Some questions on the Brownian Map motivated by its higher-genus analogues | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Some questions on the Brownian Map motivated by its higher-genus analogues

By Guillaume Chapuy

Appears in collection : Random Geometry / Géométrie aléatoire

Several operations of combinatorial surgery can be used to relate maps of a given genus g to maps of genus g' is smaller than g. One of them is the Tutte/Lehman-Walsh decomposition, but more advanced constructions exist in the combinatorial toolbox, based on the Marcus-Schaeffer/ Miermont or the trisection bijections. At the asymptotic level, these constructions lead to surprising relations between the enumeration of maps of genus g, and the genus 0 Brownian map. I will talk about some fascinating identities and (open) problems resulting from these connections, related to Voronoi diagrams, 'W-functionals', and properties of the ISE measure. Although the motivation comes from 'higher genus', these questions deal with the usual Brownian map as everyone likes it. This is not very new material, and a (mostly French) part of the audience may have heard these stories one million times. But still I hope it will be interesting to advertise them here. In particular, I do not know if recent 'Liouville-based' approaches have anything to say about all this.

Information about the video

Date of recording 20/01/2022
Date of publication 04/02/2022
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.19884603
Cite this video Chapuy, Guillaume (20/01/2022). Some questions on the Brownian Map motivated by its higher-genus analogues. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19884603
URL https://dx.doi.org/10.24350/CIRM.V.19884603

Domain(s)

Bibliography

CHAPUY, Guillaume. The structure of unicellular maps, and a connection between maps of positive genus and planar labelled trees. Probability Theory and Related Fields, 2010, vol. 147, no 3, p. 415-447. - http://dx.doi.org/10.1007/s00440-009-0211-0
CHAPUY, Guillaume. On tessellations of random maps and the $$ t_g $$ tg-recurrence. Probability Theory and Related Fields, 2019, vol. 174, no 1, p. 477-500. - http://dx.doi.org/10.1007/s00440-018-0865-6
ADDARIO-BERRY, Louigi, ANGEL, Omer, CHAPUY, Guillaume, et al. Voronoi tessellations in the CRT and continuum random maps of finite excess. In : Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2018. p. 933-946. - https://doi.org/10.1137/1.9781611975031.60

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2024

Give feedback