Seminar

Let E be a homology theory and M an E_*E-comodule. Is there a spectrum X such that M is the E-homology of X, and if so, how many? Goerss-Hopkins obstruction theory is a tool for answering such questions, including analogous ones for highly structured ring spectra. In joint work with Piotr Pstrągowski, we introduced a general infinity-categorical framework for obstruction theory using synthetic spectra. We'll set up this framework, observe it in action, and discuss the relationship between convergence of E-based obstruction theories and the homological algebra of E_*E-comodules.