In this talk, I will start with the origin of equivariant chromatic homotopy theory: Ravenel’s solution to the odd primary Kervaire invariant one problem in 1978. I will explain what the idea of the paper is, and how its ideas impact later understanding of chromatic homotopy theory.
Then I wish to (partially and vaguely) answer the following questions:
1. In algebra and topology, how can equivariant methods help in understanding chromatic homotopy theory?
2. What are some exciting examples?
3. How does genuine equivariant stable homotopy theory come into play?