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A powerful differential equation for Ising-decorated maps in arbitrary genus
Multi angle
Authors : Carrance, Ariane (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 00/00/0000 Conference Date : 24/02/2025 Subseries : Research talks arXiv category : Combinatorics ; Mathematical Physics Mathematical Area(s) : Combinatorics Format : MP4 (.mp4) - HD Video Time : 00:47:14 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-02-24_Carrance.mp4 
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Information on the Event
Event Title : Enumerative combinatorics and effective aspects of differential equations Thematic Month Week 5 / Combinatoire énumérative et aspects effectifs des équations différentielles Mois thématique semaine 5Event Organizers : Dousse, Jehanne ; Melczer, Stephen ; Mezzarobba, Marc ; Rond, Guillaume Dates : 24/02/2025 - 28/02/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3271.html
Citation Data
DOI : 10.24350/CIRM.V.20315403Cite this video as: 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 |
See Also
- [Multi angle] Summation theory of difference rings and applications - lecture 3 / Author of the conference Schneider, Carsten.
- [Multi angle] Summation theory of difference rings and applications - lecture 2 / Author of the conference Schneider, Carsten.
- [Multi angle] Lattice paths with flexible boundaries: patterns, automata, and counting / Author of the conference Selkirk, Sarah.
- [Multi angle] Summation theory of difference rings and applications - lecture 1 / Author of the conference Schneider, Carsten.
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
Imagette Video
