Topics in Quantum Geometry of Riemann Surfaces: Two-Dimensional Quantum Gravity

Abstract

Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994

42 pages. Equation (2.6) have been corrected and explained

Cited by in corpus (29)

• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Classical geometry from the quantum Liouville theory
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Proof of Polyakov conjecture for general elliptic singularities
• Liouville theory and uniformization of four-punctured sphere
• On boundary correlators in Liouville theory on AdS${}_2$
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Liouville theory, N=2 gauge theories and accessory parameters
• Semiclassical and quantum Liouville theory on the sphere
• Classical Liouville action on the sphere with three hyperbolic singularities
• Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces
• Standard and geometric approaches to quantum Liouville theory on the pseudosphere
• Polyakov conjecture for hyperbolic singularities
• Hyperbolic string tadpole
• The tetrahedron graph in Liouville theory on the pseudosphere
• Use of Quadratic Differentials for Description of Defects and Textures in Liquid Crystals and 2+1 Gravity
• Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves I. Current correlation functions
• Quantum Liouville theory on the pseudosphere with heavy charges
• ADM approach to 2+1 dimensional gravity
• Polyakov relation for the sphere and higher genus surfaces
• Zamolodchikov relations and Liouville hierarchy in SL(2,R)_k WZNW model
• Semiclassical limit of the FZZT Liouville theory
• On real projective connections, V.I. Smirnov's approach, and black hole type solutions of the Liouville equation
• A Note on Quantum Liouville Theory via Quantum Group; an Approach to Strong Coupling Liouville Theory
• On a relation between Liouville field theory and a two component scalar field theory passing through the random walk
• Diffusion of Brownian particles and Liouville field theory
• Hyperbolic 2-spheres with conical singularities, accessory parameters and Kaehler metrics on ${\mathcal{M}}_{0,n}$
• Polyakov conjecture and 2+1 dimensional gravity coupled to particles
• Non-critical string, Liouville theory and geometric bootstrap hypothesis