Motives and the algebraic theory of quadratic forms

The algebraic theory of quadratic forms (as begun by Witt in his 1937 Crelle's journal article and continued by Arason, Pfister and Knebusch) concerns the study of quadratic forms over arbitrary fields. The theory of motives invented by Grothendieck in the 1960's is a generalization of the "calculus of correspondences" used by classical algebraic geometers. Lately, the idea, championed by M. Rost, A. Vishik, and N. Karpenko, of studying quadratic forms through their motives has produced a string of breakthroughs such as Voevodsky's proof of the Milnor conjecture and Karpenko's proof of Hoffman's conjecture. I will discuss the field and some of the main techniques used.

Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).