago de Compostela, the International Congress of Mathematicians (ICM) Madrid, 2006 and the EQUADIFF 2007 in Vienna (Austria), the von Mises Lecture of Humboldt University of Berlin, in 2008, the "Giornata INdAM", Turin, 2009, "SIMAI2010", Cagliari in 2010, the "Aachen Conference on Computational Engineering Science", Aachen, 2011 and the "PASI-CIPPDE-2012" Conference in Santiago de Chile en 2012. He has also given numerous monographic courses in research at various Centres, both in Spain and overseas. He has sat on and is still an active member of the Scientific Committee of various international events, including the International Programming Committee of ICM2006. In 2026, he has been invited by the International Mathematical Union (
IMU) to deliver a Special Section Lecture at the International Congress of Mathematicians 2026 (ICM2026) on Machine Learning and Control: Foundations, Advances, and Perspectives. The ICM2026 will take place in Philadelphia, USA. He has developed a number of cooperative projects with industries such as AIRBUS-Spain and
Arteche Group. He has also been the Principal Investigator for National Plan projects and since 1990 the co-ordinator for European and NATO project networks and the first research coordinator of the i-Math CONSOLIDER Mathematics Project (2007-2011), the Madrid project SIMUMAT (2006–2009). He is Editor in Chief, in collaboration with Xu Zhang (Sichuan University, Chengdu, China) of the Journal
Mathematical Control and Related Fields, and member of the editorial board for other journals including "" ESAIM:COCV", "Journal de Mathématiques pures et appliquées", "Mathematical Models and Methods in Applied Sciences", "Numerische Mathematik", "Systems and Control Letters", "Journal of Differential Equations", "Asymptotic Analysis" and "Journal of Optimization Theory and Applications". He also belongs to the editorial board of the Series "Mathématiques et Applications" of SMAI - Springer and "Modeling, Simulation and Applications" of Springer, coordinated by
Alfio Quarteroni and coordinates the series SpringerBriefs on PDES and Data Science He has managed the Mathematics Programme (2001–2004) of the Spanish National Research Plan and directed and participated in various international panels belonging of the French
CNRS,
ANR,
IUF,
AERES and
INRIA and the German DFG amongst other agencies. He was the chair of the European Research Council's Panel A "Advanced Grants," in Mathematics, and the CIMPA's (Centre International de Mathematiques Pures et Appliquées) [http://www.cimpa-icpam.org Scientific Council in Nice. He is a member of the Scientific Committee of various Institutes such as the CUMP in Porto, Portugal CERFACS in Toulouse [http://www.cerfacs.fr , the Pedro Pascual de Benasque Science Center , and the UNESCO "Mathematics and Development," Chair co-ordinated by M.Jaoua. == Dissemination activities ==