Departmental Colloquium
Robert Bruner
Wayne State University
From Groups to Cohomology to Varieties
Abstract: If we apply a generalized cohomology theory to the classifying
space of a group, we obtain a ring whose structure reveals
something about the group. As a first approximation we can
consider the variety defined by this ring. The first result in
this direction was the work of Quillen in 1971, describing the
variety defined by the mod p cohomology in terms of the
elementary abelian subgroups. A number of such results for
other cohomology theories have now been proven. We shall review
these and discuss in detail the case of connective K-theory,
which provides a deformation from representation theory to
cohomology (at the level of varieties) and speculate on
generalizations of these results.
Friday November 11, 2005 at 3:00 PM in SEO 636