## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, October 24, 2022

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Benjamin Antieau

**Contact email:** antieau@northwestern.edu

**Contact Phone:** 847-491-5544

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