Johan Alm: The universal noncommutative A_\infty deformation of Gerstenhaber algebras

The Grothendieck-Teichmuller Lie algebra, grt, can be defined as the set of (completed) Lie words in two variables x and y that satisfy a pentagon equation in the Lie algebra of infinitesimal braids and two symmetry equations. H. Furusho proved that if a Lie word satisfies the pentagon equation and does not contain [x,y], then it automatically satisfies also the two symmetry equations. T. Willwacher reinterpreted this result as saying that the first cohomology group of the deformation complex of the canonical morphism of operads from the A_\infty operad to the Gerstenhaber operad equals grt\oplus R, where R is spanned by the class of the word [x,y]. In this talk we discuss the role played by the class [x,y] in the deformation theory of (noncommutative) Gerstenhaber algebras and the Duflo isomorphism.