Symplectic reduction along a submanifold

Peter Crooks (Northeastern University)

02-Dec-2021, 16:00-17:00 (3 years ago)

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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