François David: Random matrices and two dimensional quantum gravity

This course is a short introduction to random matrices and applications to two-dimensional quantum gravity. I shall review discrete formulations of two dimensional quantum gravity, planar maps, and the relations with the large N limit of random matrices (planar limit), and various methods to solve random matrix models: Coulomb gas methods, recursion (loop) equations, orthogonal polynomials, etc. The topological expansion, the double scaling limit and KPZ relations will be reviewed. Finally, the links between matrix models, topological 2D gravity and strings (the study of moduli space of surfaces) will be briefly discussed.

Main references that I shall use (the not too advanced material) is:

1. Lectures notes by Bertrand Eynard about random matrices and surfaces
   Random matrices: http://ipht.cea.fr/Docspht/articles/t01/014/public/publi.pdf
   Random matrices: arXiv:1510.04430
   
2. A book by B. Eynard (CRM Aisenstadt Chair lectures in Montreal of 2015)
   Counting Surfaces: http://www.springer.com/us/book/9783764387969
   

Additional references about the relation between matrix models, Liouville theory, CFT and 2D gravity (but I shall only deal with some very introductory and basic elements) are:

1. The review by Y. Nakayama
   Liouville Field Theory -- A decade after the revolution: arXiv:hep-th/0402009
   
2. Les Houches lectures by B. Duplantier
   Conformal Random Geometry: arXiv:math-ph/0608053