|Location:||MSRI: Simons Auditorium|
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.No Notes/Supplements Uploaded No Video Files Uploaded