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Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.

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Is symplectic reduction interesting from a physical point of view?

Here is a fancy example: Supersymmetry. Rigid N=1 supersymmetric theories in 4 dimension have a natural Kahler structure on the field space. The D-term is precisely a moment map. The moduli space of t …
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