WORKSHOP
Combinatorial and hyperbolic random planar geometry
Géométrie planaire aléatoire, discrète ou hyperbolique
4 – 8 August, 2025
Organizing Committee
Comité d’organisation
Thomas Budzinski (ENS Lyon)
Nicolas Curien (Université Paris-Saclay)
The aim of this workshop is to bring together specialists in random planar geometry, primarily around the themes explored in the ERC SuperGRandMA project (Hyperbolic surfaces and large random maps). We wish to gather perspectives from different backgrounds, particularly on random hyperbolic and flat surfaces (from geometric or spectral viewpoints), as well as on random maps and trees, or on two-dimensional quantum gravity. We believe that techniques developed for studying Brownian geometry (such as peeling, Markovian exploration, and self-similar trees) can be useful in other, more geometric contexts.
L’objectif de ce workshop est de réunir des spécialistes de géométrie aléatoire planaire, principalement autour des thématiques portées par l’ERC SuperGRandMA (Hyperbolic surfaces and large random maps). Nous souhaitons croiser les points de vue issus de différents horizons, en particulier autour des surfaces hyperboliques et plates aléatoires (sous un angle géométrique ou spectral), autour des cartes et arbres aléatoires, ou encore de la gravité quantique en dimension 2. Nous sommes convaincus que les techniques développées pour l’étude de la géométrie brownienne (peeling, exploration markovienne, arbres auto-similaires…) peuvent être utiles dans d’autres contextes plus géométriques.
SPEAKERS
Timothy Budd (Radboud University) Bijective enumeration of rigid quadrangulations
Frank Ferrari (Université Libre de Bruxelles and International Solvay Institutes) Random disks of constant curvature: holography, quantum gravity, combinatorics and probabilities
Rafi Kasra (University of Toronto) What does a random surface look like?
Mathieu Mourichoux (ENS de Lyon) Constructing the Brownian sphere from a random unicycle
Armand Riera (Sorbonne Université) All you ever dreamt to know about SSMT
Joe Thomas (Durham University) Spectral gap on random hyperbolic surfaces
Yi Tian (University of Cambridge) The Canonical Geodesic Metric on Simple Conformal Loop Ensemble Carpets
Fredrik Viklund (KTH Royal Institute of Technology) Geometric structures in Hele-Shaw flows
Yilin Wang (ETH Zurich) Brownian motion on Riemann surfaces and applications to length spectra
Yuhao Xue (IHES) Non-simple systoles and embedded pants on Weil-Petersson random hyperbolic surfaces
Anton Zorich (Université Paris Cité) Translation surfaces for probabilists
SPONSOR
