My research focuses on the  study  of correlated systems like transition metal oxides
on frustrated lattices by applying various analytical and numerical methods. 
It  covers the following topics:

The study of ground state properties of frustrated lattices with spin, charge and orbital degrees of freedom.

The study of magnetic excitation spectrum in systems with unquenched orbital angular momentum.

The study of the two-magnon Raman scattering on two-dimensional magnetic frustrated lattices, such as triangular, kagome stripe, and checkerboard lattices.

The study of the two-orbiton Raman scattering on frustrated lattices, when the orbital degrees of freedom plays an important role.

The study of low-dimensional magnetic systems.

Interest in these systems stems from (i) the richness of their novel properties: the unexpected variety of ordered states and transitions between them, (ii) the complexity of the underlying physics; (iii) the presence of frustration, which makes these systems highly sensitive to any internal or external perturbations. Such a richness of properties is largely connected with the  simultaneous presence of the geometrical frustration and the strongly correlated effects, which lead to a keen  interplay of different degrees of freedom in these systems: charge, spin and orbital ones as well as crystal lattice.