Theoretical research will explore the physical properties of strongly interacting many-electron systems. The problems of superconductivity near a metal-insulator transition and the competition between various types of correlations will be studied. A common feature of these problems is the need for non-perturbative procedures such as numerical simulation or infinite-order diagrammatic approximations. The research aims at combining numerical simulations and analytic many-body techniques with the goal of providing quantitative results as well as physical understanding of strongly correlated electron materials. %%% The research will combine sophisticated numerical techniques with advanced analytical ones to address the underlying physics of strongly interacting electron systems such as are found in high temperature superconductors. The group of the principal investigator is one of the leading ones in the world for computational physics.