Fuchsian Groups and Siegel´s Theorem

Specialeforsvar ved Vasileia Vagena

Titel: Fuchsian Groups and Siegel’s Theorem

Abstract: We begin this thesis presenting the basic features of two models of hyperbolic geometry, the upper half plane H and the Poincaré disc D. We study Fuchsian groups and explore some of their most important properties. Introducing the notion of fundamental region of a Fuchsian group, we construct a special kind of it, known as the Dirichlet region. This is an essential tool for our main result, the Siegel’s theorem for Fuchsian groups.

Vejleder: Jasmin Matz

Censor:   Simon Kristensen, Aarhus Universitet