Topological phases are characterized by topological order and topological invariants - numbers that describe the phase and its excitations. We will investigate topological phases in quantum Hall systems using exact diagonalization and Monte-Carlo simulations and by pursuing the connection with conformal field theories with a goal of identifying possible new topological invariants and clarifying the role of edge spin states. Also, we will study transport and thermodynamic properties of strongly correlated materials (e.g. heavy fermions, charge transfer organic salts and transition metal oxides) within dynamical mean field theory (DMFT) combined with DFT band structure calculations. We will use the continuous time quantum Monte Carlo and iterative perturbation theory to solve the effective Anderson impurity model from DMFT equations, and examine the effects of disorder near the Mott transition.