Title: Length spectrum of a hyperbolic 3-manifold

Abstract: Every geodesic in hyperbolic 3-manifold has a naturally defined complex length. All geodesics in a manifold can be ordered by their length lexicographically and create a length spectrum. There is a one-to-one correspondence between fundamental group of a hyperbolic 3-manifold and its length spectrum. In the first part of the talk we will describe some facts about length and ortholength spectra of hyperbolic 3-manifolds and demonstrate the working algorithm for the spectra. In the second part we'll consider applications of this algorithm to the proof of Exceptional Manifolds Conjecture and Dehn parental test.