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Explore a 42-minute mathematics lecture that delves into using local symplectic Lie groupoids to approximate Hamiltonian dynamics for generic Poisson structures. Learn how recursively obtained solutions of Hamilton-Jacobi-like equations are interpreted as Lagrangian bisections near the unit manifold to provide approximations for finite-dimensional conservative mechanics. Discover the application of these approximation techniques as a new tool in numerical analysis, and examine potential extensions to Hamiltonian PDEs. Delivered as part of the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" at the Erwin Schrödinger International Institute for Mathematics and Physics.
