Topological Recursion: A Recursive Way of Counting Surfaces

Explore the fascinating world of surface enumeration in this 55-minute lecture by Bertrand Eynard from the Institut de physique théorique, CEA Saclay. Delve into the importance of counting various types of surfaces in combinatorics of maps, enumerative geometry, string theory, and statistical physics. Discover how the "topological recursion" provides a universal method for enumerating surfaces of higher genus and with more boundaries, starting from the enumeration of discs and cylinders. Learn about the beautiful mathematical properties of this recursion and its connections to other areas of mathematics and physics, including integrable systems and random matrices. Gain insights into the significance of surface enumeration problems, such as Mirzakhani's recursion for hyperbolic surfaces, and understand how topological recursion serves as a powerful tool in bridging different mathematical and physical concepts.