Scientific seminar “On volumes of hyperbolic polytopes”

6 April at 12:00 MSK

Topic: On volumes of hyperbolic polytopes.

The talk will provide an overview of recent results on the theory of volumes of hyperbolic polytopes. In the first part of the lecture, our focus will be on the application of the scheme for the proof of the Sforza formula for the volume of an arbitrary non-Euclidean tetrahedron to the calculation of the volume of a hyperbolic orthoscheme and an octahedron with 4|m-symmetry. In the second part, we will consider Sabitov's method for calculating hyperbolic volumes, based on the multidimensional Stokes formula, and the application of this method to cyclic polytopes. Finally, we will talk about the volumes of permutohedra (permutation polyhedra) in the Lobachevsky space.

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