Geometry and gravity

Programme theme

The past successes of Einstein's classical General Relativity have raised deep and difficult problems, involving global differential geometry and the theory of hyperbolic differential equations, whose solution would throw light on the evolution of black holes and the nature of space-time singularities. The solution of many of these physical problems requires the development of a quantum theory of gravity. This would inevitably involve ideas from differential geometry and related branches of mathematics, and it also poses fundamental questions concerning the scope and general formalism of quantum theory. The programme will bring together mathematicians and theoretical physicists working on both classical and quantum aspects of these problems to clarify the mathematical and physical questions that need addressing, and to contribute to their resolution.

Structure of the Programme

The programme falls into four overlapping sub-programmes. Work on these sub-programmes will be most active during the following periods. Mathematical Foundations of Gravity ( January-March), Quantum Cosmology (April-May), Black Hole Physics (May-June) and Twistor Theory (April May-June). The following lecture series and meetings have been arranged:

Non-Linear Equations, Geometry and Gravity

A series of 10 Lectures by S T Yau (Harvard) at 11.30-12.30 and 2.30-3.30 on Tue 4, Wed 5, Thu 6, Fri 7 and Mon 10 January.

Quantized Calculus and Applications

A series of 16 lectures by Alain Connes (College de France) at 10.30-11.20 and 11.40-12.30 on Thu 13, Tue 18, Thu 20, Tue 25 and Thu 27 January and Tue 1, Thu 3 and Tue 8 February.

Classical and Quantum Gravity: A Survey Conference.

To be held from Mon 28 to Thu 31 March. Contributions will include:

• JB Hartle Quantum Mechanics and Gravitation;
• J Halliwell Information Theory and Gravity;
• G Horowitz The Impact of Superstring Theory on General Relativity;
• J Madore Non-Commutative Differential Geometry;
• R Penrose Twistor Theory: Aims and Achievements;
• K Kuchar Canonical General Relativity and The Problem of Time;
• T Damour Theoretical Implications of Experiments on Gravity;
• SW Hawking Euclidean Quantum Gravity;
• JM Stewart What can computers tell us about General Relativity;
• GW Gibbons Solitons and Gravity;
• CJS Clarke Lorentz Geometry:Causality and Singularities;
• L Smolin The Ashtekar Programme;
• B Kay Quantum Field Theory in a Curved Spacetime: Future Directions;
• CJ Isham Quantum Spacetime Structure

The Nature of Space and Time.

A series of 6 public lectures at 5 pm on Mon 25, Wed 27 April and Fri 29 and Mon 2, Wed 4 and Fri 6 May given alternately by Stephen Hawking and Roger Penrose followed by a debate between the two lecturers on Mon 9 May. [ Venue to be announced. ]

Classical and Quantum Gravity Saturday Meeting.

A one-day meeting on Sat 7 May with talks by members of the editorial board of Classical and Quantum Gravity and others.

Geometry of Constrained Dynamical Systems.

A three-day workshop funded by the EC and organised by John Charap on Mon 20 to Wed 22 June.

Participation

The following are expected to participate in the programme for the periods indicated:

• Aichelburg, P 15 Feb - 6 Mar Kodama, H 1 Mar - 30 Jun
• Anderson, A 1 Jan - 30 Jun Kuchar, K 1 Apr - 31 May
• Ashtekar, A 15 May - 30 Jun Laflamme, R 1 Apr - 31 May
• Bailey, T 1 Apr - 30 Jun Lebrun, C 1 May - 30 Jun
• Carlip, S 1 Jan - 31 Mar Madore, J 1 Feb - 31 Mar
• Carter, B 1 Mar - 30 Apr Mason, L 1 Apr - 30 Jun
• Connes, A 1 Jan - 31 Mar Page, D 1 Apr - 30 Jun
• de Alwis, S 15 May - 30 Jun Paz, J 1 Apr - 31 May
• Dowker, F 1 Apr - 31 May Penrose, R 24 Apr - 30 Jun
• Dubois-Violette, M 1 Mar - 15 Mar Preskill, J 1 Jun - 30 Jun
• Eastwood, M 1 Apr - 30 Jun Rovelli, C 1 Jan - 28 Feb
• Gell-Mann, M 21 Mar - 7 Apr Schwarz, A 23 Jun - 30 Jun
• Gibbons, G 1 Jan - 30 Jun Singer, I 15 Apr - 7 May
• Halliwell, J 1 Apr - 31 May Singer, M 1 May - 30 Jun
• Harms, B 1 Jan - 30 Jun Smolin, L 1 Apr - 31 May
• Hartle, J 1 Jan - 30 Jun Spence, B 24 Jan - 29 Jan
• Harvey, J 1 Jun - 30 Jun Strominger, A 5 Jun - 25 Jun
• Hawking, S 1 Jan - 30 Jun Susskind, L 1 Jun - 30 Jun
• Hoppe, J 1 Jan - 31 Mar Tod, P 1 Apr - 24 Apr,
• Horowitz, G 1 Jan - 30 Jun Ward, R 1 Apr - 30 Jun
• Hu, B 27 Mar - 15 Apr, Woodhouse, N 1 May - 30 Jun
• Isham, C 1 Jan - 30 Jun Yau, S 1 Jan - 31 Jan,
• Klimcik, C 1 Jan - 22 Jan