Exact Results in Quantum Theory

In this talk I will show the various appearances of matrix integrals in physics, from chaotic quantum systems to classical and quantum 1-D integrable systems, from 2-D CFT to 4-D SUSY theories, from 0-D gauge theories to 3-D topological QFT. Moreover, I will also discuss the topological recursion, an algorithm compute all order asymptotics of certain class of matrix integrals integrals and many other systems.