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Abstract: In this talk, I will explain how the gravitational symplectic form between nearby AAdS geometries is dual to a quantum Kahler form on the space of euclidean path integral states with sources turned on. As an application, I will show that variations of extremal volumes can be computed using this symplectic form by considering a particular variation: the “new York” variation, which I will describe in detail. Finally, I will discuss the CFT interpretation of this deformation in some concrete examples like the vacuum and the TFD state at late times.