The realization of strongly correlated quantum systems by means of ultra-cold atoms is now an achieved reality.Beyond the early studies of thermodynamic equilibrium properties, these systems offer unprecedented possibilities to study their dynamics. Crucial theoretical challenges therefore concern modeling and understanding quantum dynamics in the presence of strong correlations.Our main goal is to develop new numerical approaches to tackle questions currently intractable by state-of-the-art techniques. We will use and suitably extend the “Time-dependent Variational Monte Carlo” method, to whose early development the Fellow (Dr Giuseppe Carleo) has tightly contributed and whose accuracy has been already demonstrated.In the first phase of the Project we will concentrate on lattice bosons. We will investigate the role of the dimensionality and of long-range, dipolar interactions in the time-propagation of quantum correlations. We will moreover study the interplay of disorder and interactions, focusing on dynamical signatures of the many-body localization phenomenon. In the second phase, we will extend our numerical technique to correlated gases in continuous space, studying how the ergodic hypothesis in their approach to equilibrium can be violated. All of the mentioned dynamical regimes have been, since now, fundamentally inaccessible to accurate numerical methods.The Host Institution is the Laboratoire Charles Fabry (LCF) at Institut d'Optique and CNRS. LCF has consolidate experience in ultracold atoms with world-leading experiments and theory. The Applicant will join the theory group led by Dr Laurent Sanchez-Palencia and will develop direct collaborations with the lively experimental activity at LCF. On one hand, the mobility will be beneficial for the Fellow to be trained in the field of ultracold atoms. On the other hand, his mature skills in advanced condensed-matter numerical methods will strongly reinforce the theory group in beyond-mean-field approaches.