The aim of the school is to consider multidisciplinary aspects inside Mathematics. In many situations, mathematical concepts appear in different paradigms.These offers different point of views which deserve to be compared with rispect to their analogies and differences. These comparisons involve usually different extra-mathematics fields such as Physics, Biology, Economics, Social Sciences, etc. that will be handled in this school.The main streams considered will include:
- Typical vs. Untypical: a journey through large deviations, by Raphaël Chétrite
- ODEs vs. PDEs: the large number agent systems, by Stefano Rossi
This course discusses the rigorous derivation of effective kinetic PDEs starting from the dynamics of N particles described by a system of ODEs and the comparison between the behavior of finite and infinite-particle sytems, with regard to long-time behavior and the emergence of irreversibility.
In this course, we show how most concepts from (classical) optimal transport find their quantum counterparts in quantum mechanics through a “canonical” quantization of the Wasserstein distance. These concepts include Brenier’s theorem, bipartite matching, and Kantorovich duality.
- Human vs. Artificial Intelligence : to think or to use, by Alberto Fachechi (TBC)
- Finite vs. infinite dimension integrability, between geometry and analysis,, by Lorenzo Baroni.
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