# 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