# Vortrag

Modul:   MAT772  Geometrie-Seminar

## Cusp regions for parabolic ends of hyperbolic manifolds

Vortrag von Prof. Dr. John R. Parker

Sprecher eingeladen von: Prof. Dr. Viktor Schroeder

Datum: 19.09.18   Zeit: 15.45 - 16.45   Raum: ETH HG G 43

A hyperbolic manifold or orbifold can be written as the quotient of hyperbolic space by a discrete group of isometries. A cusp end of the orbifold corresponds to parabolic elements in the group. A consequence of discreteness is that these cusp ends contain regions of a certain shape. In dimensions two and three this is classical. More complicated things can happen in higher dimensions. In this talk I will survey the classical results, then I will discuss some more recent results in dimension four which show how continued fractions and Diophantine approximation come into play.