From random matrix theory to topological strings, a journey into integrable systems.

par Nicolas Orantin (CAMGSD Lisbonne)

jeudi 17 janv. 2013, 11:00 → 12:00 Europe/Paris

Auditorium Vivargent (Annecy-le-Vieux)

Random matrix theory has recently raised a lot of interest both in mathematics and physics. It represents one of the few solvable models, said to be integrable, which at the same time can be explicitly solved and has many applications ranging from biology to high-energy physics. This makes it not only a formidable toy model but also an important tool for studying modern complex systems as well as dualities in high-energy physics. In particular, it was recently understood that, in some regime, a large class of matrix models can be solved by a universal inductive method called topological recursion. In this elementary talk, I will review some of the main applications of this new method in problems such as statistical physics on a random lattice, topological string theories, bio-physics or integrable systems in a larger sense. I will show how combinatorics allows very often to fill the gap between a solvable system and its solution.