Introduction to Matrix Models - Fedor Levkovich-Masyluk (Lecture 2)

Описание: Part of LonTI lectures Autumn 2025.

Title: Introduction to matrix models

Lecturer: Dr. Fedor Levkovich-Masyluk (City U.)

Date: 27 Oct 2025

Place: LIMS

Topics to be discussed:

Models of random matrices can be viewed as zero-dimensional analogs of usual field theory. Despite decades of exploration, matrix models remain at the forefront of intensive research, motivated by a rich web of connections to string theory, quantum gravity, integrability, Yang-Mills theory, combinatorics, geometry and representation theory. These lectures will present a pedagogical introduction to the subject.

​Lecture 1. Motivation and basic definitions. Hermitian matrix models: Feynman rules, ribbon graphs, large N genus expansion.
Lecture 2. Reduction to eigenvalues. Large N limit, Coulomb gas approach, saddle point equations.
Lecture 3. Continuum limit of saddle point equations. Eigenvalue density and spectral curve. Examples.
Lecture 4. Orthogonal polynomials. Relation to 2d gravity and phase transitions (sketch). Outlook: loop equations, topological recursion, integrability.


See https://lonti.weebly.com/2025-26-seri... for more information.