The electronic properties of new materials such as the high-Tc superconductors, heavy fermions and layered organic superconductors are still poorly understood. The conventional theory of metals based on band structure calculations fails to reproduce many o f the observed properties. Latered molecular compounds such as the K-(BEDT-TTF)2x family of organic superconductors display metallic, superconducting and insulating phases, close to each other. One important issue is to understand the origin of the superco nductivity and its connection to the nearby antiferromagnetic phase. Quantum dots are other examples of low dimensional systems which display quantum many-body phenomena. We will explore the effect of electron correlations in these systems by combining ana lytical and numerical methods.
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