Masterclass: Stratifications and duality in modular representation theory
University of Copenhagen, 27-31 March 2017
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The goal of this Masterclass is to study the local and global structure of the stable module category of a finite group (scheme), a category which plays a fundamental role in modular representation theory. In particular, it will focus on recent groundbreaking results of Benson, Iyengar, Krause, and Pevtsova, establishing a decomposition or stratification of the stable module category in terms of group cohomology as well as a new conceptual perspective on local duality in these categories. The techniques introduced in their work are relevant far beyond modular representation theory and should lead to further insights in commutative algebra, algebraic geometry, and algebraic topology.
The Masterclass will consist of two lecture series by Henning Krause and Srikanth Iyengar, accompanied by several problem sessions, as well as four contributed talks exploring connections to closely related areas of current research.
- David Benson (University of Aberdeen)
- Natàlia Castellana (Universitat Autònoma de Barcelona)
- John Greenlees (University of Sheffield)
- Beren Sanders (University of Copenhagen)
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, including the basic theory of rings and modules, basic commutative algebra (first chapters of Atiyah/MacDonald), and basic homological algebra (derived functors, Ext, Tor).
Schedule and abstracts:
The topics of this masterclass will include the cohomology of groups, in particular Quillen's stratification theorem; the stable module category of representations; adapting methods from commutative algebra, including local cohomology and derived completions, to modular representation theory; support and cosupport; classification of localizing and colocalizing subcategories; and local duality.
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. Limited additional funds to support travel for US participants are available.
Organised by Tobias Barthel and Jesper Grodal.