Kirill Krasnov, Penn State

krasnov@phys.psu.edu

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.

Sun Feb 8 20:46:09 EST 1998