# Benoit Fresse: Cochain models of operads and topological realizations of the graded Poisson operads

**Time: **
Tue 2022-02-15 14.15 - 16.00

**Location: **
Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Benoit Fresse (Université des sciences et Technologies de Lille)

**Abstract:** In this talk, I mostly propose to survey results of myself, Victor Turchin and Thomas Willwacher about rational models and rational homotopy automorphisms of \(E_n\)-operads. The results are mainly based on a Sullivan model of the rational homotopy of operads, which gives the setting for the definition of graph complex models of \(E_n\)-operads in spaces. Then I will report on a recent work with Lorenzo Guerra and on ongoing research about the definition of cochain models for the *p*-complete homotopy theory of operads, and the definition of a graph complex operad in this setting. This graph complex operad is associated to a topological realization of the *n*-Poisson operad, but little is known about the realization space of graded Poisson operads yet, and therefore, the question remains open about the correspondence between this graph complex operad model and \(E_n\)-operads in *p*-complete homotopy theory.