Black holes: bridges between number theory and holographic quantum information

Defining a theory of quantum gravity remains one of the most challenging problems at the cutting edge of research in mathematical and theoretical physics. Unlocking this problem implies constructing a quantum field theoretic description of gravity which fully elucidates how a quantum field theory encodes gravitational spacetime background solutions. Much of the progress in shaping the language and the framework of this problem owes its genesis to a specific subset of problems in quantum gravity, namely those dealing with understanding the organisation of information in black holes.