**Title of the course:** Elliptic Curves

**Instructor:** Dr. Dino Festi

**Institution:** Mainz University

**Dates:** 7-13 August 2017

**Prerequisites:** Basic group theory and ring theory, basic complex analysis.

**Level:** Graduate, advanced undergraduate, beginning undergraduate

**Abstract:** Elliptic curves form a context where different branches of mathematics blend together in the study of a particular object. In this course we will give a twofold introduction to the theory of elliptic curves over fields of characteristic zero. First we will introduce elliptic curves as the locus of solutions of a cubic equation in two variables. On the other hand, we will show how elliptic curves also arise from the study of elliptic integrals, and we will see how this construction relates to the first definition.

**Textbook or/and course webpage:**

Silverman, `the arithmetic of elliptic curves’

Silverman, Tate, `Rational points on elliptic curves’

**Language: **EN