1.Functionaly analysis, spectral theory of differential operators, theory of functions
2. Optimal recovery of functionals in the generalized Sobolev classes and Chebyshev splines and monosplines in problems of approximation.
3. Methods of teaching mathematics at school.
4. Elliptic systems with singular coefficients in the plane, the solvability of boundary value problems for elliptic systems with a singular point in the theory of infinitesimal bendings of surfaces of positive curvature with a flat point in the theory of thin shells with features.