Equivariant homotopy theory started from geometrically motivated questions about
symmetries of manifolds. Several important equivariant phenomena occur not just for a …

This paper contains an overview of background from stable homotopy theory used by Freed–
Hopkins in their work on invertible extended topological field theories. We provide a working …

We provide a very general approach to placing model structures and semi-model structures
on algebras over symmetric colored operads. Our results require minimal hypotheses on the …

We establish a highly flexible condition that guarantees that all colored symmetric operads
in a symmetric monoidal model category are admissible, that is, the category of algebras …

The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the
Brown--Peterson spectrum. We will construct a secondary operation in mod-2 homology and …

We give a survey of the ideas of descent and nilpotence, beginning with the theory of thick
subcategories. We focus on examples arising from chromatic homotopy theory (such as …

We provide a universal de Rham model for rational G‐equivariant cohomology theories for
an arbitrary torus G. More precisely, we show that the representing category, of rational G …

We describe a construction of the cyclotomic structure on topological Hochschild homology
(THH) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis …

We show that certain tilting results for quivers are formal consequences of stability, and as
such are part of a formal calculus available in any abstract stable homotopy theory. Thus …

We extend the theory of ambidexterity developed by MJ Hopkins and J. Lurie and show that
the $\infty $-categories of $ T (n) $-local spectra are $\infty $-semiadditive for all $ n $, where …