Appears in collection : Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Foundational work of Hu—Kriz and Dugger showed that for Real spectra, we can often compute as easily as non-equivariantly. The general equivariant slice filtration was developed to show how this philosophy extends from C_2-equivariant homotopy to larger cyclic 2-groups, and this has some fantastic applications to chromatic homotopy. This talk will showcase how one can carry out computations, and some of the tools that make these computations easier.

The natural source for Real spectra is the complex points of motivic spectra over ℝ, and there is a more initial, parallel story here. I will discuss some of how the equivariant shadow can show us structure in the motivic case as well.