"On self equivalences of p-completed classifying spaces"

                       by Ran Levi (Aberdeen)

This is a survey talk on joint work with C. Broto. Let G be a finite
group. Study the mod-p homotopy type of the classifying space BG from
the point of view of its cohomology algebra over the Steenrod algebra,
enhanced by the action of the higher Bockstein operators. It is not
known whether or not cohomology in this enhanced sense determines the
respective homotopy type. In attempting to study this problem we produce
examples where the answer to this question is positive and point out
some of the difficulties involved. The study incorporates understanding
other spaces of classical interest in homotopy theory. Furthermore, it
motivates studying the concept of the so called homotopy group
extensions, which are, as the name suggests, homotopy theoretic
analogues of ordinary group extensions. We present a program for
studying such extensions and their classification, which is motivated by
the algebraic theory of group extensions, and prove some partial
results.