Symplectic reduction along a submanifold
Peter Crooks (Northeastern University)
Abstract: Noether's perspective on conserved quantities gives rise to quotient constructions in symplectic geometry. The most classical such construction is Marsden-Weinstein-Meyer reduction, while more modern variants include Ginzburg-Kazhdan reduction, Kostant-Whittaker reduction, Mikami-Weinstein reduction, symplectic cutting, and symplectic implosion.
I will outline a generalization of the quotient constructions mentioned above. This generalization will be shown to have versions in the smooth, holomorphic, complex algebraic, and derived symplectic contexts. As a corollary, I will derive a concrete and Lie-theoretic construction of "universal" symplectic quotients.
This represents joint work with Maxence Mayrand.
mathematical physicsalgebraic geometrydifferential geometryrepresentation theorysymplectic geometry
Audience: researchers in the topic
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