Nolwenn Le Quellec

Ushijima coordinates and Rigidity of the (simple) orthospectrum

In 1993, Basmajian introduces the orthospectrum: the multiset of lengths of orthogeodesics on a hyperbolic surface with boundary.
On another note, hyperbolic surfaces live in the Teichmüller space, which is usually described with Fenchel-Nielsen coordinates.
In this talk, we ask "Does the orthospectrum determine up to isometry a hyperbolic surface ?" and we will see how for hyperbolic surfaces with boundary we can use a different set of coordinates to study the rigidity of the orthospectrum and the simple orthospectrum: Usijima coordinates.