Some Generalizations of Mirzakhani's Recursion and Masur–Veech Volumes via Topological Recursions

Via Andersen–Borot–Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur–Veech polynomials was uncovered. The purpose of this article is to explore generalizations of Mirzakhani's recursion based on physical two-dimensional gravity models related to the Jackiw–Teitelboim gravity and to provide an introduction to various realizations of topological recursion. For generalized Mirzakhani's recursions involving a Masur–Veech type twist, we derive Virasoro constraints and cut-and-join equations, and also show some computations of generalized volumes for the physical two-dimensional gravity models.