The Kervaire Invariant, Equivariant Spectra, and a proof of the Blumberg-Hill Conjecture

  • When 02/03/2018 de 12:15 a 13:15 (America/Montevideo / UTC-300)
  • Where IMERL
  • Contact
  • Speaker David White
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 Title: The Kervaire Invariant, Equivariant Spectra, and a proof of the Blumberg-Hill Conjecture

 

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. The language of model categories is essential to the proof, but I will recall all the relevant technical machinery required.