Prof. José A. Carrillo

PhD, MA, MSc, BSc, FEurASc, FSIAM, MAE, FIMA

Status

Academic Faculty

- Professor of the Analysis of Nonlinear Partial Differential Equations

- Tutorial Fellow in Applied Mathematics, The Queen's College

- ICIAM Officer at Large

+44 1865 615125

Contact form

https://carrilloja.org

ORCID iD

https://orcid.org/0000-0001-8819-4660

Research groups

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

Recent Publications and Preprints

Research interests

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.

Further details

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 Scientic Advisory Board of BIRS (Canada) since 2022. He is currently serving as ICIAM Officer at Large for since July 2024.

International Recognition:

He was elected member of the European Academy of Sciences, Section Mathematics in 2018, SIAM Fellow Class 2019, and member of the Academia Europeaea in 2023. 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.

Prizes, Awards & 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. He 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.

Highlighted publications

Quantifying tissue growth, shape and collision via continuum models and Bayesian inference.

Falcó, C Cohen, D Carrillo, J Baker, R Journal of the Royal Society, Interface volume 20 issue 204 20230184-20230184 (19 Jul 2023)

Structure preserving primal dual methods for gradient flows with
nonlinear mobility transport distances

Carrillo, J Wang, L Wei, C SIAM Journal of Numerical Analysis (29 Mar 2023)

Nonlocal approximation of nonlinear diffusion equations

Carrillo, J Esposito, A Wu, J Calculus of Variations and Partial Differential Equations (16 Feb 2023)

From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials

Carrillo, J Shu, R Calculus of Variations and Partial Differential Equations volume 62 issue 1 (09 Jan 2023)

The Landau equation as a Gradient Flow

Carrillo, J Delgadino, M Desvillettes, L Wu, J Analysis and PDE (27 Nov 2022) http://arxiv.org/abs/2007.08591v1

A local continuum model of cell-cell adhesion

Falcó, C Baker, R Carrillo, J SIAM Journal on Applied Mathematics (29 Jun 2022)

Asymptotic simplification of Aggregation-Diffusion equations towards the
heat kernel

Carrillo, J Gómez-Castro, D Yao, Y Zeng, C Archive for Rational Mechanics and Analysis (01 Nov 2022) http://arxiv.org/abs/2105.13323v1

Noise-driven bifurcations in a neural field system modelling networks of grid cells

Carrillo, J Holden, H Solem, S Journal of Mathematical Biology volume 85 issue 4 (27 Oct 2022)

Global Minimizers of a Large Class of Anisotropic Attractive-Repulsive
Interaction Energies in 2D

Carrillo, J Shu, R Communications on Pure and Applied Mathematics (23 Sep 2022)

Computing equilibrium measures with power law kernels

Gutleb, T Carrillo de la Plata, J Olver, S Mathematics of Computation volume 91 issue 337 2247-2281 (14 Jun 2022)

Boltzmann to Landau from the gradient flow perspective

Carrillo, J Delgadino, M Wu, J Nonlinear Analysis volume 219 112824-112824 (Jun 2022)

Noise-driven bifurcations in a nonlinear Fokker-Planck system describing
stochastic neural fields

Carrillo, J Roux, P Solem, S Physica D: Nonlinear Phenomena (24 May 2022)

Consensus‐based sampling

Carrillo, J Hoffmann, F Stuart, A Vaes, U Studies in Applied Mathematics volume 148 issue 3 1069-1140 (05 Apr 2022)

Infinite-time concentration in aggregation–diffusion equations with a given potential

Carrillo, J Gómez-Castro, D Vázquez, J Journal de Mathématiques Pures et Appliquées volume 157 346-398 (Jan 2022)

Primal dual methods for Wasserstein gradient flows

Carrillo de la Plata, J Craig, K Wang, L Wei, C Foundations of Computational Mathematics volume 22 issue 2022 389-443 (31 Mar 2021)

Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

Carrillo, J Choi, Y ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS volume 241 issue 3 1529-1573 (2021) https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=elements_prod_1&SrcAuth=WosAPI&KeyUT=WOS:000656795700001&DestLinkType=FullRecord&DestApp=WOS_CPL

Fast Diffusion leads to partial mass concentration in Keller-Segel type
stationary solutions

Carrillo, J Delgadino, M Frank, R Lewin, M Mathematical Models and Methods in Applied Sciences (M3AS) (15 Dec 2020)

A particle method for the homogeneous Landau equation

Carrillo, J Hu, J Wang, L Wu, J Journal of Computational Physics: X volume 7 (01 Jun 2020)

Reverse Hardy–Littlewood–Sobolev inequalities

Carrillo, J Delgadino, M Dolbeault, J Frank, R Hoffmann, F Journal des Mathematiques Pures et Appliquees volume 132 133-165 (01 Dec 2019)

Mean-field limit for collective behavior models with sharp sensitivity regions

Carrillo De La Plata, J Choi, Y Hauray, M Salem, S Journal of the European Mathematical Society volume 21 issue 1 121-161 (29 Sep 2019)

Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics

Carrillo de la Plata, J Hittmeir, S Volzone, B Yao, Y Inventiones Mathematicae volume 218 issue 3 889-977 (25 Jul 2019)

A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation

Carrillo de la Plata, J Murakawa, H Sato, M Togashi, H Trush, O Journal of Theoretical Biology volume 474 14-24 (03 May 2019)

