Enumeration of maps via integrability

Valentin Bonzom (U Paris-Nord)

Apr 26. 2023, 11:45 — 12:30

People have been counting maps since the beginning of the universe since the pioneering work of Tutte in the 60s. Several methods have been developed, based on functional equations and bijective schemes. However, the most efficient recurrence formulas to enumerate maps by size and genus come from an alternative approach known in physics as integrability. Generating functions of maps indeed satisfy an infinite set of PDEs called the KP hierarchy and Goulden and Jackson in 08 have shown how to put it to good use and extract recurrence formulas for triangulations by size and genus. Carrell and Chapuy, and Kazarian and Zograf later obtained similar formulas for general maps and bipartite maps. Recently, together with Chapuy and Dolega, we found analogues of those recurrence formulas for non-oriented maps. I will explain how to derive the KP hierarchy from Tutte's equation, then how to derive the recurrence formulas, and finally why it is interesting to look at the non-oriented case.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Non-commutative Geometry meets Topological Recursion (Workshop)
Gaëtan Borot (HU Berlin)
Elba Garcia Failde (Sorbonne U, Paris)
Harald Grosse (U of Vienna)
Masoud Khalkhali (Western U, Ontario)
Hannah Markwig (U Tübingen)
Raimar Wulkenhaar (U Münster)