# Rational homotopy of operads and associators

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

**Speaker:** Benoit Fresse, University of Lille 1

**Abstract:** The operads of little n-discs are used to model a hierarchy of homotopy commutative structures, from fully homotopy associative but non-commutative (n=1) to fully homotopy associative and commutative (n=infinity).
In this talk, I will deal with various models of the operad of little 2-disc (n=2). I will explain that braided monoidal categories are related to such a model, and that the Lie algebras of chord diagrams, as introduced by Drinfeld-Kohno, give a model for the cohomology of the operad.
In a second step, I will revisit the definition of the Sullivan dg-algebra of piecewise linear differential forms. I will prove that a modified version of this functor can be used to set up a rational homotopy theory for operads in topological spaces.
The ultimate goal of my talk is to explain that the Drinfeld associators, connecting braids and chord diagrams, have a topological interpretation in terms of rational formality quasi-isomorphisms for the operad of little 2-discs.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/04/2012

**Time:** 2:30pm - 3:30pm