Colloquium

Gravity in 1+1 dimension is classically trivial but, as shown by A. Polyakov in 1981, it is a non-trivial quantum theory, in fact a conformal field theory (the Liouville theory), and also a string theory. In the last decades many important results and connexions with various areas of mathematics and theoretical physics have been established, but some important issues remain to be understood. In this colloquium I shall focus on some recent developments and new questions on the relation between discrete and continuous 2 dimensional gravity, probabilities and stochastic processes, random fractal geometries and SLE curves.

The supermassive black hole in the centre of the Milky Way, Sgr A*, is an ideal target for testing the properties of black holes. A number of experiments are being prepared or conducted, such as the monitoring of stellar orbits, the search for radio pulsars or the recording of an image of the shadow of a event horizon. The talk puts these efforts in context with other tests of general relativity and its alternatives. I will also compare the approaches in the Galactic centre, while concentrating in particular on the prospects of using pulsars as probes, also in combination with event horizon imaging.

Quantum information theory has taught us that quantum theory is just one possible probabilistic theory among many others. In the talk, I will argue that this "bird's-eye" perspective does not only allow us to derive the quantum formalism from simple physical principles, but also reveals surprising connections between the structures of spacetime and probability which can be phrased as mathematical theorems about information-theoretic scenarios.