Nonlinear Aggregation-Diffusion Equations: Gradient Flows, Free Energies and Phase Transitions 144



Jose Carrillo, University of Oxford, UK


2020.06.23 16:00-17:00





Conference ID: 931-911-76145

PIN Code: 503032


The main goal of this talk is to discuss the state-of-the-art in understanding the phenomena of phase transitions for a range of nonlinear Fokker-Planck equations with linear and nonlinear diffusion. They appear as natural macroscopic PDE descriptions of the collective behavior of particles such as Cucker-Smale models for consensus, the Keller Segel model for chemotaxis, and the Kuramoto model for synchronization. We will show the existence of phase transitions in a variety of these models using the natural free energy of the system and their interpretation as natural gradient flow structure with respect to the Wasserstein distance in probability measures. We will discuss both theoretical aspects as well as numerical schemes and simulations keeping those properties at the discrete level.

This talk is based on several works in collaboration with A. Barbaro, J.A. Canizo, X. Chen, Y.-P. Choi, P. Degond, R.S. Gvalani, L. Pareschi, G.A. Pavliotis, A. Schlichting, Q. Wang, Z. Wang, L. Zhang.


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 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. He held assistant and associate professor positions at the Universidad de Granada 1992-1998 and 2000-2003, where he also did his PhD.

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 is currently the Program Director of the SIAM activity group in Analysis of PDE. 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 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 been Highly Cited Researcher 2015, 2016, 2017, 2018 and 2019 by Web of Science. He has been awarded an ERC Advanced Grant 2019 to pursue his investigations in complex particle dynamics: phase transitions, patterns, and synchronization.