Professor:		Alexander Merkurjev
	Office:		MS 7917
	Office Hours:		By appointment
	Book:		Knus M-A., Merkurjev A., Rost M., Tignol J-P., Book of Involutions (optional).
	Material:		We are going to discuss various relations between the following seemingly different algebraic structures: 1. Quadratic forms. Grothendieck-Witt ring of quadratic forms over a field. Pfister forms. Multiplicative forms. Filtration by powers of the fundamental ideal in the Witt ring. 2. Brauer group. Central simple algebras over a field. Cyclic algebras, quaternion algebras. Brauer group as the second Galois cohomology group. Correspondence between small quadratic forms and central simple algebras. 3. Milnor K-groups. Norm residue homomorphisms connecting K-groups with quadratic forms and simple algebras. Quadratic forms and simple algebras are examples of algebraic structures with large (semisimple) automorphism groups. The role of the theory of algebraic groups will be explained.
	Exams:		No final
	Practice problems		Due: Last week of classes.