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YouTube

Random Matrix Models, 2D Quantum Gravity, and Holography - Part 1 - Clifford Johnson

Institute for Advanced Study via YouTube

Overview

Explore a pedagogical lecture on the Gaussian Unitary Ensemble, a fundamental random matrix model, and its connection to 2D quantum gravity and holography. Delve into the double scaling limit, the Airy model, and non-perturbative information computed using Fredholm determinants. Discover a previously unnoticed discrete spectrum and its holographic implications. Examine topics such as refinement diagrams, topological expansion, Dyson gas, semicircle law, orthogonal polynomial technology, and random surfaces. Gain insights into the development of techniques, the large N limit, and the connection between random matrices and toy field theory.

Syllabus

Introduction
Overview
Motivation
Refinement Diagrams
Brezza ethel
Wigner
Vignerion
Random matrices
Toy field theory
Topological expansion
Dual diagrams
Mandemon determinant
Dyson gas
Large n
Potential by potential
Semicircle law
Developing techniques
Orthogonal polynomial technology
Why should we take this as the definition
A different story from the 1990s
We made some progress
We should finish the story
Random surfaces
Nonprojective physics
Orthogonal polynomials
Harmonic oscillator
Polynomials
Even Potentials

Taught by

Institute for Advanced Study

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