Mardi 14 novembre 2006
IRMA Strasbourg (France)
Organizers : 
Hans-Werner Henn (Strasbourg) , Stefan Schwede (Bonn)
Program This "summer school type" activity on stable homotopy theory is part of the Graduiertenkolleg "Homotopy and Cohomology" at the universities of Bonn, Bochum and Düsseldorf and the "Ecole Doctorale de Mathématique, Sciences de l'Information et de l'Ingénieur" of the University of Strasbourg. There will be three series of 5 lectures each by
In addition there will be a series of talks given by students on topics related to these lectures series.
There will also be a talk by Klaus Volkert (Universität Köln) on "Poincare on his way to his conjecture", which aims at a wider audience and which touches on the historical origin of our subject.
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](http://www-irma.u-strasbg.fr/%7Ehenn/semaine_speciale/summer_schoola.html) Programme détaillé
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Mardi 14 novembre 2006
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Paul Goerss, Northwestern University
Calculations in stable homotopy theory, from quantitative towards qualitative phenomena
- The Classical Adams Spectral Sequence: Review and definitions, Adams periodicity. - Applying the geometry of formal groups: The Adams-Novikov Spectral Sequence. Hopf algebroids; the E_2 term. Chromatic spectral sequence; change of rings. Image of J. Higher order periodic phenomena. - Monochromatic Calculations: what formal groups of single height can say: Chromatic convergence and fracture squares. Group cohomology and collapsing results. Some calculations. Topological decompositions. -
John Greenlees, University of Sheffield
Structured spectra
- Motivation: reminder of spectra as representing objects and as stable spaces. Things one might want to do with structured spectra (Geometric topology, algebraic K-theory, brave new algebra, derived algebraic geometry). - EKMM spectra, symmetric spectra, orthogonal spectra. Diagram spectra. Examples. - Applications. Possibilities include outline of the use of THH and TC to calculate algebraic K-theory. Completion theorems. Morita theorems and classification results. Brave new commutative algebra, Gorenstein ring spectra and duality theorems. -
Stefan Schwede, Universität Bonn
Model categories and rigidity in stable homotopy theory
- Basics on model categories: axioms, homotopy category, spaces and chain complexes as examples - More on model categories: Quillen functors/equivalences, simplicial sets, simplicial model categories, more examples. - Spectra as a model category: sequential (aka "Bousfield-Friedlander-") spectra with the stable model structure. Universal property: spectra are "free stable model category on one generator". - Rigidity theorem: the stable homotopy category has a unique model up to Quillen equivalence