The visible universe has edges, known as event horizons. These may surround a black hole, a region of the universe speeding away faster than light or a region inaccessible from the worldline chosen by a given observer. Event horizons lie not only at the edge of what we can see, but also at the edge of our knowledge about the physical universe. Their partially understood, but still enigmatic, behavior will be the focal point of this project. Black hole horizons are governed by a beautiful set of quantum laws discovered 40 years ago by Bekenstein and Hawking. These laws indicate that they are at once the simplest and most complex objects in the physical universe. They are simple because, according to Einstein's general relativity there is nothing inside - space ends at the horizon. They are complex because the laws imply that they must carry the maximal allowable information. The coexistence of these dichotomous descriptions underlies a deep paradox whose resolution is a focal point of modern physics. It is both enticing and surprising that these universal laws and properties also apply to both cosmological and observer horizons. In this project we propose specific approaches, all based on diffeomorphism symmetry, to analyze the common universal behavior of black hole, cosmological and observer horizons. For black holes, the observational and theoretical implications of the recently discovered conformal symmetry of extreme Kerr black holes (such as GRS1915+105) will be assessed. For the observer horizon at Minkowski null infinity, implications and generalizations of the recently discovered equivalence of BMS symmetries and Weinberg’s soft-graviton theorem will be developed. To accomplish these goals, a core group of scientists, one postdoctoral fellow and four graduate students, dedicated to this problem and versatile with the requisite tools, will be assembled. The results of the project will be summarized and disseminated at a concluding workshop.