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.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3946