The goal of this internship is to compute the effects of quantum fluctuations on gravitational dynamics and in strongly-coupled quantum field theories through the use of gauge/gravity duality (aka holography). Gauge/gravity duality is a first-principle framework which captures the dynamics of strongly-coupled states of matter. It originates from string theory, where it was discovered as a duality with a specific supersymmetric gauge theory. In the limit of infinite rank of the gauge group and large coupling, this gauge theory is dual to Einstein gravity coupled to a number of matter fields, in a higher number of spacetime dimensions. Thus, by solving the gravity equations, we can access the correlation functions of the dual field theory. An important class of black hole spacetimes have a near-horizon geometry which displays an emergent two-dimensional copy of anti de Sitter spacetime (AdS2) near extremality (at low Hawking temperatures). Their low-temperature dynamics is particularly simple and given by the Schwarzian derivative of the AdS2 boundary time. This action has been quantized and its correlation functions are known. In the near-extremal limit, where quantum fluctuations are dominated by this effective action, quantum corrections may be computed. We will address this issue in the various sectors of four-dimensional black holes, building on ongoing work.