Course content: Quadratic forms (= homogeneous polynomials of degree 2) have played an important role in many parts of mathematics throughout history: the description of the conic sections studied by the ancient Greeks, several famous theorems from number theory like Lagrange’s Four-Square Theorem, and the modern development of real algebra, all involve quadratic forms in one way or the other.
In the middle of the 20th century, Ernst Witt and Albrecht Pfister started developing the algebraic theory of quadratic forms over arbitrary base fields. This course will give an introduction to their general theory, with applications to number theory.

When and where: every Wednesday 9:00-10:30, starting 21/2, in room K10C.
Please note: There will be no class on 27/03, 01/05, and 08/05.

Lecture material

The lecture notes for the course will be developed in the course of the coming weeks. A version containing the material for the first ten lectures can be found here; the source code is available on GitHub. Any feedback on the notes (mistakes, gaps, suggestions, …) is welcome.