# Scaling limits and effective theories in classical and quantum mechanics

Typical systems of interest in physics, biology and applied sciences can be described by models with a large number of components. The microscopic behavior of such systems is driven by fundamental equations like the Newton or the Schroedinger equation. Observers, on the other hand, are interested in the collective behavior of these systems, arising on space and time scales which are much larger than the ones characterizing the microscopic dynamics. On such macroscopic scales, the systems appear much simpler, and can be usually described by nonlinear partial differential equations depending on a small number of degrees of freedom. The exact derivation of effective equations from first principle theories is one of the central problems of non-equilibrium statistical mechanics.

The main goal of this meeting is to promote the exchange of information among researchers interested in the derivation and in the analysis of effective macroscopic equations emerging from classical as well as quantum dynamics. In particular, we plan to discuss results concerning derivations of the Boltzmann equation, the Landau equation, the Vlasov equation, Hartree and Hartree-Fock equations, and of the Gross-Pitaevskii equation. Special attention will be payed to the comparison of methods and tools coming from different contexts.