Dan Dugger : Sums-of-squares formulas and motivic homotopy theory

Posted by , part of the Departmental Colloquium.

At

Feb. 23, 2007, 3 p.m.

In

SEO 636

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.