Geometric Recursion for Combinatorial Teichmüller Spaces and Applications

Explore a comprehensive lecture on Geometric Recursion for Combinatorial Teichmüller Spaces and their applications, delivered by Séverin Charbonnier from the Max Planck Institute for Mathematics. Delve into the definition of Geometric Recursion using measurable functions on combinatorial Teichmüller spaces, illustrated through a combinatorial version of the Mirzakhani-McShane identity. Examine how stronger admissibility conditions for initial Geometric Recursion data lead to Topological Recursion satisfaction for integrals over combinatorial moduli spaces, providing an alternative proof of the Witten-Kontsevich theorem. Discover a discrete version of Topological Recursion based on integral structures of combinatorial Teichmüller spaces, which reproduces Norbury's polynomials for integral points of combinatorial moduli spaces. Gain insights into additional applications of Geometric Recursion in this context, stemming from collaborative work with renowned mathematicians in the field.