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Recently, there have been a number of very promising new developments in numerical methods for strongly correlated quantum systems. These methods include quantum Monte Carlo, the density-matrix renormalization group (DMRG) and its generalizations (so-called tensor network algorithms), and self-consistent dynamical cluster methods. The aim of this project is to form a coherent network of active researchers in Germany, Austria, and Switzerland, who have made significant contributions to this progress in numerical methods, in order to share expertise and ideas as well as to develop efficient algorithms for the current generation of high-performance computing hardware. Applications include strongly correlated materials, nanostructures, and cold atomic gases. There is potential to make significant advances in long-standing fundamental problems in correlated quantum systems such as frustrated magnetism, doped Mott insulators, and interacting bosonic and coupled fermion-boson systems.