# About me

I am a researcher in the Department of Theoretical Physics of the NPI. Being a mathematical physicist, I like to study problems that are physically well motivated by the methods that are (sufficiently) rigorous.

# Research Interests

In recent years, my main research topic has been the analysis of
systems described by one- or two-dimensional Dirac equation that is motivated by the physics of
Dirac materials (graphene, germanene, silicene,...). I follow
two different, yet complementary approaches: construction of exactly solvable models, and qualitative spectral analysis
based on the variational principle.

See e.g. here

I also work on the exactly solvable models of optical systems with
PT-symmetric interactions.

See e.g. here

- Algebraic and analytical methods in quantum physics
- Dressing methods (Crum-Darboux transformations), intertwining relations
- Hidden symmetries and nonlinear symmetries
- Systems described by (2+1) and (1+1) Dirac equation (Dirac materials, e.g. graphene )
- Exact and quasi-exact solvability
- Qualitative spectral analysis