The purpose of the research school 'Coulomb Gas, Integrability and Painlevé Equations' is to introduce a new generation of researchers to the various aspects of integrability that emerge in random systems. The participants will learn about modern methods from several branches of contemporary Mathematics and Mathematical Physics, together with their fruitful applications.

The topic includes:
a) Determinantal point processes that arise in a wide range of problems in asymptotic combinatorics, representation theory and mathematical physics.
b) Toepliz determinants that appear in many statistical mechanics models.
c) Operator theory of beta ensembles that describes random matrix theory as an asymptotic spectral theory.
d) Connections between random matrices and number theory.
e) Integrable systems with random initial data.

The school will bring together PhD. students, Postdoctoral researchers, and faculty members, to focus on the new developments in these fertile lines of research.