Orientable surfaces are classified by their type and number of edge components. Topological recursion is a general framework for "counting objects on surfaces" due tu B. Eynard and N. Orantin (2007).
The main example of the course will be graphs in surfaces also called combinatorial maps. For example, we will explain how to quickly compute the number of quadrangulations on a surface of gender with faces. We will discuss the analytical properties of the generating functions of combinatorial maps.
At the end of the course, we will discuss some other situations where topological recursion applies. course page
PEC: BBB connection: https://webconf.u-bordeaux.fr/b/vin-xx9-hxj