What links gas molecules, charged particles, bacteria and fish?  Partial differential equations help us understanding their collective behaviour. Kinetic modelling allows for a multi-scale strategy in a number of important applications in science and technology.  Mean field limits and kinetic descriptions have become one of the most powerful tools in applied mathematics to bridge microscopic and macroscopic descriptions of many body systems. They typically involve a huge number of individuals, showing some sort of “collective behaviour”, from which we want to extract macroscopic information. Some classical and modern instances of applications are: molecules in gases, electron transport in semiconductor materials, grains or beads in granular flows, endothelial cells in chemotactic movement, and many others. The individual behaviour of the “particles” is typically modelled via stochastic/deterministic ODEs leading to the most detailed description of the dynamics. From this microscopic picture, one obtains mesoscopic descriptions based on kinetic type PDEs, while the average dynamics is usually described via continuum mechanics systems of hyperbolic, diffusive, or hydrodynamic type. They are obtained as asymptotic limits of the kinetic descriptions.

Biosketch: Since 2012, José A. Carrillo has held a Chair in Applied and Numerical Analysis at Imperial College London. He was formerly  ICREA Research Professor at the Universitat Autònoma de Barcelona during the period 2003-2012. He was visiting professor in several French universities including Paris-Dauphine, Paris-Sud, Toulouse, Marseille, Nice among others, CAS-Oslo (Norway), NUS (Singapore), Tsinghua-Beijing (China), Mittag-Leffler (Sweden) and has given more than 200 seminars in leading mathematics departments worldwide. He serves as chair of the Applied Mathematics Committee of the European Mathematical Society.

His research program focuses on long-time asymptotics, qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations for modelling the collective behaviour of many-body systems such as rarefied gases, granular media, charge particle transport in semiconductors, or cell movement by chemotaxis. He was recognised with the SEMA prize (2003) and the GAMM Richard Von-Mises prize (2006) for young researchers. He is a recipient of a Wolfson Research Merit Award by the Royal Society.