New Maths Fellow joins College and wins ERC Advanced Grant
Although so far we have only been able to extend him a virtual welcome, we are pleased to report that Prof. José A. Carrillo joined the College at the start of this month.
José is a Fellow in Applied Mathematics and Professor of the Analysis of Nonlinear Partial Differential Equations, and previously held the Chair in Applied and Numerical Analysis at Imperial College London from 2012 to 2020. He will teach the whole breadth of the undergraduate core courses in applied mathematics at Queen’s, together with option topics in Calculus of Variations and Manifolds, as well as supervising graduate students and post-doctoral researchers.
José was recently awarded a European Research Council (ERC) Advanced Grant, which will fund his research on ‘Nonlocal Partial Differential Equations for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization’ for five years starting in October 2020. The ERC grants are highly competitive, with over 1880 proposals submitted for this round of funding.
José will focus on the development of mathematical tools to analyse theoretical, numerical and modelling aspects of novel applications of nonlinear nonlocal aggregation-diffusion equations in Mathematical Biology and in classical problems of kinetic theory. Among the numerous areas of applications of kinetic modelling in Mathematical Biology, he will concentrate on phenomena identified, at the modelling stage, as systems involving a large number of ‘individuals’ showing ‘collective behaviour’ and how to obtain ‘averaged’ information from them.
The proposed research is centred on developing tools underpinning the analysis of long time asymptotics, phase transitions, stability of patterns, consensus and clustering, and qualitative properties of these models. Designing numerical schemes to accurately solve these models is key not only to understanding the theoretical issues but also essential for applications. Some of the applications include the Landau equation in weakly nonlinear plasmas crucial in the understanding of fusion energy, the zebra fish patterning formation as an example of spontaneous self-organisation processes in developmental biology, and grid cells for navigation in mammals, as a prototype for the synchronisation of neural networks. This project connects with other areas of current interest in science and technology such as agent-based models in engineering with applications in global optimization, clustering, and social sciences.