2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56991Over 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 2001Mathematical PhysicsGeneral Relativity and Quantum Cosmologytext