The category of rational G-spectra for finite groups G is understood in terms of a Quillen equivalent abelian category. One can attempt to generalise this result to the case of profionite groups (an inverse limit of a cofiltered diagram). This talk will focus on the case where the group is the p-adic integers.

Study of the cone of non-negative, decreasing functions leads to the notion of the down space of a Banach function space. The real interpolation method is used to give a characterization of the down spaces of all universally rearrangement invariant spaces.

Rapoport and Pappas introduced a class of moduli problems of bundles on curves, or Riemann surfaces. This class contains on the one hand classical problems, like vector bundes or princial bundles, possibly with some level structure. On the other hand they also include twisted versions, which contain bundles on orbifold curves. They also made precise conjectures on the geometry of these moduli spaces.

I would like to explain what these moduli problems are, where they arise and why this level of generality simplifies the study the geometry of the moduli problems in question. At the end of the talk I would like to give an application to an artihmetic question over function fields.

This is the first talk in a learning seminar about the Steenrod algebra. See the

seminar web page

for more information.

After the talk, we will discuss the schedule for future talks in this seminar.