BCAM Scientific Seminar | Cell-cell Adhesion micro- and macroscopic models via Aggregation- Diffusion systems
Date: Tue, Mar 25 2025
Hour: 16:00
Location: Maryam Mirzakhani Seminar Room at BCAM
Speakers: José A. Carrillo (Mathematical Institute, University of Oxford, UK)
Abstract
We discuss microscopic and continuum cell-cell adhesion models and their derivation based on the underlying microscopic assumptions. We will derive these macroscopic limits via mean-field assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. Asymptotic models are obtained via Cahn-Hilliard approximations. The new models are able to capture both qualitatively and quantitatively experiments. We also review some of the applications of these models in other areas of tissue growth in developmental biology. We will analyse the mathematical properties of the resulting aggregation-diffusion, Cahn-Hilliard and reaction-diffusion systems based on variational tools.
Confirmed speakers:
José A. Carrillo (Mathematical Institute, University of Oxford, UK)
José A. Carrillo is currently Professor of the Analysis of Nonlinear Partial Differential Equations at the Mathematical Institute and Tutorial Fellow in Applied Mathematics at The Queen's College, University of Oxford associated to the OxPDE, Numerical Analysis and WCMB groups. He was previously Chair in Applied and Numerical Analysis at Imperial College London from October 2012 till March 2020 and 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; and held assistant and associate professor positions at the Universidad de Granada 1992-1998 and 2000-2003, where he also did his PhD.
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 and lately in collective behaviour. His main scholarship contributions in analysis of PDEs are in aggregation-diffusion problems, i.e. nonlinear Fokker-Planck type equations; the use of optimal transport techniques and entropy methods to analyse gradient-flow structures for PDEs and their singularities; the analysis of kinetic models for self-organization, and their implications in biology and global optimization. He has also developed numerical schemes for nonlinear aggregation-diffusions preserving the free energy decay property. Other interests in mathematical biology include the understanding of cell sorting by differential adhesion and synchronization phenomena in neuroscience.
He served as chair of the Applied Mathematics Committee of the European Mathematical Society 2014-2017 and 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, now member of its board; and member of the Scientific Committee of the Spanish National Science Agency 2021-2024. He is currently officer at large at the International Council for Industrial and Applied Mathematics 2024-2028. He was elected as member of the European Academy of Sciences,
Section Mathematics in 2018, SIAM Fellow Class 2019, Fellow of the Institute of Mathematics and its Applications, and Foreign Member of the Royal Academy of Sciences of Spain in 2021.
He is now the head of the Division of the European Academy of Sciences, Section Mathematics. He was recognised with the SEMA prize (2003) and the GAMM Richard Von-Mises prize (2006) for young researchers, a Wolfson Research Merit Award by the Royal Society 2012-2017, and the 2016 SACA award for best PhD supervision at Imperial College London. He has been Highly Cited Researcher in 2015, 2016, 2017, 2018, 2019, and 2020 by Web of Science. He received the 2022 Echegaray Medal of the Royal Spanish Academy of Sciences. This is the highest scientific award granted by the Spanish Royal Academy of Sciences and is awarded in recognition of an exceptional scientific career. He was awarded the International Prize «Prof. Luigi Tartufari» for Mathematics, Mechanics and Applications 2024, Accademia Nazionale dei Lincei, Italy. He has been plenary speaker in important conferences of the area among which the International Congress on Industrial and Applied Mathematics at Tokyo in 2023. He has been awarded an ERC Advanced Grant 2019 to pursue his investigations in complex particle dynamics: phase transitions, patterns, and synchronization.
Web page: https://www.maths.ox.ac.uk/people/jose.carrillodelaplata
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