Speaker: John E. Harper from University of Western Ontario, London

Title: On a homotopy completion tower for algebras over operads in symmetric spectra.

Abstract: In Haynes Miller's proof of the Sullivan conjecture on maps from classifying spaces, Quillen's derived functor notion of homology (in the case of commutative algebras) is a critical ingredient. This suggests that homology for the larger class of algebraic structures parametrized by an operad O will also provide interesting and useful invariants. Working in the context of symmetric spectra, we introduce a completion tower for algebras over operads and prove that under appropriate connectivity conditions this tower interpolates between topological Quillen homology and the identity functor. This is part of a larger goal to attack the problem: how much of an O-algebra can be recovered from its topological Quillen homology? We also prove analogous results for algebras over operads in unbounded chain complexes. This talk is an introduction to these results (joint with K. Hess) with an emphasis on several of the motivating ideas.