|University of Bath||PHD Candidate in Applied Mathematics||2015 - Present|
|AXA||Analyst and Audit||2014 - 2015|
|Institut de Mathematiques de Toulouse||Master of Science degree in Probability and Statistics||2013 – 2014|
|Toulouse School of Economics||Master of Science degree in Economy||2012 – 2013|
|Institut de Mathematiques de Toulouse||Four years degree in Pure Mathematics||2007 – 2012|
The study of interacting particle systems is a large and growing field in science. The nature and size of the particles can be very different, ranging from atoms, molecules, defects, to insects, birds, people, cars. The variety of the systems that can be broadly be thought of as particle systems makes this field very relevant across disciplines, and the tools developed in the analysis widely applicable. In most of the systems of interest it is relatively well-understood how the individual particles interact and how they move, but this information is often of no practical use since the number of individuals in such systems is huge. In particular, simulations can be done only for very small systems. Motivated by this problem, there is a very strong interest in understanding the emerging properties of these systems, namely in replacing the discrete, individual based description of the systems by a continuous, group led one. In mathematical terms, this amounts in replacing the individual positions of the particles by a density function, which captures the overall behaviour of the system without keeping track of the behaviour of the single particles. We are interested in performing this discrete to continuum derivation for several particle systems, in the framework of Gamma convergence, a convergence concept for the energies of the systems. Our starting point will be, therefore, the interaction energy of the particle system, namely a variational model of the system. The macroscopic limit will be taken as the number of particles becomes increasingly large, and the limit energy will be a continuous energy depending on the density, which is in turn obtained as the limit of the discrete measure (empirical measure) associated to the discrete system. Besides the convergence of the energies, which gives information on the equilibrium states of the system, we will also study the convergence of the evolutions, by combining Gamma-convergence and gradient flows techniques. In particular, we are interested in the limit behaviour of discrete evolutions when noise is added.