A key feature in the theory of 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 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.
