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Formality theorem and Kontsevich-Duflo theorem for Lie pairs

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Speaker: 
Hsuan-Yi Liao
Affiliation: 
Penn State
Date: 
Wed, 2017-09-27 10:30 - 12:00
Location: 
MPIM Seminar Room

A Lie pair $(L,A)$ consists of a Lie algebroid $L$ together with a 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 algebra actions. We establish the formality theorem for Lie pairs. As an application, we obtain Kontsevich-Duflo type theorems for Lie pairs. In this talk, I'll start with the case of $\mathbf{g}$-manifolds, i.e., smooth manifolds equipped with Lie algebra actions. After that, I'll explain formality theorem and Kontsevich-Duflo theorem for Lie pairs and other geometrical situations.

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