Abstract: The (stable) chromatic spectral sequence has had a significant impact on our understanding of the stable homotopy groups of the spheres. I will talk about preliminary attempts to construct an unstable version. I will try to describe a filtration of the stable chromatic spectral sequence induced by the Hopf rings for the odd spheres. There are natural questions that arise in the unstable world (e.g. an unstable version of the Morava stabilizer algebra) and a chromatic interpretation of the Hopf invariant.

Abstract: Normal forms have been used since Poincare. The problem of converting an element in a Lie algebra into its normal form can be a difficult calculation. In joint work with Rick Churchill we have applied the method of spectral sequences to this problem. The talk will be both an introduction to normal forms and (to a lesser degree) an introduction to spectral sequences.