An Introduction to Chromatic Homotopy Theory

Delve into the third lecture of a series on chromatic homotopy theory, presented by Mike Hill at the Hausdorff Center for Mathematics. Explore key concepts such as Morava K-theories and Morava E-theories, and understand their significance in the stable homotopy category. Discover the relationship between Morava K-theories and the Balmer spectrum, and learn why homotopy theorists are drawn to studying K(n)-local categories. Examine the role of E-theory and group cohomology in analyzing these categories. This one-hour lecture, part of the HIM Summer School "Spectral methods in algebra, geometry, and topology," requires some familiarity with the stable homotopy category and offers an in-depth exploration of this advanced mathematical subject.