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

Transfer systems are combinatorial objects that encode information about equivariant operations. More precisely, a transfer system encodes the transfers (or wrong-way maps) carried by algebras over certain equivariant operads. Thus, transfer systems allow us to use combinatorial tools to study equivariant homotopy theory. This talk will be an overview of various properties, including some structural and combinatorial results. We will concentrate on multiplicative structures, using the idea of operad pairs of May. The results presented are part of various collaborations, including Scott Balchin, David Chan, Myungsin Cho, Evan Franchere, Usman Hafeez, Peter Marcus, Kristen Mazur, David Mehrle, Pablo S. Ocal, Kyle Ormbsy, Weihang Qin, Constanze Roitzheim, Rekha Santhanam, Ben Szczesny, Danika Van Niel, Paula Verdugo, Riley Waugh, and Valentina Zapata Castro.

VH 570

Abstract not available

Abstract not available