Mathematical foundations of Computer Science

• Logic of types, formal grammars and their applications to Computer Science
• Combinatorics, graph theory

Differential equations

• Dynamical systems and ergodic theory
• Nonlinear partial differential equations
• Qualitative theory of differential equations

Geometry and its applications

• Global differential geometry, geometric structures on smooth manifolds
• Incidence geometry, computational geometry
• Symplectic and Contact Topology
• Lie group theory, representation theory
• Integrable systems

Algebraic topology

• Homotopy theory
• Homotopy theory of graphs

Mathematical Physics, Experimental Physics

• General Relativity Theory
• Theory of solitons
• Mathematical and computer modeling of quantum systems
• Applications of Nuclear Magnetic Resonance technique to problems of medical diagnostics and safety of food control

Applied Mathematics

• Mathematical modeling in medicine
• Statistics