The dynamic cluster quantum Monte Carlo approximation provides an optimal tool to study supercondutivity in the two-dimensional Hubbard model of cuprate high-temperature superconductors. In this talk I will review the algorithmic and computational advances that have enabled us to systematically explore the superconducting transition in this model, the pairing mechanism responsible for superconductivity as well as the effects of disorder and nano-scale inhomogeneities on the pair- formation and superconducting transition temperature.
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