A blob method for diffusion

Carrillo de la Plata, J Craig, K Patacchini, F Calculus of Variations and Partial Differential Equations volume 58 issue 2 (16 Feb 2019)

Existence of ground states for aggregation-diffusion equations

Carrillo de la Plata, J Delgadino, M Patacchini, F Analysis and Applications volume 17 issue 3 393-423 (16 Oct 2018)

Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces

Carrillo de la Plata, J Choi, Y Tse, O Communications in Mathematical Physics volume 365 329-361 (04 Oct 2018)

Ground states in the diffusion-dominated regime

Carrillo de la Plata, J Hoffmann, F Mainini, E Volzone, B Calculus of Variations and Partial Differential Equations volume 57 issue 5 (11 Aug 2018)

An analytical framework for consensus-based global optimization method

Carrillo de la Plata, J Choi, Y Totzeck, C Tse, O Mathematical Models and Methods in Applied Sciences volume 28 issue 6 1037-1066 (11 Apr 2018)

Phase transitions in a kinetic flocking model of Cucker--Smale type

Barbaro, A Canizo, J Carrillo de la Plata, J Degond, P Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal volume 14 issue 3 1063-1088 (30 Aug 2016)

Regularity of local minimizers of the interaction energy via obstacle problems

Carrillo de la Plata, J Delgadino, M Mellet, A Communications in Mathematical Physics volume 343 issue 3 747-781 (17 Mar 2016)

Critical thresholds in 1D Euler equations with non-local forces

Carrillo, J Choi, Y Tadmor, E Tan, C MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES volume 26 issue 1 (2016) https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=elements_prod_1&SrcAuth=WosAPI&KeyUT=WOS:000364233000006&DestLinkType=FullRecord&DestApp=WOS_CPL

Existence of Compactly Supported Global Minimisers for the Interaction Energy

Cañizo, J Carrillo, J Patacchini, F Archive for Rational Mechanics and Analysis volume 217 issue 3 1197-1217 (04 Sep 2015)

Dimensionality of Local Minimizers of the Interaction Energy

Balagué, D Carrillo, J Laurent, T Raoul, G Archive for Rational Mechanics and Analysis volume 209 issue 3 1055-1088 (22 Sep 2013)

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

Carrillo, J DiFrancesco, M Figalli, A Laurent, T Slepčev, D Duke Mathematical Journal volume 156 issue 2 229-271 (01 Feb 2011)

Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.

Carlen, E Carrillo, J Loss, M Proceedings of the National Academy of Sciences of the United States of America volume 107 issue 46 19696-19701 (Nov 2010)

Nonlinear mobility continuity equations and generalized displacement convexity

Carrillo, J Lisini, S Savaré, G Slepčev, D Journal of Functional Analysis volume 258 issue 4 1273-1309 (Feb 2010)

Asymptotic Flocking Dynamics for the Kinetic CuckerSmale Model

Carrillo, J Fornasier, M Rosado, J Toscani, G SIAM Journal on Mathematical Analysis volume 42 issue 1 218-236 (26 Jan 2010)

Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions

Blanchet, A Carrillo, J Laurençot, P Calculus of Variations and Partial Differential Equations volume 35 issue 2 133-168 (13 Jun 2009)

Blow-up in multidimensional aggregation equations with mildly singular interaction kernels**This paper is published as part of a collection in honour of Todd Dupont's 65th birthday.

Bertozzi, A Carrillo, J Laurent, T Nonlinearity volume 22 issue 3 683-710 (01 Mar 2009)

Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2

Blanchet, A Carrillo, J Masmoudi, N Communications on Pure and Applied Mathematics volume 61 issue 10 1449-1481 (30 Oct 2008)

Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical PatlakKellerSegel Model

Blanchet, A Calvez, V Carrillo, J SIAM Journal on Numerical Analysis volume 46 issue 2 691-721 (01 Jan 2008)

Tanaka Theorem for Inelastic Maxwell Models

Bolley, F Carrillo, J Communications in Mathematical Physics volume 276 issue 2 287-314 (21 Dec 2007)

Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media

Carrillo, J McCann, R Villani, C Archive for Rational Mechanics and Analysis volume 179 issue 2 217-263 (23 Feb 2006)

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

Carrillo, J McCann, R Villani, C Revista Matemática Iberoamericana volume 19 issue 3 971-1018 (31 Dec 2003)

A WENO-solver for the transients of Boltzmann–Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods

Carrillo, J Gamba, I Majorana, A Shu, C Journal of Computational Physics volume 184 issue 2 498-525 (Jan 2003)

Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

Carrillo, J Toscani, G Communications in Mathematical Physics volume 225 issue 3 551-571 (Feb 2002)

Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities

Carrillo, J Jüngel, A Markowich, P Toscani, G Unterreiter, A Monatshefte für Mathematik volume 133 issue 1 1-82 (May 2001)

Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity

Carrillo, J Toscani, G Indiana University Mathematics Journal volume 49 issue 1 0-0 (2000)

Minimizers of 3D anisotropic interaction energies

Carrillo, J Shu, R Advances in Calculus of Variations http://arxiv.org/abs/2206.14054v1

Existence of radial global smooth solutions to the pressureless
Euler-Poisson equations with quadratic confinement

Carrillo, J Shu, R Archive for Rational Mechanics and Analysis

Bound-Preserving Finite-Volume Schemes for Systems of Continuity
Equations with Saturation

Bailo, R Carrillo, J Hu, J SIAM Journal on Applied Mathematics http://arxiv.org/abs/2110.08186v2

Prizes, awards, and scholarships