The main research areas of the Laboratory are Differential Geometry and Topology and their Applications. The main directions of acivity are:

- Global Riemannian Geometry, Spectral Geometry;
- Riemannian and Pseudo-Riemannian Holonomy Groups;
- Integral Geometry;
- Geometrical Inverse Problems, Mathematical Tomography;
- Semigroups of Linear Operators;
- Applied Topology;
- Topological Methods in Parallel Processing.

Seminar «Computational Geometry and Topology in Applications» works in the Laboratory.