Holonomies for the Severa-Willwacher connections

In this talk I will discuss a construction of holonomies for connections with values in $L$-infinity algebras which is based on an $A$-infty version of de-Rham's theorem. Then I will explain how this construction, applied to the Severa-Willwacher connections, is related to the proof of formality of the little $d$-disks operad. This talk is based on work in progress joint with F. Schaetz.