Title Promoter Affiliations Abstract "Solvable models of quantum gravity and holography" "Thomas Mertens" "Department of Physics and astronomy" "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." "Solvable Models of Quantum Gravity" "Thomas Mertens" "Department of Physics and astronomy" " Understanding quantum gravity is one of the most important unsolved problems in high energy theoretical physics. The past six years have seen remarkable progress in this field in terms of exactly solvable holographic lower dimensional models, starting with the SYK model and 2d JT gravity. In this project, we aim to understand this class of solvable models better, with two goals in mind. Firstly, we want to characterize how large this class of solvable models is. Secondly, we want to develop an understanding of their universality and impact for quantum gravitational physics beyond these specific models, with a particular emphasis on their relevance for black hole physics in our universe. In order to achieve this, we will combine techniques from the fields of holography, random matrix theory, and representation theory." "Many-body systems: from independent particles to collective behaviour" "Dimitri Van Neck" "Department of Physics and astronomy" "The way how collective behaviour is developed within a particular many-body system, remains an open question. This project will address this problem twofold. A first part will embody the study of exactly-solvable Richardson-Gaudin systems for nuclear shell-model calculations. A second part will be devoted to the further development of the Collective model in the Cartan-Weyl basis."