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Topology Seminar

Thu., Jan. 21, 2021 4:30 p.m.

Location: Live Stream

Speaker: Duncan Clark, Ohio State University

Title: An intrinsic operad structure for the derivatives of the identity

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

Abstract: A long standing slogan in Goodwillie's functor calculus is that the derivatives of the identity functor on a suitable model category should come equipped with a natural operad structure. A result of this type was first shown by Ching for the category of based topological spaces. It has long been expected that in the category of algebras over a reduced operad O of spectra that the derivatives of the identity should be equivalent to O as operads.

In this talk I will discuss my recent work which gives a positive answer to the above conjecture. My method is to induce a "highly homotopy coherent" operad structure on the derivatives of the identity via a pairing of underlying cosimplicial objects with respect to the box product. This cosimplicial object naturally arises by analyzing the derivatives of the Bousfield-Kan cosimplicial resolution of the identity via the stabilization adjunction for O-algebras. Time permitting, I will describe some additional applications of these box product pairings including a new description of an operad structure on the derivatives of the identity in spaces.