Then using basis of $\xi\partial$-monomials and employing elements of Groebner bases theory we prove homological purity of the
higher cyclic Hochschild complex and as a consequence obtain $L_\infty$-formality. This is based on a joint work with M. Kontsevich.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/5312