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.