Topology seminar

 Hill-Hopkins-Ravanel norms give a lift of tensor-induction from the category of $H$-spectra to $G$-spectra for $H \subseteq G$ a subgroup of a finite group, and they were crucial to their resolution of the Kervaire Invariant one problem in all but one dimension; analogously, the influential Angelveit-Blumberg-Gerhardt-Hill-Lawson-Mandell perspective on (twisted) topological Hochschild homology expresses it as a norm from finite subgroups of the circle group. Following this, Blumberg-Hill-Mandell issued a series of conjectures concerning \emph{equivariant factorization homology} as a technique for constructing norms along closed subgroup inclusions between compact Lie groups (extending the above examples) and computing their geometric fixed points. Following work-in-progress with Juran, I will sketch a resolution of these conjectures.

VH 570

Green functors are an equivariant generalization of rings which underlie multiplicative equivariant cohomology theories. In this talk, I will introduce the notion of Green functors and discuss some recent work on understanding the categories of modules over Green functors through the lens of algebraic K-theory. I will also talk about some tools for computing algebraic K-groups of Green functors. This is joint work with Noah Wisdom.

VH 570

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