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Topology Seminar

Thu., Jan. 28, 2021 4:30 p.m.

Location: Live Stream

Speaker: Niko Schonsheck, Ohio State University

Title: Fibration theorems, functor calculus, and chromatic connections in O-algebras

Zoom: https://uregina-ca.zoom.us/j/99127226830?pwd=bnFQR1R3UUdyWUxqSS9JMExMRlZwZz09

Abstract: By considering algebras over an operad O in one's preferred category of spectra, we can encode various flavors of algebraic structure (e.g. commutative ring spectra). Topological Quillen (TQ) homology is a naturally occurring notion of homology for these objects, with analogies to both singular homology and stabilization of spaces. In this talk, we will begin by discussing a fibration theorem for TQ-completion, showing that TQ-completion preserves fibration sequences in which the base and total O-algebra are connected. We will then describe a few results that hint towards an intrinsic connection between TQ-completion and the convergence of the Taylor tower of the identity functor in the category of O-algebras. Lastly, time permitting, we will discuss recent joint work with Crichton Ogle on the chromatic localization of the homotopy completion tower of O-algebras and connections to functor calculus.