In this talk, we will introduce the theory of higher semiadditivity with an emphasis on proving that the category of T(n)-local spectra is infinitely semiadditive, following the paper by Carmelli, Schlank and Yanovski. We will go over key notions in ambidexterity, construct algebraic tools such as additive p-derivation, and talk about their application in chromatic homotopy theory. Time permitting, we will talk about the application to more general localization of spectra. No background in ambidexterity is assumed, but some knowledge in Bousfield localization and Sp_{T(n)} might be helpful.
