Deformations of chromatic homotopy theory

Speaker: Torgeir Aambø – Norwegian University of Science and Technology (NTNU)

Abstract: Chromatic homotopy theory is the “quantum mechanics” of stable homotopy theory, where we split the theory down and study its smallest and most fundamental pieces. It has gotten the name “chromatic” as each piece operates at a certain fundamental frequency, or a certain wavelength. This gives a filtration of the pure white light $Sp$ into colors $Sp_{K(n)}$, and collections of colors $Sp_{E(n)}$.

Physics analogies aside, there are several well known deformations of $Sp$, for example Pstrągowski’s category of synthetic spectra $Syn_E$, or Patchkoria–Pstrągowski’s perfect derived category $D^\omega_H(Sp).$ In the talk we will survey the relevant deformations for $Sp_{E(n)}$ and discuss some possible models for deformations of $Sp_{K(n)}$.