Equivariant Operads, the Kervaire Invariant, and the Blumberg-Hill Conjecture

David White – 11 April 2018

In a 2016 Annals paper, Hill, Hopkins, and Ravenel resolved the Kervaire Invariant One problem using tools from equivariant stable homotopy theory. Of particular importance were equivariant commutative ring spectra and their multiplicative norms. A more thorough investigation of multiplicative norms, using the language of operads, was recently conducted by Blumberg and Hill, though the existence of their new "N-infinity" operads was left as a conjecture. In this talk, I will provide an overview of the Kervaire problem and its solution, I will explain where the operads enter the story, and I will prove the Blumberg-Hill conjecture using a new model structure on the category of equivariant operads. This is joint work with Javier Gutierrez.