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Title:
Review of symplectic vortex equation
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Abstract:
In this talk, I will explain the basic theory of the symplectic vortex equation as the first part of the preparation for the symplectic geometry construction of the gauged linear sigma model (GLSM). If V is a symplectic manifold with a Hamiltonian group action, then analogous to the holomorphic curve equation, one has a first order elliptic system over a Riemann surface. Depending on different choices of domain metrics, one can (in principle) either define Gromov--Witten type invariants on the equivariant cohomology or the cohomology of the quotient space.
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