The black hole information paradox raised by Hawking in the '70s and other related problems in the quantization of gravity have remained unanswered for quite some time. The difficulties regarding the non-renormalizability of the Einstein-Hilbert action can be averted by working in lower dimensions. By formulating this theory in the context of holography, we are guided by the major breakthroughs in that field throughout the years. In this framework, a particularly fruitful model is 1+1d Jackiw Teitelboim (JT) gravity. Interest in this model has exploded in recent years as it is seen to capture the low-energy dynamics of a particular SYK many-body quantum system, and describes the universal dynamics of rapidly rotating black holes. It provides an interesting exactly solvable model
of quantum gravity at all orders, and leads to an improved understanding of the information paradox. This research proposal aims to understand whether the lessons of JT gravity generalize to other related models of lower-dimensional gravity, and to go up in the number of dimensions. A unifying approach for these goals is to exploit the underlying symmetries. We will investigate the holographic
dual of SYK models in suitable regimes, and their gauge-theoretical relation to other gravity models. We further aim to exploit the exact results of JT gravity to understand the inner workings of 2+1d gravity by an in-depth investigation of the underlying quantum symmetry group governing its amplitudes.