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Global Problems in Mathematical Relativity

8th August 2005 to 23rd December 2005

Organisers: Prof PT Chrusciel (Tours), Prof H Friedrich (Golm), Prof P Tod (Oxford)

Programme theme

General relativity has been around for a long time as a physical theory and an object of mathematical study. It was a subject of intense interest in the 1960’s and 1970’s when advances included the discovery of the Kerr solution, the study of black holes and singularity theorems and the introduction of asymptopia as a framework for studying asymptotic properties, including gravitational radiation. At the same time there were many mathematical problems which resisted mathematical analysis. In recent years there have been significant advances in our understanding of the topological, geometrical and PDE aspects of general relativity and progress is once again becoming rapid. New results are being obtained, and older results re-proved in greater generality.

This programme will be structured around four themes:

  1. Elliptic aspects of general relativity: new methods of solving the constraint equations, developments from the solution of the Riemannian Penrose inequality, the study of static and stationary solutions including black holes.
  2. Hyperbolic aspects of general relativity: local and global evolution problems, Cosmic Censorship conjecture, and the nature of singularities.
  3. Global Lorentzian geometry: global techniques and asymptotic structure, splitting theorems and extendibility.
  4. New methods in general relativity: inverse scattering and boundary-value problems, scattering theory for linear field equations, new methods from Riemannian geometry.

While all four themes will be worked on throughout the programme, and indeed it would be neither possible nor desirable to keep them rigidly separate, there will be periods of more focus on each. The overall emphasis will be on mathematical results and global properties of solutions of the Einstein equations, but it is worth noting that there is a clear motivation from physics to deepen our understanding of general relativity, at a time when gravitational wave detectors around the world have started collecting data.

Thematic Diary

8 - 21 August
Hyperbolic problems (organised by I Rodnianski and H Friedrich)
15 - 21 August
Numerical relativity (organised by L Lehner and H Friedrich, including a Satellite Meeting in Southampton organised by C Gundlach and H Friedrich)
21 - 27 August
Euroconference - Global general relativity
30 August - 11 September
Black holes (organised by R Wald and PT Chrusciel)
12 - 25 September
Dynamical systems (organised by A Rendall and H Ringström and P Tod)
26 September - 9 October
Riemannian geometry and GR (organised by M Anderson and PT Chrusciel)
10 - 16 October
Lorentzian geometry (organised by A Zeghib and PT Chrusciel)
17 - 23 October
Global techniques (organised by G Galloway and PT Chrusciel)
17 October - 13 November
Quantum aspects (organised by A Ashtekar and PT Chrusciel)
14 - 20 November
Asymptotic structure
21 - 27 November
Inverse scattering and integrability (organised by G Neugebauer and P Tod)
28 November - 11 December
Static/stationary solutions (organised by R Beig and PT Chrusciel)
5 - 23 December
Constraint equations (organised by J Isenberg and PT Chrusciel)
12 - 16 December
Einstein Constraint Equations (organised by J Isenberg and PT Chrusciel)

This structure is intended to indicate at which period somebody who is interested in a particular subject is more likely to meet people interested in the same subject.

Final Scientific Report: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons