I am interested in the general problem of understanding quantum many-body systems that are out of reach of current analytical and numerical methods. During my PhD I have developed an efficient numerical code based on the Density Matrix Renormalization Group Algorithm that allows to tackle (within some liimits) the exact dynamics of one-dimensional strongly interacting quantum systems. I used this method to investigate several phenomena such as spin-drag, dynamics of impurities, quantum shock waves and transport phenomena at a superfluid-Mott insulator transition. I have also worked in the field of superconductivity, more specifically I have studied various aspects of the Josephson effect in tunnel junctions. Here at Aalto I started working on the problem of superconductivity in flat band systems.