Symplectic reduction along a submanifold and the Moore-Tachikawa TQFT
Maxence Mayrand (University of Toronto)
Abstract: In 2011, Moore and Tachikawa conjectured the existence of certain complex Hamiltonian varieties which generate two-dimensional TQFTs where the target category has complex reductive groups as objects and holomorphic symplectic varieties as arrows. It was solved by Ginzburg and Kazhdan using an ad hoc technique which can be thought of as a kind of "symplectic reduction by a group scheme." We clarify their construction by introducing a general notion of "symplectic reduction by a groupoid along a submanifold," which generalizes many constructions at once, such as standard symplectic reduction, preimages of Slodowy slices, the Mikami-Weinstein reduction, and the Ginzburg-Kazhdan examples. This is joint work with Peter Crooks.
mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry
Audience: researchers in the topic
Geometry, Physics, and Representation Theory Seminar
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