Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Natalya Iyudu
Affiliation:

The University of Edinburgh/MPIM
Date:

Tue, 2019-12-10 14:00 - 15:00 We formulate the notion of pre-Calabi-Yau structure via the higher cyclic Hochschild complex and study its cohomology.

A small quasi-isomorphic subcomplex in higher cyclic Hochschild complex gives rise to the graphical calculus of $\xi\partial$-monomials.

Within this calculus we are able to give a nice combinatorial formulation of the Lie structure on the corresponding Lie subalgebra.

A small quasi-isomorphic subcomplex in higher cyclic Hochschild complex gives rise to the graphical calculus of $\xi\partial$-monomials.

Within this calculus we are able to give a nice combinatorial formulation of the Lie structure on the corresponding Lie subalgebra.

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/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/5312