Quantum Geometry In Action: Big Bang and Black Holes

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Over the last three years, a number of fundamental issues in quantum gravity were addressed in the framework of quantum geometry, discussed extensively by John Baez in this conference. In particular, these include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes cosmological horizons, and a natural resolution of the big-bang singularity. The goal of this article is to communicate these advances in general terms.
18 pages, 2 figures; to appear in the proceedings of the conference "Graphs and Patterns in Mathematics and Theoretical Physics" celebrating 60th birthday of Dennis Sullivan, held at Stony Brook in June 2001

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