1. Differential equations and equations of mathematical physics.
2. Theory of functions and functional analysis.
3. Algebra, mathematical logic and geometry.
4. Probability theory and mathematical statistics.
5. Inverse and ill-posed problems.
6. Optimal control.
7. Mathematical and computer modeling.
8. Computational and information technologies.
9. Theoretical and applied mechanics, continuum mechanics.
10. Methods of teaching mathematics and the history of mathematics.