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ABSTRACT:
The interaction between electrons leads to a host of interesting phenomena including the Mott metal-insulator transition, unusual metallic states, and high temperature superconductivity. Some of these effects occur at strong coupling, or involve disorder in an essential way, and pose a major challenge for theory. Using the Mott transition as an example I will quickly review how the field has evolved over the decades and then present an approach that casts the difficult original quantum problem into a more tractable, but approximate, coupled quantum-classical problem. I will try to show how this leads to an intuitive description of the Mott insulator-metal transition, and, time permitting, the physics of strongly coupled and disordered superconductors.
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