Equivariant Homotopy Theory

This course will serve as an introduction to equivariant homotopy theory, with an emphasis on intuition and with a grounding in concrete computations. We will begin with the homotopy theory of equivariant spaces, seeing what can be said here that mirrors the non-equivariant cases, before introducing stabilization and discussing the kinds of problems stabilization works to solve. Here, we have lots of choices for how we stabilize, and we will spend a little time discussing this and the consequences. Having developed the foundations, the end of the course will focus on student-led presentations on applications of equivariant homotopy theory.