Global problems in Mathematical Relativity

at the Isaac Newton Institute

Jim Isenberg, University of Oregon
Appropriately coinciding with last year's centenary of Einstein's great papers, the Isaac Newton Institute in Cambridge, England, sponsored and hosted during 2005 a nearly 5 month long programme on "Global Problems in Mathematical Relativity". The programme (organized by Piotr Chrusciel, Helmut Friedrich, and Paul Tod) was remarkably rich, extensive, and varied. Included were weeks of concentration on each of the following topics:

-the analysis of hyperbolic PDEs, including Einstein's equations
-numerical relativity
-black holes
-Einstein's theory as a dynamical system
-applications of Riemannian geometry in general relativity
-applications of Lorentzian geometry in general relativity
-global analysis and global techniques
-quantum aspects of gravity
-asymptotic structures in general relativistic spacetimes
-the application of inverse scattering techniques to the studies of solutions of Einstein's equations
-static and stationary solutions
-the Einstein constraint equations and their solutions

Each of these concentration periods attracted researchers from all over the world. In addition to the 7 mathematical relativists plus 2 graduate students who were there for the entire programme from early August until the end of December, there were roughly 10 to 15 shorter term visitors during any given time. With a light schedule of 3 or 4 talks per week, the emphasis was on concentrated collaborations among the participants. It was not unusual to see intense black board sessions occurring at all hours from 7 in the morning until well past midnight. By last count, at least 26 papers submitted for publication have resulted from collaborations carried out during the programme.

In addition to the weekly schedule of talks included in the programme, there were 4 special conferences. One of them was held as a satellite meeting at Southampton University. It focussed on numerical relativity, and reported on some of the breakthroughs for binary black hole simulations that have happened just this past year. The other special conferences were held at the Newton Institute. The first of these, the week long Euroconference on "Global General Relativity", included talks on a very wide range of topics, from recent developments on quasilocal mass to the latest observational data pertaining to astrophysical black holes, and from numerical simulations of classical solutions to recently developed ideas on quantum field theory in curved spacetimes. This conference was very popular, attracting over 100 participants. Equally popular was the one day "Spitalfields Day" (co-sponsored by the London Mathematical Society), which consisted of three lectures on the general theme of "Einstein and Beyond". These less technical lectures, delivered by Abhay Ashtekar, Roger Penrose, and Karsten Danzmann, attracted standing-room-only audiences for discussions of gravitational radiation detection, quantum gravity, and the nature of the universe at late times. The five month long Newton Institute programme was capped by a week long Euroconference in December which focussed on studies of the Einstein constraint equations and on a number of related mathematical and physical themes. This conference particularly highlighted the very important symbiotic relationship between geometrical analysis and mathematical relativity.

In addition to publicizing some of the particular recent triumphs which have occurred in mathematical relativity (including gains in understanding the nature of gravitational fields near cosmological and black hole singularities, as well as the rapid development of powerful new techniques for studying the stability of black hole spacetimes), and in addition to providing a perfect environment for the development of collaborations among workers whose home bases are widely scattered around the globe, the Newton Institute programme served as an important notice to the community of mathematicians and physicists that mathematical relativity is a very healthy discipline, which has had a great impact on both physics and mathematics, and will continue to do so. As the programme broke up just before the end of the Einstein centenary year of 2005, the participants all hoped to soon have another opportunity to collaborate and to share ideas in such an ideal setting.

Jorge Pullin 2006-02-28