Nanophysics. Atomic and continual models of elementary excitations in nanoscale systems, analytic approaches to physical models on finite crystal lattices. Effects of confinement (size, surface, dimensionality) and external fields on electronic, magnetic and mechanical properties (equilibrium and transport) of thin layered structures, quantum wells, quantum wires, quantum dots, optomechanical resonators, NEMS, etc. Nanodetectors (electromagnetic radiation, heat, mass, etc.). Quantum effects at the nanoscale.

High-Tc superconductivity and emerging materials. Properties and mechanisms related to strong electron correlations, electron-phonon interaction, spin and orbital excitations, SDW, CDW; connections between anomalies found by different experimental probes (e.g., optics, EELS, ARPES, NMR etc.). Many-body methods for strongly correlated electron systems. Graphene and carbon nanotubes. Disordered systems (spin and orientational glasses).