Prof. José A. Carrillo is Professor of the Analysis of Nonlinear Partial Differential Equations at the Mathematical Institute, University of Oxford, and Tutorial Fellow in Applied Mathematics at The Queen's College. His research focuses on kinetic equations, nonlinear and nonlocal diffusion equations, and their applications in granular media, semiconductors, and collective behaviour. He is internationally recognised for his work on aggregation-diffusion models, nonlinear Fokker-Planck equations, and the use of optimal transport and entropy methods to analyse gradient flows and singularity formation in PDEs.

Prof. Carrillo has made major contributions to the mathematical understanding of self-organisation phenomena, with applications in biology, control engineering, and global optimisation. He was Chair of the Applied Mathematics Committee of the European Mathematical Society (2014–2017), Chair of the 2018 Year of Mathematical Biology, and Program Director of the SIAM Activity Group on Analysis of PDEs (2019–2020).

He is a Foreign Member of the Royal Academy of Sciences of Spain (2021), SIAM Fellow (Class of 2019), and recipient of the SEMA Prize (2003) and the GAMM Richard von Mises Prize (2006). He received a Royal Society Wolfson Research Merit Award (2012–2017), and was awarded an ERC Advanced Grant (2019) to support his research on complex particle dynamics, phase transitions, patterns, and synchronisation.

Prof. José A. Carrillo has served as Head of the Mathematics Division across two mandates: March 2020 – February 2023, extended until April 2024 due to the COVID-19 pandemic; May 2025 – April 2028 (current and second consecutive term, in accordance with the EurASc Bylaws).