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SUMMARY:An Intrinsic Operad Structure for the Derivatives of the Identity
DTSTART:20201020T170000
DTEND:20201020T180000
DTSTAMP:20260609T204547Z
UID:d7a9df75f8ba6d43c49f57c0eca8c4e9525aaaa1263bf54053ab67f1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Duncan Clark\, Ohio State University\nA long standing slogan 
 in Goodwillie's functor calculus is that the derivatives of the identity f
 unctor on a suitable model category should come equipped with a natural op
 erad structure. A result of this type was first shown by Ching for the cat
 egory of based topological spaces. It has long been expected that in the c
 ategory of algebras over a reduced operad $\\mathcal{O}$ of spectra that t
 he derivatives of the identity should be equivalent to $\\mathcal{O}$ as o
 perads.\n \nIn this talk I will discuss my recent work which gives a posi
 tive answer to the above conjecture. My method is to induce a ``highly hom
 otopy coherent'' operad structure on the derivatives of the identity via a
 n pairing of underlying cosimplicial objects with respect to the box produ
 ct. This cosimplicial object naturally arises by analyzing the derivatives
  of the Bousfield-Kan cosimplicial resolution of the identity via the stab
 ilization adjunction for $\\mathcal{O}$-algebras. Time permitting\, I will
  describe some additional applications of these box product pairings. In p
 articular\, I will show how a similar box product pairing may be utilized 
 to provide a new description of an operad structure on the derivatives of 
 the identity in spaces.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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