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.
It has now become clear that the radio jet in the giant elliptical galaxy M87 must turn on very close to the black hole. This implies the efficient acceleration of leptons within the jet at scales much smaller than feasible by the typical dissipative events usually invoked to explain jet synchrotron emission. Here we show that the stagnation surface, the separatrix between material that falls back into the black hole and material that is accelerated outward forming the jet, is a natural site of pair formation and particle acceleration. This occurs via an inverse-Compton pair catastrophe driven by unscreened electric fields within the charge-starved region about the stagnation surface and substantially amplified by a post-gap cascade. For typical estimates of the jet properties in M87, we find excellent quantitive agreement between the predicted relativistic lepton densities and those required by recent high-frequency radio observations of M87.