Quantum gravity subprogram at the Isaac Newton Institute

Jorma Louko, University of Nottingham jorma.louko-at-nottingham.ac.uk

The Isaac Newton Institute programme ``Global Problems in Mathematical Relativity'', which spanned close to 5 months in the autumn of 2005, contained in October-November a four-week subprogramme on quantum gravity, organized by Abhay Ashtekar and Piotr Chrusciel. While quantum issues did feature throughout the mathematical relativity programme, and especially during the black holes theme weeks in August-September, the purpose of the quantum gravity subprogramme was to focus on loop quantum gravity and related topics.

There were two formal and three informal seminars each week. The formal seminars were pedagogical, targeted at a classical relativity audience, while the informal seminars were more specialized. Questions raised at a formal seminar would typically set the agenda for the next informal seminar or two. In my perception this organization worked well in stimulating interaction between participants from different backgrounds, and the informal seminars often drew a substantial non-specialist audience. Outside the official activities there were numerous informal discussions on specific topics, and the celebrated layout of the institute building encouraged all interested to join these discussions. Several postdocs and research students from the Department of Applied Mathematics and Theoretical Physics (University of Cambridge) participated in the activities on a regular basis.

A main theme was the dynamics of loop quantum gravity, including the mathematical structure of the associated Hilbert spaces and the concomitant quantization ambiguities. Talks on these topics were presented by Jerzy Lewandowski, Alejandro Perez, Hanno Sahlmann and Thomas Thiemann. Abhay Ashtekar and Martin Bojowald gave talks on spacetime singularity avoidance in loop quantum gravity, mainly in the context of quantized cosmological models but with a view to black hole singularities. Carlo Rovelli's talk addressed the semiclassical limit of $n$-point functions in loop quantum gravity.

John Barrett reviewed spin foam models of quantum gravity in three and four dimensions. Jorma Louko addressed group averaging techniques in quantization.

Among the informal seminars, Chris Fewster gave a pedagogical introduction into algebraic quantum field theory in curved spacetime and discussed recent work on energy inequalities. Ian Moss and David Jennings talked about quantum field effects on accelerated brane worlds.

The London Mathematical Society organized an afternoon of three talks aimed at the general mathematical community. Abhay Ashtekar gave here an overview of loop quantum gravity, and Karsten Danzmann reviewed the status of gravitational wave observatories. Roger Penrose presented a new perspective on the Weyl curvature hypothesis, suggesting that the future infinity of a spacetime dominated by a positive cosmological constant could be conformally reinterpreted as the initial singularity of a new spacetime.

The subprogramme was intensive and will undoubtedly prove valuable. It was also fortuitous in overlapping with a Cambridge production of Carl Djerassi's play ``Calculus'', which dramatizes events around the Royal Society Committee that passed judgment on the Newton-Leibnitz priority dispute. A number of participants went to see the play; however, none were to my knowledge among those audience members who were invited to the stage to become, if only momentarily, members of the Royal Society.