Prof. José A. Carrillo
- Professor of the Analysis of Nonlinear Partial Differential Equations
- Tutorial Fellow in Applied Mathematics, The Queen's College
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
heat kernel
Interaction Energies in 2D
stationary solutions
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. 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 has been awarded the Echegaray Medal of the Royal Academy of Sciences of Spain in 2022.
Recent Publications and Preprints
Book Chapters and Surveys:
- J. A. Carrillo, J. Hu, Z. Ma, T. Rey, Recent development in kinetic theory of granular materials: analysis and numerical methods. Trails in kinetic theory, 1–36, SEMA SIMAI Springer Ser., 25, Springer, Cham, 2021.
- J. A. Carrillo, D. Matthes, M.-T. Wolfram, Lagrangian schemes for Wasserstein gradient flows, Chapter 4, Handbook of Numerical Analysis 22, 271-311, Elsevier, 2021.
- J. A. Carrillo, K. Craig, Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, in N. Bellomo, P. Degond, and E. Tadmor (Eds.), Active Particles Vol. II: Advances in Theory, Models, and Applications, Series: Modelling and Simulation in Science and Technology, Birkhäuser Basel, 65-108, 2019.
- R. Bailo, J. A. Carrillo, P. Degond, Pedestrian Models based on Rational Behaviour, in: Gibelli L., Bellomo N. (eds) Crowd Dynamics, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham, 259-292, 2018. Supplementary Material: Movies and Simulations.
- V. Calvez, J. A. Carrillo, F. Hoffmann, The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime, Lecture Notes in Mathematics 2186, CIME Foundation Subseries, Springer, 2018.
- J. A. Carrillo, Y.-P. Choi, S. Pérez, A review on attractive-repulsive hydrodynamics for consensus in collective behavior, in N. Bellomo, P. Degond, and E. Tadmor (Eds.), Active Particles Vol. I: Advances in Theory, Models, and Applications, Series: Modelling and Simulation in Science and Technology, Birkhäuser Basel, 259-298, 2017.
- J. A. Carrillo, Y.-P. Choi, M. Hauray, The derivation of Swarming models: Mean-Field Limit and Wasserstein distances, Collective Dynamics from Bacteria to Crowds: An Excursion Through Modeling, Analysis and Simulation Series, CISM International Centre for Mechanical Sciences, Vol. 553, 1-46, 2014.
- J. A. Carrillo, M. Fornasier, G. Toscani, F. Vecil, Particle, Kinetic, and Hydrodynamic Models of Swarming, in Naldi, G., Pareschi, L., Toscani, G. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Series: Modelling and Simulation in Science and Technology, Birkhauser, (2010), 297-336.
- J. A. Carrillo, G. Toscani, Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations, Notes of the 2006 Porto Ercole Summer School, Rivista Matemàtica di Parma 6, 75-198, 2007.
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 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.
Previous positions:
José A. Carrillo was previously Chair in Applied and Numerical Analysis at Imperial College London from October 2012 till March 2020. He was formerly ICREA Research Professor at the Universitat Autònoma de Barcelona during the period 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. He was the 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 is vice-president of the European Society for Mathematical and Theoretical Biology 2021-2023. He is member of the Scientific Committee of the Spanish National Science Agency 2021-2024.
International Recognition:
He has been elected as member of the European Academy of Sciences, Section Mathematics, in 2018 and SIAM Fellow Class 2019. 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, and the SIAM-PDE meeting in 2022. He is plenary speaker at the ICIAM 2023 and the ENUMATH 2023.