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Prof. José A. Carrillo

PhD, MA, MSc, BSc, FEurASc, FSIAM, FIMA
Status
Academic Faculty

- Professor of the Analysis of Nonlinear Partial Differential Equations

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

Contact form
https://carrilloja.org
CV
+44 1865 615125
ORCID iD
https://orcid.org/0000-0001-8819-4660
Research groups
  • Oxford Centre for Nonlinear PDE
  • Mathematical Biology

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

Highlighted publications
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)
On the singularity formation and relaxation to equilibrium in 1D Fokker–Planck model with superlinear drift
Carrillo de la Plata, J Hopf, K Rodrigo, J Advances in Mathematics volume 360 (12 Nov 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)
Long-time behaviour and phase transitions for the Mckean–Vlasov equation on the torus
Carrillo de la Plata, J Gvalani, R Pavliotis, G Schlichting, A Archive for Rational Mechanics and Analysis volume 235 issue 1 635-690 (26 Jul 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)
The ellipse law: Kirchhoff meets dislocations
Carrillo de la Plata, J Mateu, J Mora, M Rondi, L Scardia, L Verdera, J Communications in Mathematical Physics volume 373 issue 2 507-524 (24 Apr 2019)
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)
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)
Existence of Compactly Supported Global Minimisers for the Interaction Energy
Canizo, J Carrillo, J Patacchini, F ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS volume 217 issue 3 1197-1217 (Sep 2015) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000356246500010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
Dimensionality of Local Minimizers of the Interaction Energy
Balague, D Carrillo, J Laurent, T Raoul, G ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS volume 209 issue 3 1055-1088 (Sep 2013) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000320576100008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
GLOBAL-IN-TIME WEAK MEASURE SOLUTIONS AND FINITE-TIME AGGREGATION FOR NONLOCAL INTERACTION EQUATIONS
Carrillo, J Difrancesco, M Figalli, A Laurent, T Slepcev, D DUKE MATHEMATICAL JOURNAL volume 156 issue 2 229-271 (01 Feb 2011) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000286706300002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
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)
Infinite time aggregation for the critical Patlak-Keller-Segel model in R-2
Blanchet, A Carrillo, J Masmoudi, N COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS volume 61 issue 10 1449-1481 (Oct 2008) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000259289100003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
Granular hydrodynamics and pattern formation in vertically oscillated granular disk layers
Carrillo, J Poschel, T Saluena, C JOURNAL OF FLUID MECHANICS volume 597 119-144 (25 Feb 2008) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254394400005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
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 (Feb 2006) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000234920700002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
Carrillo, J McCann, R Villani, C REVISTA MATEMATICA IBEROAMERICANA volume 19 issue 3 971-1018 (2003) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000221115100009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
Asymptotic L-1-decay of solutions of the porous medium equations to self-similarity
Carrillo, J Toscani, G INDIANA UNIVERSITY MATHEMATICS JOURNAL volume 49 issue 1 113-142 (2000) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000089184800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
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

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.
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 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, the SIAM-PDE meeting in 2022 and the ENUMATH 2023.

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