# Bruhat-Tits Buildings and Applications

Specialeforsvar: Esben Folke Ydesen

Titel: Bruhat-Tits Buildings and Applications

Abstract: This thesis is concerned with the structure theory of semisimple, simply connected algebraic groups defined over non-Archimedian local fields. We will present a geometric parameterization of this structure known as the Bruhat-Tits building, and explore how the building behaves under extension of the underlying field. In particular, we will discuss how the volumes change under such an extension and obtain a strikingly simple formula. Lastly, we will use the construction of the Bruhat-Tits building to calculate orbital integrals over GL2.

Vejleder: Jasmin Matz
Censor:    Simon Kristensen, Aarhus Universitet