String Theory Journal Club

A few years ago, in the context of matrix models a powerful recursion relation was introduced to compute asymptotic expansion of random matrix integrals. Then it was extended axiomatically to other integrable systems, which turn out to yield various geometric invariants, like Gromov-Witten invariants and knot polynomials. This method has given many new results in enumerative geometry, random surfaces, quantum curves and many more. Very recently the topological recursion was found to be a particular case of a deformation quantization procedure, and the notion of quantum Airy structures has been introduced. So, in this presentation I will talk about how an Airy structure is defined as a Lagrangian obeying certain commutation relations. Also, I will show how the recursion relation arises as a solution to a family of Schroedinger equations and discuss some symmetries and properties of the Airy structures.