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Agent Models of 1st and 2nd order: From micro to macro

José A. Carrillo,  Imperial College London

During this course I will discuss microscopic models of collective behavior and consensus of first and second order, their rich dynamical structure and the stability properties of particular solutions such as flocks and mills. I will also discuss how to coarse grain these models into kinetic and macroscopic PDEs and how to connect and analyse the different type of models.

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Short Bio:

José A. Carrillo currently holds a Chair in Applied and Numerical Analysis at Imperial College London appointed in October 2012. He was formerly  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 Committeeof the European Mathematical Society 2014-2017.

His research field is Partial Differential Equations (PDEs). They constitute the basic language in which most of the laws in physics or engineering can be written and one of the most important mathematical tools for modelling in life and socio-economical sciences. The modelling based on PDEs, their mathematical analysis, the numerical schemes, and their simulation in applications are his general topics of research. His expertise comprises long-time asymptotics, qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations in the modelling of 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 was a recipient of a Wolfson Research Merit Award by the Royal Society 2012-2017.

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