Enumeration of Maps via Integrability

Explore the fascinating world of map enumeration in this 46-minute lecture by Valentin Bonzom at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the history of map counting, from Tutte's pioneering work in the 1960s to modern approaches using integrability. Learn how generating functions of maps satisfy the KP hierarchy and how this leads to efficient recurrence formulas for enumerating maps by size and genus. Discover the work of Goulden and Jackson on triangulations, as well as contributions by Carrell, Chapuy, Kazarian, and Zograf on general and bipartite maps. Examine recent developments in non-oriented map enumeration, including Bonzom's collaborative work with Chapuy and Dolega. Gain insights into deriving the KP hierarchy from Tutte's equation, understanding recurrence formulas, and appreciating the significance of non-oriented cases in map enumeration.