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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
CV
ORCID iD
https://orcid.org/0000-0001-8819-4660
Research groups
  • Mathematical Biology
  • Oxford Centre for Nonlinear PDE
  • Numerical Analysis
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Major / recent publications

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

Prizes, awards, and scholarships

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.

 

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. He has received an ERC Advanced Grant 2019 to develop his research in nonlocal PDEs for complex particle dynamics: phase transitions, patterns and synchronization. 

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. 

 

 

 

Highlighted publications
Nonlinear partial differential equations in neuroscience: from modelling to mathematical theory
Carrillo De La Plata, J Roux, P Mathematical Models and Methods in Applied Sciences volume 35 issue 2 403-584 (04 Mar 2025)
The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau
Equations
Bailo, R Carrillo, J Hu, J Journal of Plasma Physics (09 Jul 2024) http://arxiv.org/abs/2401.01689v2
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)
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)
A local continuum model of cell-cell adhesion
Falcó, C Baker, R Carrillo, J SIAM Journal on Applied Mathematics (29 Jun 2022)
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)
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)
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 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)
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)
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 (16 Nov 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)
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)
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)
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)
Research interests

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.

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