Mathematical Sciences Geometry/Topology Seminar

May 8 (Monday), 1:10 PM: (Note unusual date and time) (joint with the combinatorics seminar)
Speaker: Daniel Biss (University of Chicago)
Title: Annihilators in Cayley-Dickson algebras

ABSTRACT: The Cayley-Dickson algebras form a sequence of R-algebras beginning with the real numbers, the complex numbers, the quaternions, and the octonions. We rarely hear about the subsequent members of this sequence, since they not only lack associativity but also have zero-divisors (as the Hopf invariant 1 theorem demands). These zero-divisors, however, can be viewed not as a pathology but rather as an opportunity; the zero-divisors in the 16-dimensional Cayley-Dickson algebra give rise to the Lie group G_2, and in the larger algebras they seem to be even more interesting. We'll describe joint results with Dan Christensen, Dan Dugger and Dan Isaksen about the geometry of these spaces of zero-divisors.