I. Differential geometry (Finsler manifolds and Minkowski geometry)
- The theory of generalized Berwald manifolds: generalized conics and the alternatives of the Riemannian geometry.
- Average processes and their applications in Finsler geometry.
II. Geometric tomography
- Generalized conics' theory and its application in geometric tomography: the reconstruction of hv-konvex planar sets by the coordinate X-ray functions, deterministic and stochastic algorithms.
III. Linear functional equations
- The discrete Pompeiu problem.
- The application of spectral analysis in the theory of functional equations.
- The application of spectral synthesis in the theory of functional equations.