Research to explore the physical properties of strongly interacting many-electron systems is proposed. The problems of superconductivity near the metal-insulator transition of the two- dimensional Hubbard model and the two-dimensional electron-phonon Holstein model will be studied. In addition, work on dynamic impurities in metals, periodic Anderson and Kondo lattices is proposed. A common feature of these problems is the need to use non-perturbative procedures such as numerical simulation or infinite-order diagrammatic approximations. This work aims at combining numerical simulations and analytic many-body techniques.
