Local-global conjectures in modular representation theory.

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• Stefano Sannella, University of Birmingham
• Friday 26 January 2018, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Nicolas Dupré.

The representation theory of a finite group G over a field F of positive characteristic carries many questions that have not been answered yet. Most of them can be stated as global/local conjectures: in various forms, they state that the representation theory of G is somehow controlled by its p-local subgroups. Here we will mostly focus on one of these conjectures, Broué’s Abelian Defect Group Conjecture, which might be considered as an attempt to give a structural explanation of what is actually connecting G and its local p-subgroups in the abelian defect case. In particular, we explain how the strategy of looking for a perverse equivalence (a specific type of derived equivalence) works successfully in some cases and how this procedure is related to some Deligne-Lusztig varieties.

This talk is part of the Junior Algebra and Number Theory seminar series.

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