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Stability problems and differential graded Lie algebras

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Karandeep Jandu Singh
Thu, 18/04/2024 - 15:00 - 16:00
MPIM Lecture Hall
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Stability problems appear in various forms throughout geometry and algebra. In differential geometry, given a vector field on a manifold that vanishes in a point, one can ask when nearby vector fields also vanish in a point. In algebra, given a Lie algebra and a subalgebra, one can ask when all deformations of the ambient Lie algebra also admit a Lie subalgebra of the same dimension. I will show that both questions are instances of a general question about differential graded Lie algebras. Under a finite-dimensionality assumption which is satisfied in the examples above, I will give a sufficient condition for a positive answer to the general question. I will then discuss some applications.

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