Research areas:

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.