Lecturer: N. Karpenko, Dean's Distinguished Visitor

Following [1, Part 1], we develop the basics of the theory of quadratic forms over arbitrary fields. In the second half of the course we briefly introduce the Chow groups and then apply them to get some of more advanced results of [1, Part 3].

Here is the program in more details:
1. Bilinear forms.
2. Quadratic forms.
3. Forms over rational function fields.
4. Function fields of quadrics.
5. Forms and algebraic extensions.
6. u-invariants.
7. Applications of the Milnor conjecture.
8. Chow groups.
9. Cycles on powers of quadrics.
10. Izhboldin dimension.

References:
1. R. Elman, N. Karpenko, A. Merkurjev.
The Algebraic and Geometric Theory of Quadratic Forms.
American Mathematical Society Colloquium Publications, 56. American Mathematical Society, Providence, RI, 2008. 435 pp.