Week 26.10.2025 – 01.11.2025

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.

TBA