Rune Haugseng: Spectral Sequences for the Cohomology of Finite and Infinite Loop Spaces

Using the Bousfield-Kan 2-completion tower of a spectrum or a space we can construct spectral sequences that, in good cases, converge to the mod-2 cohomology of the corresponding infinite loop space or k-fold loop space, respectively. I will give a description of the E 2 -terms of these spectral sequences in terms of certain well-studied derived functors, and discuss some simple examples. This is joint work with Haynes Miller.