In this talk, I will discuss the Linearization Conjecture. This conjecture predicts the equivariant homotopy type of the functional dual of Morava E-theory, an object that plays a central role in chromatic homotopy theory. I will motivate the conjecture via an example from real Lie group theory.

The material in this talk is joint work with Paul Goerss, Mike Hopkins and Vesna Stojanoska.