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.