21/07/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building Daniel Dugger, University of Oregon
The Hurwitz sum-of-squares problem meets motivic cohomology
In 1898 Hurwitz posed the problem of determining the possible dimensions for certain kinds of 'sums-of-squares' formulas. This problem arose as a generalization of the now classical '1,2,4,8-theorem' concerning the normed division algebras over the real numbers. While Hurwitz's problem is completely elementary, it is still wildy unsolved. I will describe an old cohomological approach to this problem (originally due to Hopf), and explain some recent advances using motivic cohomology and algebraic K-theory.
