A powerful differential equation for Ising-decorated maps in arbitrary genus | Vidéo | Carmin.tv

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A powerful differential equation for Ising-decorated maps in arbitrary genus

By Ariane Carrance

Appears in collection : Enumerative combinatorics and effective aspects of differential equations Thematic Month Week 5 / Combinatoire énumérative et aspects effectifs des équations différentielles Mois thématique semaine 5

Maps decorated by the Ising model are a remarkable instance of a model of non-uniform maps with very nice enumerative properties. In this talk, I will first explain how one can obtain a differential equation for the generating function of Ising-decorated cubic maps in arbitrary genus, related to the Kadomtsev--Petviashvili (KP) hierarchy. In particular, this leads to an efficient algorithm to enumerate Ising cubic maps in high genus. I will also present and compare implementations of this algorithm in Maple and SageMath. This is based on a joint work with Mireille Bousquet-Mélou and Baptiste Louf.

Information about the video

Date of recording 24/02/2025
Date of publication 13/03/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20315403
Cite this video Carrance, Ariane (24/02/2025). A powerful differential equation for Ising-decorated maps in arbitrary genus. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20315403
URL https://dx.doi.org/10.24350/CIRM.V.20315403

Domain(s)

Bibliography

BOUSQUET-MELOU, Mireille, CARRANCE, Ariane, et LOUF, Baptiste. The Ising model on cubic maps: arbitrary genus (preliminary version). 2025. - https://carrance.perso.math.cnrs.fr/pdf/IsingCubic.pdf

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