Kirill Krasnov, Penn State
At the Baltimore meeting of the American Mathematical Society, there was a special session on quantum gravity and low-dimensional topology. The session was organized by J. Baez (University of California, Riverside) and S. Sawin (Fairfield University). The session lasted two days: January 7 and the morning of January 8. This and the other sessions of the AMS meeting took place at Baltimore Convention Center, located in the tourist attraction center of Baltimore called Inner Harbor.
On the first day, Louis H. Kauffman spoke about ``Discrete Physics'', Abhay Ashtekar on ``Quantum Theory of Riemannian Geometry'' and Jim Stasheff, gave ``A Survey of Cohomological Physics''. Roger Picken spoke about ``Kontsevich Integrals, Knot Invariants and TQFT'', Lee Smolin discussed how to get ``Perturbative Strings from Perturbations of Evolving Spin Networks'' Alexander A. Voronov presented ``The Homotopy Algebraic Structure of Topological Gravity'' and John W. Barrett talked on ``Quantum Gravity: Path Integrals and state Sums''. Louis Crane presented ``A State Sum Formulation for Quantum General Relativity'' and Seth A. Major discussed his work with Roumen Borissov on ``Q-Deformed Loop Representation for Quantum Gravity: Structure and Open Problems''. Kirill V. Krasnov discussed ``Spin Networks, Chern-Simons Theory and Black Holes'' and Donald M. Marolf presented his work with Jerzy Lewandowski ``Loop Constraints: A Habitat and their Algebra''
In the evening of that day Edward Witten delivered his Josiah Willard Gibbs Lecture on M Theory to more than a thousand mathematicians gathered at the Ballroom of the Convention Center.
The session continued in the morning of the next day with David N. Yetter talking about a ``Grist for a 4-D State-Sum Mill: Examples of Monoidal Bicategories'', Carlo Rovelli presenting ``From Loop Quantum Gravity to a Sum over Surfaces'' and Dana S. Fine discussing ``Path Integrals Linking Chern-Simons and WZW Partition Functions''. Laurel T. Langford spoke on ``2-Tangles as a Free Braided Monoidal 2-Category with Duals'' and Fotini G. Markopoulou discussed ``Quantum Space and Causality'', Takashi Kimura presented his work with Alexandre Kabanov on ``Tautological Classes and Cohomological Field Theories in Genus One'' and Doug Bullock his work with Charles Frohman and Joanna Kania-Bartoszynska on ``Lattice Gauge Field Theory and Deformation Quantization''. Finally, Steven J. Carlip discussed ``Einstein Manifolds, Spacetime Foam, and the Cosmological Constant''.
The session was a very interesting mixture of mathematics and physics: talks on Topological Quantum Field Theory and Quantum Gravity usually followed each other. In fact, it was quite surprising to see the growing influence of the two fields on one another: many of the talks on the Quantum Gravity side were devoted to the application of the ideas and techniques from TQFT's to gravity and some talks given by mathematicians were on issues that used to be of interest only to physicists. Belonging to this last category were the two very exciting talks by J. Barrett and L. Crane on their new state sum formulation of quantum general relativity.
After the session was finished, some of us gathered for an informal discussion guided by J. Baez, L. Crane, C. Rovelli and L. Smolin. The discussion was devoted to some aspects of the path integral formulation of quantum gravity.