Speaker: Torgeir Aambø – Norwegian University of Science and Technology
Abstract: Chromatic homotopy theory views the stable homotopy category as certain nicely behaved layers glued together along formal neighborhoods. These are respectively described by the famous Morava E-theories $E(n)$ and Morava K-theories $K(n)$. We can single out one of these layers – in some sense reducing the entire colorful spectrum down to a single chroma – giving us monochromatic homotopy theory. During the talk we will see some properties of this theory, in particular focusing on its local duality with $K(n)$-local spectra and exotic algebraicity.