Venue: Chern Lecture Hall
Class Timings: Tuesday from 1:45 PM - 3:15 PM
First Meeting: 11 Aug 2026
Motivation for random matrix models---nuclear spectra, large N gauge theories, statistical mechanics, random surfaces, string theory, quantum Chaos
Examples of matrix integrals: Orthogonal, Hermitian and Symplectic ensembles. Computations in Gaussian and non-Gaussian Hermitian.models; ‘tHooft’s planar expansion; Large N saddle point evaluation and related puzzles.
Dynamically triangulated random surfaces, 2D quantum gravity and non-critical string theory. Double scaled matrix integrals.
Matrix Quantum Mechanics--- free fermions, relation to string theory; the first example of “holography”; hint of spacetime lattice structure.
Level statistics; spectral form factor; thermalization; Bohigas-Giannoni-Schmit conjecture
Jackiw-Teitelboim gravity and matrix models; “gravity as a random Ensemble”
Large N phase transitions (Gross-Witten-Wadia). matrix models from gauge theory path integrals (Polyakov loops). Deconfinement phase Transition
Multi-matrix models; exact results; applications to solitons and D branes; target space entanglement entropy.
- Familiarity with old and new techniques of matrix models.
- Ability to apply matrix models to problems of statistical mechanics and string theory.
- Development of insight into thermalization and quantum chaos using random matrices as a paradigm.
- Teacher: Gautam Mandal