Title of the mini-course: Morava stabilizer groups and their cohomology by Hans-Werner Henn (University de Strasbourg).

Abstract:

This course will start with a survey talk on chromatic homotopy theory, in particular on recent developments in chromatic stable homotopy theory at chromatic level 2 at odd primes. For the homotopy groups of spheres this captures the next level of complexity beyond the image of J studied in the 1960′s by Adams, Toda, Quillen, Sullivan  and others.

The subsequent talks will concentrate on algebraic aspects of this development.

For a  finite spectrum X the chromatic homotopy type  at chromatic level n>0 and a given prime p is largely controlled by the continuous cohomology of a certain p-adic Lie group, in stable homotopy theory known under the name of Morava stabilizer group of level n at p, with coefficient in the corresponding Morava module of X.

The course will start by introducing the basic properties of these groups and its continuous cohomology with coeffients in a Morava module.

After recalling the classical case of chromatic level 1 (closely related to the image of J) the course will concentrate on chromatic level 2 which is at the edge of current knowledge.

The course aims to introduce participants to joint recent work with Goerss, Mahowald and Rezk which gives a new approach based on methods of group cohomology to previous work by Miller, Ravenel, Wilson, and by Shimomura and collaborators.

Tentative dates:

Friday, August 02, 2013

2:00 pm – 3:30 pm; Room: C2; Part I

Monday, August 05, 2013

3:00 pm – 4:30 pm; Room: C2; Part II

Tuesday, August 06, 2013

3:00 pm – 4:30 pm; Room: C2; Part III

Thursday , August 08, 2013

3:00 pm – 4:30 pm; Room: C2; Part IV

Venue: Vietnam Institute for Advanced Study in Mathematics.