相关论文: 2D Quantum Gravity, Matrix Models and Graph Combin…

Lecture notes prepared for the Les Houches school "Quantum Geometry: Mathematical Methods for Gravity, Gauge Theories and Non-Perturbative Physics" that took place during the summer 2024. We cover the techniques to perform the exact…

These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date. 0. Canned…

This report summarizes some of the material that was presented by the author during the 2015 Les Houches Summerschool on "Random Matrices and Stochastic Processes". In these Lectures, various applications of Random Matrix Theory in modern…

I review some recent works on the Hermitean one-matrix and d-dimensional gauge-invariant matrix models. Special attention is paid to solving the models at large-N by the loop equations. For the one-matrix model the main result concerns…

Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).

You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free…

These notes are based on lectures presented at the 2001 Les Houches Summerschool ``Unity from Duality: Gravity, Gauge Theory and Strings''

Brief lecture notes for a course about random matrices given at the University of Cambridge.

Notes from 11 October 2004 lecture presented at the Joint Institute for Nuclear Astrophysics R-Matrix School at Notre Dame University.

Some approaches to $2d$ gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different…

Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the…

We review the recent exact solution of a matrix model which interpolates between flat and random lattices. The importance of the results is twofold: Firstly, we have developed a new large N technique capable of treating a class of matrix…

These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications", held in July 2024 at Les Houches in France. They present the basic definitions and mathematical…

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

A short lecture given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009.

Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory".

Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…

This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).

In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…