Math 604 Introduction to Quadratic Forms Semester: Fall 2016

Description of course: This course will provide an introduction to the algebraic theory of quadratic forms over fields. Topics will include the elementary invariants (discriminant and Hasse invariant), classification over various fields (real numbers, rational numbers, p-adic numbers, finite fields, and rational function fields), isotropy and the u-invariant, the Witt group, and Pfister forms. Along the way, we will also cover the basic theory of quaternion algebras. Special topics might include local-global principals (e.g., Hasse-Minkowski), sums of squares (e.g., Lagrange’s theorem and Pfister’s bound for the Pythagoras number), Milnor K-theory, and orthogonal groups, depending on the interests of the participants.

Expected background: Some prior experience with linear algebra and Galois theory will be necessary.

Grading: Your grade will be based on class participation and a final project.