Algebra/Topology Seminar

Speaker: Jørgen Ellegaard Andersen

Title: Geometric Recursion

Abstract: Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identities, certain mapping class group invariant functions and closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections. We will then discuss how averaged of volume forms constructed by geometric recursion satisfies topological recursion and thereby argue that Geometric Recursion can in these cases also be seen as a tool for proving that various topological quantities satisfies Topological Recursion.