Complex systems provide a good description for many natural and social phenomena. Ecosystems, social networks, financial markets, quantum many body systems (e.g., superfluid helium 3), self-organizing artificial intelligence (such as neural systems) are all characterized by having many elements (species, members, traders, atoms), which interact locally, but give rise to phenomena, which cannot be explained by the properties of the single elements themselves (the emergence of fads and trends, financial market booms and crashes, superfluidity). Essential characteristics of a complex system include: feedbacks between processes occurring at different scales, amplification of minor variations in initial conditions, and the emergence of patterns in the absence of a global controller. The research at Labex MME-DII focuses both on the study of abstract mathematical models of such systems (PDEs, Markov Processes, the Schroedinger problem, mean field analysis) and on the application of such models to the analysis of specific complex systems (financial markets, quantum many body systems, networks). Some of the topics of interest are:
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