Bose-Einstein condensation in systems of interacting and noninteracting bosons.

Lattice models for two-dimensional electrons. Spectral node engineering and Hall plateaux formation.

Disorder and interactions in systems of two- and three-dimensional electrons with spectral nodes.

Anderson localization and quantum Hall transition. 

Topological phase transitions in systems of interacting electrons.

Superconductivity in Dirac bilayers and mixed double layers with Dirac and conventional particles.

Renormalization group (RG) techniques in a variety of variants: functional, perturbative, field-theoretical RG.

Different averaging techniques in application to disordered systems: Supersymmetry, replica trick, perturbative averaging.

Bosonization in functional integral framework

Entanglement of miltipartite quantum states and axiomatics of quantum mechanics.

2023/25 Research grants of the Julian Schwinger Foundation for Physics Research

2022/24 Personal research grant of Agencia Estatal de Investigacion Espania (Version of Marie-Curie fellowship)