Solutions of integrable hierarchies via combinatorial maps and topological recursion

20.10.2022 13:45

Solutions of some integrable hierarchies such as KdV, KP or 2-Toda can be proved to satisfy Topological Recursion, a procedure developed by Chekhov, Eynard and Orantin and which appears in various branches of mathematical physics, geometry and combinatorics. One way to tackle this result is to encode the tau-functions of the hierarchies as generating functions of combinatorial maps. Those combinatorial objects are particularly well-suited to prove that the generating functions satisfy topological recursion. I will show two instances of such combinatorial treatment of the solutions of integrable hierarchies: ciliated maps for the r-KdV hierarchy (j.w. Belliard, Eynard and Garcia-Failde), and constellations for the Orlov-Sherbin tau-functions of the 2-Toda hierarchy (j.w. Bonzom, Chapuy and Garcia-Failde).

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Physical Mathematics Seminar Series"

entrée libre