K(n)-local homotopy from a Galois theory perspective - 2

The goal of these two talks is to give an overview of a perspective on K(n)-local homotopy theory that lends itself to computations. I will introduce some of the key players of the workshop such as the Morava K and E-theories. The introduction will emphasize the Galois theory inherent to the situation and be designed to lead us to consider finite resolutions of the K(n)-local sphere. I will then explain how these perspectives have helped us gain a better understanding on problems in chromatic homotopy theory such as the study of invertible elements and chromatic reassembly.