## Geometry Seminar - Abstracts

### Talk

Tuesday 3 October 2023, 16:00 - 17:00 in HG00.616

**João Mestre** (University of Coimbra)

*Deformations of holomorphic groupoids*

### Abstract

Lie groupoids can encode geometric objects such as smooth
actions, and foliations; deformations of Lie groupoids also relate to
deformations of such objects. In this talk we’ll see the deformation
cohomology of a (real) Lie groupoid, mention a few relations to the
mentioned examples, and and how a interpretation in terms of vector
bundles over a Lie groupoid can be used to study deformations of
holomorphic groupoids.
The deformation complex obtained for a holomorphic groupoid arises as
the total complex of a double complex. It combines the deformation
complex of the groupoid structure and the Kodaira-Spencer complex
controlling deformations of the underlying complex manifold. The talk is
based on ongoing work with Luca Vitagliano.

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