Speaker: Alice Hedenlund (University of Oslo)
Title: Tate constructions and the Tate spectral sequence
Abstract: Classically, Tate cohomology is a way to splice together group homology and group cohomology into a single cohomology theory, and was first introduced by John Tate in his research in class field theory. The Tate construction on a G-spectrum is a higher categorical analogue of this construction. In this talk, I will define the Tate construction and related concepts, such as the dualising spectrum and the norm map, in a way that is accessible to someone with a basic understanding of higher category theory. I will also mention how it relates to classical topics in topology, such as Poincaré duality. Finally, I want to discuss some of my own contributions to the subject relating to various constructions of the Tate spectral sequence, a computational tool to understand the homotopy groups of the Tate construction. This includes joint work with Rognes and Krause-Nikolaus.