## Séminaire de Géométrie et Quantification |

**Ping
Xu **

(Penn State)

Lundi 29 mai à 15h30, salle 01, IHP

*Title:*
Formality theorem and Kontsevich-Duflo theorem for Lie pairs

*Résumé:* A Lie pair (L,A) consists of a Lie
algebra (or more generally, a Lie algebroid) L together with a
Lie subalgebra (or Lie subalgebroid) A. A wide range of
geometric situations can be described in terms of Lie
pairs including complex manifolds, foliations, and manifolds
equipped with Lie group actions. To each Lie pair (L,A) are
associated two L-infinity algebras, which play roles similar to the
spaces of polyvector fields and polydifferential operators. We
establish the formality theorem for Lie pairs.

As an application, we obtain Kontsevich-Duflo type theorem for Lie pairs. Besides using Kontsevich formality theorem, our approach is based on the construction of a dg manifold (L[1] + L/A, Q) together with a dg foliation, called the Fedosov dg Lie algebroid. This is a joint work with Hsuan-Yi Liao and Mathieu Stiénon