University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Reverse Hardy–Littlewood–Sobolev inequalities
Journal des Mathematiques Pures et Appliquees volume 132 page 133-165 (1 December 2019)
On the singularity formation and relaxation to equilibrium in 1D Fokker–Planck model with superlinear drift
Advances in Mathematics issue ARTN 106883 volume 360 (12 November 2019)
Mean-field limit for collective behavior models with sharp sensitivity regions
Journal of the European Mathematical Society issue 1 volume 21 page 121-161 (29 September 2019)
Long-time behaviour and phase transitions for the Mckean–Vlasov equation on the torus
Archive for Rational Mechanics and Analysis issue 1 volume 235 page 635-690 (26 July 2019)
Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
Inventiones Mathematicae issue 3 volume 218 page 889-977 (25 July 2019)
A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation
Journal of Theoretical Biology volume 474 page 14-24 (3 May 2019)
The ellipse law: Kirchhoff meets dislocations
Communications in Mathematical Physics issue 2 volume 373 page 507-524 (24 April 2019)
On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions
Mathematical Models and Methods in Applied Sciences issue 1 volume 29 page 31-63 (28 December 2018)
Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces
Communications in Mathematical Physics issue 1 volume 365 page 329-361 (4 October 2018)
An analytical framework for consensus-based global optimization method
Mathematical Models and Methods in Applied Sciences issue 6 volume 28 page 1037-1066 (11 April 2018)
Existence of Compactly Supported Global Minimisers for the Interaction Energy
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS issue 3 volume 217 page 1197-1217 (September 2015) Full text available
Dimensionality of Local Minimizers of the Interaction Energy
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS issue 3 volume 209 page 1055-1088 (September 2013) Full text available
GLOBAL-IN-TIME WEAK MEASURE SOLUTIONS AND FINITE-TIME AGGREGATION FOR NONLOCAL INTERACTION EQUATIONS
DUKE MATHEMATICAL JOURNAL issue 2 volume 156 page 229-271 (1 February 2011) Full text available
Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.
Proceedings of the National Academy of Sciences of the United States of America issue 46 volume 107 page 19696-19701 (November 2010)
Infinite time aggregation for the critical Patlak-Keller-Segel model in R-2
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS issue 10 volume 61 page 1449-1481 (October 2008) Full text available
Granular hydrodynamics and pattern formation in vertically oscillated granular disk layers
JOURNAL OF FLUID MECHANICS volume 597 page 119-144 (25 February 2008) Full text available
Contractions in the 2-Wasserstein length space and thermalization of granular media
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS issue 2 volume 179 page 217-263 (February 2006) Full text available
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
REVISTA MATEMATICA IBEROAMERICANA issue 3 volume 19 page 971-1018 (2003) Full text available
Asymptotic L-1-decay of solutions of the porous medium equations to self-similarity
INDIANA UNIVERSITY MATHEMATICS JOURNAL issue 1 volume 49 page 113-142 (2000) Full text available
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.
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 is currently the Program Director of the SIAM activity group in Analysis of PDE.
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.
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. He has received an ERC Advanced Grant 2019 to develop his research in nonlocal PDEs for complex particle dynamics: phase transitions, patterns and synchronization.
Major / recent publications:
Book Chapter and Reviews:
- 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.