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Title:
Adiabatic limit of gauged Witten equation and mirror map
Speaker:
Abstract:
In this talk, I will review the adiabatic limit analysis of both the vortex equation and the gauged Witten equation. If one rescales the metric on the domain curves by a large constant, then as proved by Gaio-Salamon, vortices should approximate holomorphic curves in the symplectic quotient, modulo bubbling of “point-like instantons.” This picture leads to an isomorphism between the gauged Gromov-Witten theory and the usual Gromov-Witten theory of the quotient up to a change of variable (the quantum Kirwan map). I will show you how to extend this picture to the gauged Witten equation and how to obtain the precise relation between the GLSM CohFT and the Gromov-Witten CohFT of the classical vacuum. This is a joint work in progress with Gang Tian.
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