Given a geometric structure which induces a foliation on a manifold and a leaf of this foliation, one can ask when the leaf is preserved under deformations of the geometric structure. For Poisson structures and Lie algebroids, this question was addressed by Marius Crainic and Rui Loja Fernandes, and they showed that a leaf is stable when a certain cohomology group vanishes. I will give a general approach to such questions in terms of the L-infinity-algebra governing the deformations of the geometric structure, and an L-infinity-subalgebra. I will then give an application to the stability of fixed points of Dirac structures in general Courant algebroids, which include twisted Poisson structures in exact Courant algebroids. This is joint work with Marco Zambon.

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