English
A powerful differential equation for Ising-decorated maps in arbitrary genus
Multi angle
Auteurs : Carrance, Ariane (Auteur de la Conférence)
CIRM (Editeur )
05A15 - Exact enumeration problems, generating functions
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
CIRM (Editeur )
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Résumé :
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.
Keywords : random maps; Ising model; KP hierarchy
Codes MSC : Keywords : random maps; Ising model; KP hierarchy
05A15 - Exact enumeration problems, generating functions
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 00/00/0000 Date de captation : 24/02/2025 Sous collection : Research talks arXiv category : Combinatorics ; Mathematical Physics Domaine : Combinatorics Format : MP4 (.mp4) - HD Durée : 00:47:14 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-02-24_Carrance.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Enumerative combinatorics and effective aspects of differential equations Thematic Month Week 5 / Combinatoire énumérative et aspects effectifs des équations différentielles Mois thématique semaine 5Organisateurs de la rencontre : Dousse, Jehanne ; Melczer, Stephen ; Mezzarobba, Marc ; Rond, Guillaume Dates : 24/02/2025 - 28/02/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3271.html
Données de citation
DOI : 10.24350/CIRM.V.20315403Citer cette vidéo: Carrance, Ariane (2025). A powerful differential equation for Ising-decorated maps in arbitrary genus. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20315403 URI : http://dx.doi.org/10.24350/CIRM.V.20315403 |
Voir aussi
- [Multi angle] Summation theory of difference rings and applications - lecture 3 / Auteur de la Conférence Schneider, Carsten.
- [Multi angle] Summation theory of difference rings and applications - lecture 2 / Auteur de la Conférence Schneider, Carsten.
- [Multi angle] Lattice paths with flexible boundaries: patterns, automata, and counting / Auteur de la Conférence Selkirk, Sarah.
- [Multi angle] Summation theory of difference rings and applications - lecture 1 / Auteur de la Conférence Schneider, Carsten.
Bibliographie
- 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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