Quantifying gravity physics using CFT methods

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The purpose of this PhD thesis is to explore quantitative aspects of quantum gravity using CFT tools through the AdS/CFT correspondence in a fairly broad context. We will explore aspects of CFT derivations of Page curves in black hole physics and how to quantify operator growth in CFT terms. We will also be interested in exploring the possibility of extendingtypicality arguments in quantum mechanics to CFTs in 2d and their relation to local ETH. On the more speculative side, we can consider whether these typicality ideas have any connection with recent ideas suggesting that certain semiclassical gravitational theories provide ensemble average predictions and whether any of our tools in 2d can be extended to higher dimensions or whether they can apply to a broader holographic context. The tools used along the thesis are expected to be based on CFT methods, but we also envision a fair training in gravitational techniques, as required in many applications of AdS/CFT.