Motivic homotopy theory and some applications

Motivic homotopy theory is concerned with studying generalized cohomology theories for algebraic varieties (perhaps over characteristic p fields). I will explain a little about what this means, and discuss an application to a classical problem of Hurwitz concerning ``sums-of-squares" identities. Certain techniques from this application lead one to think about quadratic bundles over schemes, which in particular can be used to construct an algebro-geometric analog of real K-theory (over any field!). I'll discuss some of this story.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).