EVENT DETAILS AND ABSTRACT

Title: Mod p homology of labeled configuration spaces via spectral Lie algebras
Speaker: Adela Zhang
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

The labeled configuration spectrum B_k(M;X) of a manifold M with labels in a spectrum X generalizes the notion of unordered configuration spaces B_k(M)=B_k(M;S^0). Knudsen identified labeled configuration spectra with the topological Quillen homology objects of certain spectral Lie algebras. This allows us to extract information about the mod p homology of B_k(M;X) using a bar spectral sequence and power operations on spectral Lie algebras, following the work of Knudsen on the rational homology of B_k(M;X) and Brantner-Hahn-Knudsen on its Morava E-theory. In this talk, I will explain how to compute the E^2-page of this bar spectral sequence via a May spectral sequence when p=2. Time permitting, I will talk about ongoing work with Andrew Senger on identifying the higher differentials via one-parameter deformation of comonads.