General Relativity and Quantum Gravity, at the

XIIIIth International Congress on Mathematical Physics

Abhay Ashtekar, Penn State
The International Association of Mathematical Physics hosts a tri-annual congress to review the recent developments in the field. The 13th congress in this series took place at Imperial College, London, from 17th to 22nd July 2000. While quantum field theory and statistical mechanics have been the major components of these conferences, general relativity and quantum gravity have been well represented at least since the early eighties and, over the years, interest in sessions in our field has steadily increased. At the London conference, Gerhard Huisken gave a plenary lecture on Energy inequalities for isolated gravitating systems in which he presented the recent proofs of the Penrose inequality (in the case of a maximal slice). Roughly, the inequality says that the total mass should be greater than the square-root of the area of the apparent horizon and thus strengthens the positive mass theorems proved in the late seventies. It was a lucid presentation of deep results, much appreciated also by participants outside general relativity. In addition, there were two invited sessions. The first talk in the classical gravity session was given by Lars Andersson in which he summarized recent results on approach to singularities in general relativity coupled to a scalar field. In a well-defined sense, the scenario put forward by Belinskii, Khalatnikov and Lifshitz (BKL) in the early sixties can now be rigorously justified in this case. In the second talk, Piotr Bizon first gave a succinct and exceptionally clear review of the ``critical phenomena'' first discovered by Choptuik and then summarized recent work which shows that many of the key features arise already in simpler dynamical systems and are thus not unique to Einstein's equations. In the invited session on quantum gravity, John Barrett provided an overview of the state sum models, emphasizing the use of combinatorial methods and bringing out relation between diverse ideas that have come from mathematics and physics. John Baez summarized the recent results on black hole entropy based on the quantum geometry of isolated, non-rotating horizons. Although the subject involves rather technical ideas from diverse fields, he demonstrated his exceptional skill at zeroing-in on the essentials and making everything fit together naturally. In addition, there were two contributed sessions which were also well attended. The classical gravity session emphasized recent mathematical results on black holes. In the quantum gravity session, while the first two talks were on ``standard'' mathematical physics topics on the interface of general relativity and quantum physics, the last two were on the interface between quantum gravity, philosophy of science and quantum computing. Unfortunately, this attempt to broaden and reach out to neighboring field did not succeed; there was a marked difference in the level of precision and emphasis between the two sets of talks. Finally, there was a poster session which contained a number of exceptionally interesting presentations. In addition to these sessions which Peter Aichelburg and I organized, there were other activities related to gravitational physics. In particular, there were two round-table discussions. The first was on Quantum theory of space-time, organized by Chris Isham and chaired by John Klauder, in which John Barrett, Fay Dowker, Renate Loll and Andre Lukas presented very interesting but strikingly different perspectives. In the second round table, entitled Entropy and information: Classical & quantum, chaired by Joel Lebowitz, John Baez spoke about entropy in the context of black hole thermodynamics. Finally, the congress had a Young Researchers Symposium, with a number of plenary lectures intended to introduce graduate students and post-docs to the exciting recent developments in various areas of mathematical physics ranging from biophysics to quantum chaos. I represented gravitational physics and spoke on the Interface of general relativity, quantum mechanics and statistical physics. All three sessions drew a large number of participants also from other sub-fields of mathematical physics.