Main directions of scientific research of faculty:

- Exterior geometry of multidimensional submanifolds.
- Convex surfaces in Riemannian manifolds, layers on Riemannian manifolds.
- Function theory, functional analysis.

Mathematical control theory. - Nonlinear differential equations.
- Numerical simulation of the problems of mathematical physics.
- Operator beads and operator-differential and functional-differential equations.
- Mathematical and computer modeling of physical, technical, financial and economic systems.
- Research in the field of fluid mechanics, gas and plasma, in particular from magnetic hydrodynamics, ferrohydrodynamics and biomechanics.