Geometric recursion and recursion for volumes of moduli spaces

Gaetan Borot

I will present the formalism of geometric recursion (GR), developed with Andersen and Orantin. Let B be the category of bordered surfaces with morphisms given by isotopy classes of diffeomorphisms. Given a functor from B to another category V together with some extra data, the goal of GR is to construct functorial assignments valued in E (which can roughly be thought as a twisted field theory), exploiting the idea of glueing. This will be illustrated with E(S) = Functions on Teich(S), and the GR functions are designed such that their integration over the moduli space against the Weil-Petersson volume form satisfy a topological recursion. I will give a few examples of applications. This is based on joint works with Andersen, Orantin, Charbonnier, Delecroix, Giacchetto, Lewanski and Wheeler.

http://scgp.stonybrook.edu/video_portal/video.php?id=4117

Simons- Workshop: String field theory, BV quantization, and moduli spaces