> ABSTRACT: > Back in 1997, Maxim Kontsevich proved that the algebra of polydifferential > operators on a smooth manifold is formal (i.e. quasi-isomorphic to its > cohomology). > The known constructions of Kontsevich's formality quasi-isomorphism > involve "transcendental" tools: the original construction, due to Kontsevich, > is based on the configuration space integral, while Tamarkin's construction > involves Drinfeld's associator. > In my talk, I will describe an explicit recursive > construction whose output is a formality quasi-isomorphism for > polydifferential operators > defined over rationals. The operad OCHA governing the open-closed > homotopy algebras is essential for this construction. > My talk is partially based on the paper http://arxiv.org/abs/1306.6733