En attendant de préparer le texte de cette page, je vous laisse avec un projet de recherche que j’avais écrit à l’époque.
Since the beginning of my Mathematical research journey, I have been interested in applying
Mathematics to human society. As a consequence, the topic of my probability thesis : Particles
systems with game interactions. I work on evolutionary game theory with the main goal of
drawing population behavior. Thus I have learned to use :
— Modelization of complex individuals system with games,
— Stochastic processes (Infinitesimal generators, Martingales problems,…) and Individual
systems (Empirical measure, Generators depending on a measure,…),
— homogenization techniques allowing to deal with systems when the speed of the signal is
far bigger than the speed of evolution,
— propagation of chaos techniques allowing to deal with systems of low correlated individuals.
— non linear Markov processes analysis (using coupling techniques). These tools (Mean field
models) are particularly useful to modelize a typical individual in an infinite low correlated
population.
— Netlogo (simulation software designed to simulate multi agent systems) and scilab (useful
to analyze data)
All the aforementioned tools can be applied to evolutionary game theory as well as to social
learning in networks. Social networks are complex individual systems. Since there is a lot of
randomness in individuals, putting a stochastic individual system on it can be a (good) idea
of modelization. If we add learning on this system, a common assumption is that the information
travels far quicker than the decision process. We necessitate homogenization techniques to
describe properly this decision process. Furthermore since in real life persuasion is not 100 % effective,
there is small correlation in the population. Hence the model converges using propagation
of chaos techniques to a mean field model. Given that Mean field models are Non linear Markov
process, and given that I learned during my PhD how to study these kinds of models, I would
be able to apply them to Social Network as well.
Furthermore, since my main interest in Science is Mathematics applied to human society, I
have been very open to any of this kind of mathematics and as a result I have studied :
— Voting systems in networks with Ayaldi Ganesh (Bristol University) in LAAS,
— Working group on machine learning,
— Random graphs and large deviation on random graphs with Sourav Chaterjee (Standford
University) in Saint Flour course 2015,
— Statistics in high dimension as a Master course and also with Sara Van de Geer (ETH
Zurich) in Saint Flour course 2015,
— Workshop on Congestion Games in Singapore
— Random matrices with Paul Bourgade (New York University) in Saint Flour course 2016.