**Title of the course:** Quadratic Forms and the Hasse-Minkowski Theorem

**Instructor:** Dr. Martin Djukanovic

**Institution:** Ulm University

**Dates:** 6-12 August 2018

**Prerequisites:** Basic algebra, basic analysis helps but is not necessary.

**Level:** Graduate, advanced undergraduate

**Abstract:**We recall the concept of a Diophantine equation and some classical results and examples. We introduce the Legendre symbol and prove the Quadratic Reciprocity Law. Then we introduce p-adic numbers and prove Hensel's Lemma. We examine ternary quadratic forms over the p-adics and prove the basic properties of the Hilbert symbol. Finally, if time permits, we state and prove the Hasse-Minkowski theorem for arbitrary quadratic forms over the rationals.

**Language: **EN