Title: Borel Equivariance in Homotopy Theory
Abstract: In equivariant homotopy theory, we are interested in studying homotopical objects with the additional requirement that they come with a notion of a group acting on them. The most natural examples are spaces or spectra with a coherent action of a group G. While these examples could be considered the initial reasons to develop such a theory, it is well known by this point that it is beneficial to work in the larger setting of "genuine" G-spaces and G-spectra. In this talk our goal will be to introduce the two notions as well as how to move between the two. In particular we will discuss how one might try to extend these ideas into the setting of motivic homotopy theory.
