My research activity includes subjects that are at the interface between complex systems, cosmology and gravitational dynamics.In general, my aim is to apply concepts and tools of the physics of complex systems to study specific problems in astrophysics and cosmology. During the last few years I have been involved both in the study of the relaxation process of an isolated self gravitating cloud and in the study of the large scale structures in the universe.
 Galaxy redshift surveys represent one of the cornerstones of modern cosmology. In the past decades we have assisted to an exponential growth of the data, which have revealed that galaxies are organized in a large-scale network of filaments and voids. Statistical analysis of these surveys have shown that these structures correspond to power-law correlations. Correspondingly, the density fluctuations follow the Gumbel distribution of extreme value statistics that is clearly distinguishable from a Gaussian distribution, which would arise in case of a homogeneous galaxy spatial configuration. There are thus important similarities between the galaxy distribution and critical systems of statistical physics, at least of scales smaller than 100 Mpc. Whether or not, on larger scales, correlations decay and the distribution crossovers to uniformity, is still matter of considerable debate. The principal questions we would like to clarify in this part of the project concern indeed the nature of galaxy structures, the type of correlations and their spatial extension and the statistical properties of fluctuations distribution. The clarification of these points is crucial for the testing of cosmological models of structure formation.
 From a theoretical point of view, the evolution of a very large set of massive particles interacting solely by Newtonian gravity is a paradigmatic problem for the statistical physics of long range interacting systems finding application in many different areas of astrophysics and cosmology. Some examples are the study of globular clusters, galaxies and gravitational clustering in the expanding universe. Gravitational clustering of mass structures is a well-posed problem of out-of-equilibrium statistical mechanics that can be studied through N-body simulations. While such simulations constitute a very powerful tool, they lack the valuable guidance that a fuller analytic understanding of the problem would provide. The non-linear dynamics of self-gravitating systems is thus both a fascinating theoretical problem of out of equilibrium statistical mechanics, directly relevant both in the context of cosmology, astrophysics and, more generally, in the physics of systems with long-range interactions. Approaching the problem in the context of statistical mechanics, as we propose here, it is natural to start by reducing as much as possible the complexity of the analogous astrophysical and cosmological problems: our goal is to identify the main features of the (non-linear) gravitational dynamics, which shape the structures observed in the sky.