**Florian Sprung**

Princeton University, USA

January 20, 2015

**The arithmetic of elliptic curves in towers of number fields**:
Iwasawa Theory was introduced into the arithmetic of elliptic curves in the hopes of proving the conjectures of Birch and Swinnerton-Dyer. The aim of this talk is to give an introduction to Iwasawa Theory, elliptic curves, and how they interact with each other.