On a method for calculating the volumes of polyhedra in hyperbolic space.

The lecture is devoted to the method of calculating the volumes of polyhedra in hyperbolic space (given by the Poincare model in the upper half-space), proposed in 2013 by I.H. Sabitov. In the first part of the talk, we will derive a formula for the volume of an arbitrary hyperbolic tetrahedron (in standard position) through the coordinates of its vertices. In the final part, the volumes of the so-called cyclic and permutation polyhedra in the hyperbolic case will be studied. The report will be accompanied by formulations of unsolved problems in the volume theory of non-Euclidean polyhedra. No special knowledge is required to understand the talk.