Jérôme Benoit is interested in bridging advanced mathematics with experimental or observational sciences, namely, in mathematical physics. He defended his Ph.D. in Theoretical Physics at the University of Cergy-Pontoise (France), with his dissertation thesis entitled “Symmetry, Geometry, Topology and Spin: Heisenberg spins in the continuum limit/magnetic vesicles“; he previously received his Master’s Degree in Fundamental Physics (with Theoretical Physics as advanced subject) at Orsay University (France).
The common denominator of his investigations has been the study of complex phenomena in condensed/soft matter and biological/social inspired systems. He has a predilection for geometrical topology, network theory, and information theory, all with a strong mathematical inclination.
So far, his research investigations have offered (i) pertinent insights on topological frustration phenomena, and (ii) an important technical point in epidemics modelization. He showed how an antiferromagnetic film whose spins combine into a topological wave-particle can deform itself as a results of the impossibility for the topological wave-particle to reach a saturated configuration. He demonstrated afterwards how the same topological mechanism applies to elastic surfaces. The resulting framework predicts the existence of biological vesicles of arbitrary genus and gives their minimal elastic energy. As concerns epidemics, he established a family of correlated pair approximations that allows to model epidemics spreads on realistic complex networks such as the Watts-Strogatz small-world networks. As an illustration of this, he built a naive but amenable demographic SIR epidemics spread on a Watts-Strogatz-like ring.
Currently, his interests focus on the statistical self-similarity of unplanned or self-organized urban street networks for which a comprehensive theory is missing. His working hypothesis is that self-organized urban street networks are statistical self-similar mesoscopic fluctuating systems at equilibrium. His working framework is the maximum entropy formalism (MaxEnt) with the statistical self-similarity as prior hypothesis. He has already predicted the degree distribution scale-freeness of their dual informational networks. He has also already equipped his fluctuating model with a simulational tool, specifically, an adaptation of the Metropolis algorithm. He aims now to explore qualitative behaviours. Such knowledge on self-organized urban street networks provides new insights into their spontaneous dynamics or self-sustainability. Using Central London as illustration, he was able to demonstrate a small-world crossover.
Alongside he hacks or writes scientific code; he is a proud Debian Developer.