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Home » AT Open Problems/Work in Progress Seminar: Koszul duality and homotopy automorphisms of E_n-operads

Seminar

AT Open Problems/Work in Progress Seminar: Koszul duality and homotopy automorphisms of E_n-operads March 03, 2014 (01:45 PM PST - 03:00 PM PST)
Parent Program: Algebraic Topology
Location: MSRI: Simons Auditorium
Speaker(s) Benoit Fresse (Université Lille 1)
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Abstract/Media

The goal of this talk is to explain a method to compute the homotopy of the space of homotopy automorphisms of an E_n-operad.

 

I will focus on the case n=2. I will quickly review the relationship between E_2-operads and braided monoidal categories in the first part of my talk. I will explain an operadic interpretation of the notion of a Drinfeld associator afterwards.

 

Then I will tackle the main purposes of my talk: explain the definition of a double obstruction spectral sequence to compute the homotopy automorphism spaces of operads; explain how the Koszul duality of E_2-operads can be used to prove that this spectral sequence reduces to Drinfeld's description of the set of associators.

 

The question is how far phenomena occurring in the E_2 case extend to the E_n-operads of higher dimension.

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