Research

 

Major research areas

Mathematical foundations of computer science

  • rough sets theory and its application in approximative reasoning
  • theory of types, formal grammars and their applications in computer science

Qualitative theory of differential equations

  • dynamical systems and ergodic theory
  • elliptic nonlinear boundary value problems in piecewise smooth domains
  • blow-up solutions in mathematical models of population dynamics

Geometry and its applications in mathematical physics and cosmology

  • global differential geometry of structures on smooth manifolds
  • incidence geometries and construction of exotic geometric and algebraic structures
  • geometric methods in the theory of integrable systems
  • space-time with variable vacuum density and pressures
  • regular cosmology and gravitating systems at extreme conditions

Molecular and atomic physics, mathematical modeling in science and technology

  • mathematical and computer modeling of quantum-mechanical systems
  • investigation of spectra lines of the cosmic masers, noble gases, and metals in the gaseous phase
  • numerical methods in science and technology
  • mathematical and computer modeling of immune system
  • mathematical models in geodesy