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The success of mathematical physics in the investigation of modern physics phenomena ranging from meso- and microscopic scales, as for the kinetic theory of rarified gases, up to the quantum realm and beyond has been astonishing in the last 20 years. A rigorous approach towards the understanding of physical effective theories has proven to be very fruitful in shedding light on the range of applicability of such theories as well as on the accuracy of the approximation. Our interests cover such kind of questions related to phenomena as superconductivity and superfluidity, interaction between light and matter, emergence of classical behavior for quantum systems, quantum Hall effect, Hawking effect also in analogous black holes and quantum fields on black hole manifolds, occurrence of decoherence for open quantum systems, kinetic theory of rarefied gases and the Boltzmann equation, Smoluchowski kinetic equation and its applications to biomedical research.

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