#### Research area & expertise:

Condensed Matter Theory

*Theory of strongly correlated electrons*

Model description of electron correlations, Hubbard and Anderson impurity models, collective and cooperative phenomena, the 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 non-commutativity of relevant operators on critical behavior, formation of bound and resonant pair states, the 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.

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