Model description of electron correlations, Hubbard and Anderson impurity models, collective and cooperative phenomena, transition from weak to strong coupling regimes, breakdown of Fermi-liquid phase, (dynamical) mean-field theory for intermediate and strong coupling, Kondo and insulating regimes; implementation of electron correlations in realistic calculation schemes

Quantum coherence and quantum phase transitions in itinerant systems

Quantitative description of quantum criticality, interaction-driven quantum phase transitions in metals, effects of noncommutativity of relevant operators on critical behavior, formation of bound and resonant pair states, structure of order parameters of quantum phases, transverse magnetic order, superconductivity

Transport properties of disordered electron systems

Vertex corrections in the electrical conductivity in impure metals, quantum diffusion and coherence, diagrammatic theory of weak and strong electron localization, metal-insulator transition

Theory of spin glasses and other random systems

Mean-field theory based on real replicas in the thermodynamic approach of Thouless, Anderson and Palmer for Ising and Heisenberg spin glasses and related models

Field-theoretic and diagrammatic methods for quantum two-particle functions

Feynman diagrams and many-body Green functions for nonrelativistic quantum interacting systems, advanced approximations for two-particle Green functions, vertex corrections, parquet approach to two-particle vertex functions

Superconducting nanostructures

Interacting quantum dots attached to superconducting leads, Andreev bound states, 0-pi transition, perturbation theory with anomalous functions