Masterclass: Rigidity and algebraic models in stable homotopy theory

Participants, April 2018 - Click for large photo

University of Copenhagen, 9-13 April 2018

The goal of this Masterclass is to study models of equivariant, non-equivariant, and local stable homotopy theory and their applications. Modelling a problem or theory is central to all of mathematics, and takes different incarnations in the various fields. One way it arises in topology is in finding a model category or infinity category to study a homotopy theory, and to understand the different ways in which this can be done. A good and simple enough model is both key to a good understanding of the theory and to concrete computations. This Masterclass will be centered around two cornerstones of the theory: The first one is Schwede's celebrated rigidity result, which states that the stable homotopy category admits an essentially unique model. The second one deals with the construction of efficient algebraic models for (rational) equivariant homotopy theory due to Greenlees and his coauthors. 

The Masterclass will consist of two lecture series by John Greenlees and Stefan Schwede, accompanied by several problem sessions, as well as five contributed talks exploring connections to closely related areas of current research.  

Lecture series:

• John Greenlees (Sheffield): Algebraic models of rational equivariant cohomology theories for compact Lie groups
• Stefan Schwede (Bonn): Rigidity of the stable homotopy category

Speakers:

• David Barnes (Belfast)
• Magdalena Kedziorek (Bonn)
• Irakli Patchkoria (Bonn)
• Constanze Roitzheim (Kent)
• Neil Strickland (Sheffield)

Venue:

The masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen, with support from the Centre for Symmetry and Deformation. See detailed instructions on how to reach Copenhagen and the conference venue.

Prerequisites and references:

A solid background in algebra as well as some familiarity with the basics of category theory and algebraic topology will be assumed.  

Room, schedule and abstracts:

A preliminary schedule as well as a preliminary description of the lectures can be found below. All lectures and exercise sessions will take place in Aud 4. 

• Preliminary schedule
• Greenlees's lecture
• Schwede's lecture
• Titles and Abstracts

Lecture notes

(Thanks to Malte Leip for making available his notes for most of the talks of the Masterclass.)

• Greenlees
• Schwede
• Barnes
• Kedziorek
• Patchkoria
• Roitzheim & Roitzheim's original notes
• Strickland (slides)

Additional material

• G-cohomology theories and G-spectra: A formulary
• Rational equivariant cohomology theories (summary of known results)
  
• Open problem session

Financial support:

Graduate students and other early career researchers can apply for financial support to partly cover local expenses. If you wish to apply for support, please indicate this on the registration form. The support should be roughly DKK 500 per day, at most DKK 2500 in total. 

Registration and Participants:

The deadline for funding applications is February 28th, 2018. If you are not applying for funding, please register by March 31st, 2018. 

Organised by Tobias Barthel and Markus Hausmann.