Quantum Monte Carlo simulations are used to study the dynamics and the critical properties of strongly, correlated systems relevant to the fields of cold quantum gasses and high-T-c superconductivity. Recent advances in cooling techniques of quantum gasses allow to reach the degenerate regime for fermionic samples. Loading these systems on optical lattices can bring the gas to a strongly, correlated regime. We analyze the properties of trapped degenerate Fermi gasses on optical lattices and show that they display quantum critical behavior and universality at the boundaries between metallic and Mott insulating phases. On our other field of interest, high-T-c superconductivity, a Quantum Monte Carlo algorithm we developed recently is used to study the cl dynamics of the nearest-neighbor (n.n) t-J model relevant to the low energy properties of the copper oxides materials. We show that antiholons identified in the supersymmetric inverse squared (ISE) t-J model are generic excitation of the n.n. model since they are clearly visible in the single-particle spectral function of the n.n. t-J model in the whole Luttinger-liquid regime. We have further shown that even the analysis of the two-particle spectral functions of the n.n. t-J model can be based on the elementary excitations of the ISE t-J model.