CORDIS Project
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This project investigates the local normal forms of geometric structures, particularly in Poisson geometry related to Lie algebras. It aims to resolve long-standing questions about identifying Poisson structures near singularities, contributing to a deeper understanding of mathematical frameworks.
Given a geometric structure, can we find local coordinates such that the structure has a particular nice expression?That is one of the most fundamental questions for any geometric structure, that of a local normal form.
In Poisson geometry, this question is directly related to the study of Lie algebras, as any Lie algebra is equivalent to a linear Poisson structure on its dual.Given a Poisson structure with a singularity, can we locally identify the Poisson structure always with its linear (firs…
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