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** Head of Mathematics Division from March 2020 to March 2024
José A. Carrillo is currently Professor of the Analysis of Nonlinear Partial Differential Equations in the Mathematical Institute at the University of Oxford and Tutorial Fellow in Applied Mathematics at The Queen's College. He works on kinetic equations and nonlinear nonlocal diffusion equations. He has contributed to the theoretical and numerical analysis of PDEs, and their simulation in different applications such as granular media, semiconductors, collective behaviour, mathematical biology, and plasma physics. His main scholarship contributions in Analysis of PDEs are in aggregation-diffusion problems: nonlinear Fokker-Planck type equations; the use of optimal transport techniques and entropy methods to analyse theoretically and numerically gradient-flow structures for PDEs and their singularities; the analysis of kinetic models for self-organization, and their implications in mathematical biology, control engineering and global optimization.
He has been elected as 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 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 was 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. 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 has been plenary speaker at the ICIAM 2023 and the ENUMATH 2023.
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.