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I will show how to construct a global Kuranishi chart for Gromov--Witten moduli spaces (parametrizing closed holomorphic curves of some fixed genus in a symplectic manifold) which generalizes the genus 0 construction of Abouzaid--McLean--Smith. The global chart and its smoothness properties allow us to give a simple definition of virtual classes, identify the resulting classes with their algebro-geometric counterparts and prove a torus localization formula in the symplectic setting. This is based on joint work-in-progress with Amanda Hirschi.

FHT Program Seminar: Global Charts For Higher Genus Gromov--Witten Moduli Spaces