In this talk, we first present a detailed analysis of theclassical geometry of generic null hypersurfaces. We then reformulatethe Einstein equations as conservation laws for the intrinsicgeometric data on these hypersurfaces. Following this, we derive thesymplectic structure and the corresponding Poisson bracket. Uponquantizing this phase space, we propose that the projected Einsteintensor obeys the operator product expansion of the stress tensor in aconformal field theory along null time. This hypothesis is supportedby explicit computations in simplified scenarios, such as the absenceof radiation and within the framework of perturbative gravity.Notably, we discover a non-vanishing central charge, which counts thelocal geometric degrees of freedom and diverges in the classicallimit. We suggest that this central charge is a fundamental principleunderlying the emergence of time in quantum gravity. If time permits,we will conclude by introducing a mesoscopic model of quantum gravityon null hypersurfaces, based on the concept of the "embadon," anoperator that creates localized bits of area on cuts.