Departmental Colloquium
Dan Dugger
University of Oregon
Sums-of-squares formulas and motivic homotopy theory
Abstract: A "sums-of-squares formula" is a certain type of algebraic
identity, considered by Hurwitz in his investigation into the
existence of composition algebras. One of the earliest applications
of algebraic topology was to prove that certain kinds of sums-of-squares
formulas cannot exist over the real numbers, or more generally over
fields of characteristic zero. The question of what happens over
characteristic p fields was raised in the 1970s, but then left
unsettled as algebraic techniques proved inadequate. In this talk
I'll describe some recent progress on this problem using etale
homotopy theory, and I'll try to explain how the problem ties in
to current work in motivic homotopy theory.
Friday February 23, 2007 at 3:00 PM in SEO 636