Geometric mechanics and its relation to numerical algorithms for mechanical systems, symplectic integration, variational methods for collisions

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Recent Research

My recent research concerns mathematical modelling and analysis of swarming and self-collective
behaviour. The topic has received a great amount of interest in recent years due to applications of
such models in a variety of areas, including population biology (chemotaxis of cells, swarming or
flocking of animals), physics and chemistry (self-assembly of nano-particles), robotics and space
missions, traffic and pedestrian flow, opinion formation.
One of the goals of my research is to understand the emergent behaviour in continuum and multi-particle
systems with non-local interactions. The models I have worked on have demonstrated emergence of very
complex behaviour as a consequence of individuals following simple interaction rules, without any
leader or external coordination. Indeed, natural swarms (birds or fish for instance) achieve
self-organizing behaviour through local signalling, in the absence of a centralized decision-making
mechanism. Such biologically-inspired swarming considerations are at the core of the models I have
studied.

From the point of view of theory, I have investigated qualitative properties of
swarm equilibria (in free space, as well as in domains with boundaries), existence of
global minimizers of the interaction energy, regularization by diffusion, the effect of
anisotropy, and extensions of aggregation models to surface and manifold settings. In terms
of applications, I have worked on biological swarms, autonomous robots, opinion formation
and crime modelling. Click on the link below to find my publications.

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Math Links