Piotr Pstragowski (University of Copenhagen, Denmark): Synthetic spectra. (Oberseminar Topologie)
Montag, 20.01.2020 14:00 im Raum SRZ 216
To any Adams-type homology theory one can associate a notion of a synthetic spectrum, their homotopy theory is in a precise sense a deformation of the derived category of quasi-coherent sheaves on a certain algebraic stack whose generic fibre is given by the category of spectra.
In this talk, I will survey some of the applications of synthetic spectra, such as the problem of algebraicity of chromatic homotopy theory, or the classification of highly-connected manifolds of Burklund-Hahn-Senger. I will also discuss some conjectures on the universal property of synthetic spectra and possible generalizations to a general homology theory.