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2D Gravity and Non-Perturbative Effects: Diffusion Equation,
Continuum Limit and Universality in 2D Quantum Gravity; O. Alvarez,
et al. On Triangles and Squares; C. Bachas. Non-Perturbative
Effects in 2D Gravity and Matrix Modles; F. David. Integrable
Models of 2D Quantum Gravity; P. Di Francesco, et al. Topological
Strings and Loop Equations; R. Dijkgraaf, et al. The Two Matrix
Model; M.R. Douglas. Action Principle and Large Order Behavior of
Non-Perturbative Gravity; P. Ginsparg, et al. D = 1 Strings and
String Field Theory: Matrix Models, String Field Theory and
Topology; T. Banks. Multipoint Correlation Functions in
One-Dimensional String Theory; D. Boulativ. The Penner Model and D
= 1 String Theory J. Distler, et al. Non-Perturbative String
Theory; D.J. Gross. Bosonic Strings and String Field Theories in
One-Dimensional Target Space; V. Kazakov. Liouville Theory andD 1:
Random Surfaces in Dimensions Larger than One; J. Ambjorn. On Gauge
Invariances in Stochastic Quantization; L. Baulieu. The Quantum
Group Structure of Quantum Gravity in Two Dimensions; J.L. Gervais.
Notes on Quantum Liouville Theory and Quantum Gravity; N. Seiberg.
8 additional articles. Index.
The Cargese Workshop Random Surfaces and Quantum Gravity was held
from May 27 to June 2, 1990. Little was known about string theory
in the non-perturbative regime before Oetober 1989 when
non-perturbative equations for the string partition functions were
found by using methods based on the random triangulations of
surfaees. This set of methods pro vides a deseription of
non-eritical string theory or equivalently of the coupling of
matter fields to quantum gravity in two dimensions. The Cargese
meeting was very successful in that it provided the first
opportunity to gather most of the active workers in the field for a
fuH week of lectures and extensive informal discussions about these
exeiting new developments. The main results were reviewed, recent
advances were explained, new results and conjectures (which appear
for the first time in these proceedings) were presented and
discussed. Among the most important topics discussed at the
workshop were: The relation of KdV theory to loop equations and the
Virasoro algebra, new results in Liouville field theory, effective
(1 + 1) dimensional theory for 2 - D quantum gravity coupled to c =
1 matter and its fermionization, proposal for a new geometrical
interpretation of the string equation and possible definition of
quantum Riemann surfaces, discussion of the string equation for the
multi-matrix models, links with topological field theories of
gravity, issues in using target space supersymmetry to define good
theories, definition of the partition function via analytic
continuation, new models of random surfaces
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