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Deformations of Lagrangian submanifolds in log-symplectic manifolds

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Stephane Geudens
Wed, 2021-11-17 10:30 - 12:00
MPIM Lecture Hall

Log-symplectic structures are a type of Poisson structures that are symplectic outside of a hypersurface. The aim of this talk is to discuss whether the deformation theory of Lagrangian submanifolds in this setting is as well-behaved as in symplectic geometry. Since the case of Lagrangians transverse to the singular hypersurface is well understood, we will mostly focus on Lagrangian submanifolds contained in the singular locus. We establish a normal form theorem around such submanifolds, and we show that their deformations are governed by a DGLA. This allows us to draw some geometric consequences: we discuss whether the Lagrangian admits deformations not contained in the singular locus, and we give precise criteria for unobstructedness of first order deformations. This talk is based on joint work with Marco Zambon.

The talk is hybrid. For the time being, in person participation is only allowed for members of MPIM with a vaccination/recovery certificate.

Zoom ID: 547 147 1640
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