## Geometry Seminar - Abstracts

### Talk

Tuesday 31 May 2022, 16:00 - 17:00 in HG03.085
David Barnes (Belfast)
Equivariant sheaves in the profinite setting

### Abstract

Sheaves sit at an interface of algebra and geometry. Equivariant sheaves offer even more structure, allowing for different group actions at different stalks. We are interested in the case where both the base space and group of equivariance are profinite (that is, compact, Hausdorff and totally disconnected). This combination provides many useful consequences, such as good notion of equivariant presheaves and an explicit construction of infinite products. Furthermore, the category of rational $$G$$-Mackey functors (for $$G$$ profinite) is equivalent to a certain class of $$G$$-equivariant sheaves, thus providing a more geometric description of an important category from algebra. The content is motivated by the 2019 result of Sugrue that provides an algebraic model for rational $$G$$-equivariant stable homotopy theory. If time permits I will give an overview of this result and some consequences and future directions.

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