For more information about this meeting, contact Calder Daenzer, Nigel Higson, Mathieu Stienon, Ping Xu.

Title: | Rational homotopy of operads and associators |

Seminar: | GAP Seminar |

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: | MB106 |

Date: | 09 / 04 / 2012 |

Time: | 02:30pm - 03:30pm |