Topological recursion, Airy structures, and its generalisations

Topological recursion has become known as a powerful recursive formalism to compute a variety of invariants in mathematics and physics. The list of applications includes matrix model correlation functions, 2d gravity amplitudes, topological string theory amplitudes, and more. Interestingly, recent study has shown that by introducing the notion of Airy structures, topological recursion can be described in terms of twisted representations of the Virasoro algebra. In this talk, I will first give an introductory overview of topological recursion as well as Airy structures. Then, I will present how one can generalise the current formalism of topological recursion, e.g. by upgrading the Virasoro algebra to the super Virasoro algebra or the q-Virasoro algebra. If time permits, I will also discuss expected applications of such generalisations. This is in part joint with Vincent Bouchard and also in part joint with Nitin Chidambaram.