The aim of the school is to consider multidisciplinary aspects within Mathematics. In many situations, mathematical concepts appear in different paradigms. These offer different points of view which deserve to be compared with respect to their analogies and differences. These comparisons usually involve different extra-mathematical fields, such as Physics, Biology, Economics, Social Sciences, etc., that will be addressed in this school.
The main streams considered will include:
- Typical vs. Untypical: conditioning and large deviations, by Raphaël Chétrite
This course introduces the basic theory of large deviations and its main mathematical tools. It also presents applications to interacting particle systems, highlighting how large deviation principles provide a powerful framework for studying nonequilibrium phenomena.
- ODEs vs. PDEs in kinetic theory: collective dynamics and scaling limits, by Stefano Rossi
This course discusses the derivation of effective kinetic PDEs starting from the deterministic dynamics of N particles described by a system of ODEs, presenting rigorous results where available. The main focus will be on the mean-field regime and, time permitting, the low-density (Boltzmann–Grad) regime.
- Quantum vs. Classical optimal transport: quantizing Wasserstein, by Thierry Paul
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.
- Order vs. Disorder in neural networks: a journey through associative memories, by Alberto Fachechi
This course introduces the fundamental principles of associative neural networks through the lens of the equilibrium statistical mechanics of spin glasses. The course highlights how analytical techniques provide a quantitative understanding of memory retrieval or not, storage capacity, and phase transitions.
- Finite vs. Infinite dimension integrability: large dynamical systems, by Lorenzo Baroni
This course aims to extend ideas and techniques from finite to infinite dimensional Hamiltonian dynamics, focusing on Liouville–Arnold integrability. By a proper choice of topology, one provides a decomposition of the phase space as rigid as in the classical case. A task that other approaches miss.
together with talks by the participants (Thomas Borsoni, Antonin Chodron de Courcel, Théophile Dolmaire, Diego Fiorletta, Benjamin Kalfa, Ivan Moyano, Riccardo Piombo, Vincenzo Rossi, Lara Trussardi, a.o.), visits, trekking, and relaxed evenings "sotto il cielo d'Arpino".
Raphaël Chétrite, Thierry Paul, and Stefano Rossi, orgs.
To register please contact one of the organizers at
raphael.chetrite@univ-cotedazur.fr, thierry.paul@cnrs.fr or stefano.rossi2@uniroma1.it
Co-funded by the CNRS/INdAM IRL 2019 LYSM "Laboratoire Hypatia des Sciences Mathématiques" and the European Union through the ERC CoG KiLiM grant "project number 1011251621".
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