Prof. José A. Carrillo
- Professor of the Analysis of Nonlinear Partial Differential Equations
- Tutorial Fellow in Applied Mathematics, The Queen's College
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research Topics:
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.
Recent Publications and Preprints
My expertise comprises long-time asymptotics, qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations in the modelling of collective behaviour 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 am lately interested in the interplay between interacting particle systems, optimal transport, and PDEs in the mathematical foundations of data science and articial intelligence.
José A. Carrillo has been awarded the Echegaray Medal of the Royal Academy of Sciences of Spain in 2022 and the International Tartufari prize on Mathematics, Mechanics and their applications of the Accademia Nazionale dei Lincei in 2024.
Previous positions:
José A. Carrillo was Chair in Applied and Numerical Analysis at Imperial College London 2012-2020. He was ICREA Research Professor at the Universitat Autònoma de Barcelona 2003-2012. He was a lecturer at the University of Texas at Austin 1998-2000. He held assistant and associate professor positions at the Universidad de Granada 1992-1998 and 2000-2003, where he also did his PhD.
Service to the community:
He served as chair of the Applied Mathematics Committee of the European Mathematical Society 2014-2017 and as chair of the 2018 Year of Mathematical Biology. He was the Program Director of the SIAM activity group in Analysis of PDE 2019-2020. He was vice-president of the European Society for Mathematical and Theoretical Biology 2021-2023 and member of his Board 2024-2026. He is member of the Scientific Committee of the Spanish National Science Agency 2021-2024. He is member of the Scientific Advisory Board of BIRS (Canada) since 2022. He is currently serving as ICIAM Officer at Large since July 2024.
International Recognition:
He was elected member of the European Academy of Sciences, Section Mathematics in 2018, SIAM Fellow Class 2019, member of the Academia Europeaea in 2023, and AMS Fellow Class 2026. He is currently the head of the Division of the European Academy of Sciences, Section Mathematics. He is Fellow of the Institute of Mathematics and its Applications and Foreign Member of the Royal Academy of Sciences of Spain since 2021. He has been invited speaker at the 2008 European Conference of Mathematics and plenary speaker at the Joint SIAM-CAIMS Annual Meeting 2020, the Joint British Mathematics Colloquium 2021, the SIAM-PDE 2022, the ICIAM 2023 in Tokyo and the ENUMATH 2023. He has received an ERC Advanced Grant 2019 to develop his research in nonlocal PDEs for complex particle dynamics: phase transitions, patterns and synchronization. He was elected in the first cohort of the UK Academy for the Mathematical Sciences 2026.
Further Prizes, awards, and scholarships:
He was recognised with the SEMA prize (2003) and the GAMM Richard Von-Mises prize (2006) for young researchers. He was a recipient of a Wolfson Research Merit Award by the Royal Society 2012-2017. He was awarded the 2016 SACA award for best PhD supervision at Imperial College London.