Power Operations and Normed Spectra

A key feature in the theory of \(E_\infty\) ring spectra in algebraic topology is that their homology and homotopy admit a theory of power operations. It is straightforward to introduce the direct analog of \(E_\infty\) ring spectra in motivic homotopy theory, but the power operations arising from this structure are not as useful.  There is a subtler theory of normed motivic spectra, introduced by Bachmann-Hoyois. In recent preprints, joint with Tom Bachmann and Elden Elmanto, we develop a theory of power operations on normed algebras over the mod-2 motivic cohomology spectrum. I'll discuss this construction and some applications of the resulting theory.

There will be a pre-talk aimed at graduate students 2:30-3:15pm in THO 234.