computer science:

• framework in Prolog for analysis and verification of CEP systems;
• natural language analysis using neural networks and other machine learning methods;
• construction of algebraic structures for advanced logarithmic image processing to improve their quality and intelligent analysis;

• reference set editing and reduction for the nearest neighbor rule. 
   

  physics:

• classical and quantum dynamical systems, their symmetries, integrability and superintegrability;
• foundations of quantum mechanics including the Bell inequalities (analysed by group-theoretical methods), quantum speed limits and related topics;
• classical solutions in general relativity and their relations to electromagnetic field configurations (in particular the double copy conjecture);
• classical and quantum dynamics on coadjoint orbits;
• geometry of accretion on compact objects (black holes, neutron stars);
• modeling of physical processes responsible for the generation of X-ray radiation observed from the close vicinity of compact objects;
• influence of the effects of general relativity on the spectra observed from X-ray sources;
• reduction and time-dependent/averaged analysis of data registered by X-ray satellite instruments;
• code development/adaptation of models from XSPEC (main public X-ray data analysis tool) for specific research purposes. 

      mathematics:

• study of K-theory of multipullback odd-dimensional quantum spheres and quantum complex projective spaces.