In 1960s and '70s there was a flurry of activity developing A-infinity-algebraic techniques with an aim toward computing the Eilenberg-Moore spectral sequence of a homotopy pullback (for example, a loop space or homogeneous space). Arguably the most powerful result this program produced was the 1974 theorem of Munkholm that the sequence collapses when the three input spaces have polynomial cohomology over a given principal ideal domain, which gives the whole story on cohomology groups but sheds little light on the ring structure.

I will review this history and extend Munkholm's theorem to a ring isomorphism. The proof hinges on homotopy properties of the category of augmented differential graded algebras and the commutativity of some large but hopefully photogenic diagrams. Speaker(s): Jeff Carlson (Imperial College (London))