GATP Seminar – Florian Zeiser (Imperial): Local normal forms in Poisson geometry

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Poisson geometry provides a natural framework for Hamiltonian systems with symmetries and constraints. Understanding the behaviour of such systems near singularities naturally leads to local normal form problems. In particular, a central question is whether a Poisson structure can be linearized near a singular point, that is, whether it is locally equivalent to its linear approximation, given by the Lie–Poisson structure associated with a Lie algebra. In this talk, we will survey known results, counterexamples, and open questions concerning this linearization problem, with particular emphasis…