Stephanie Ziegenhagen: A Hodge decomposition spectral sequence for E_n-homology

The classical Hodge decomposition for Hochschild homology allows to express Hochschild homology of a commutative algebra in terms of higher order André-Quillen homology in characteristic zero. Teimuraz Pirashvili showed that a similar decomposition exists for Hochschild homology of higher order n, and that the terms occuring in these decompositions only depend on the parity of n, hence allowing calculations of higher order Hochschild homology via knowledge of the Hodge summands for n=1 or n=2. A generalization of higher order Hochschild homology to algebras which are commutative only up to coherent higher homotopies is E_n-homology. In this talk, I will recall the construction of the spectral sequence yielding the classical Hodge decomposition. I will introduce higher order Hochschild homology and discuss the Hodge decomposition in this case. Finally, we will see how to obtain a Hodge decomposition spectral sequence for E_n-homology of E_infinity algebras.