The main goal of the educational activity in the doctoral program is to create highly qualified scientists in the field of differential geometry, who have knowledge and skills for solving complex problems of scientific and scientific-applied nature.
The teaching and research activities in the doctoral program contribute to obtaining new results in key areas of fundamental and applied knowledge in the field of differential geometry and geometric analysis, mathematical physics, real and complex analysis, topology, algebra and group theory, such as
- Riemannian and sub-Riemannian geometries: the classical theory of curves and surfaces in Euclidean space.
- Definitions and properties of differentiable manifolds, structures on smooth manifolds - almost complex, complex, almost contact, contact, quaternionic-Kaehler, quaternionic-contact; Bochner-type vanishing theorems, Weizenbock formulas, and the Yamabe problem for manifolds with different structures.
- Pseudo-Riemannian geometry and theoretical physics, supersymmetric string theories, harmonic maps and - models, operation and fractional calculus, classical mechanics.