The last few years have seen the techniques of loop quantum gravity applied to a growing number of problems. They have been used to compute the entropy of various sorts of black holes, including those with non-minimally coupled matter, for which the entropy is not proportional to the area. Perhaps more importantly, loop quantum gravity has given us a clear picture of the quantum geometry of the horizon, which accounts for the microscopic degrees of freedom responsible for black hole entropy. There are tantalizing connections to Hod's work on quasinormal modes, but these remain mysterious. Combined with traditional ideas on quantum cosmology, loop quantum gravity has led to new insights on how quantization can eliminate the singular behavior of geometry at the big bang - perhaps with testable consequences. Predictions of Lorentz symmetry violation may also be experimentally testable, but these remain controversial. Finally, the dynamics of the theory is being studied with the help of spin foam models. My talk surveys all this work with a bare minimum of technical details.
Click on these to see the slides:
Here are the papers by Lewandowski, Domagala and Meissner which corrected a mistake Ashtekar, Corichi, Krasnov and myself made in the computation of black hole entropy:
You can also see photos of the conference where I gave this talk!
I also wrote an issue of This Week's Finds about this conference: week207.