# Colloquium abstracts

**Otmar Venjakob**

Universitat Heidelberg, Germany

March 11, 2010

**Are L-functions able to solve Diophantine equations?**: An introduction to (non-commutative) Iwasawa theory

Starting from old problems in diophantine geometry we first try to explain how Iwasawa was motivated to develop classical Iwasawa theory. Then we describe the generalisations towards non-commutative Iwasawa theory and we shall make some comments on known results.