ERC Consolidator Grant "SuPerGRandMa"

101087572

The goal of this ERC is to study geometric properties of random planar surfaces such as hyperbolic surfaces or random planar maps. We are also broadly interested in understanding large scale properties of random objects (random trees, random graphs...).
Two canonical models of random continuum surfaces have been introduced in the past decade, namely the Brownian sphere obtained as the scaling limit of uniform random planar triangulations, and the Liouville Quantum Gravity metric obtained formally from the exponential of the Gaussian free field on the sphere. Our objective is to broaden our understanding of random planar metrics to the case of metrics with ``holes'' or ``hubs'', and to the causal (when a time dimension is singled out) paradigm. We also plan on studying random maps in high genus and to connect to models of 2-dimensional hyperbolic geometry such as the Brook-Makover model, random pants decompositions or Weil-Petersson random surfaces.
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Members

2023-Now         Nicolas Curien         Principal investigator
2023-Now         Jean-Francois Le Gall         Senior researcher
Nov 2023- Aug 2025         Matteo d'Achille         Post-Doc         now Assistant Prof at Metz
Feb 2024-Sep 2024         Arthur Blanc-Renaudie         Post-Doc         now CNRS researcher at Rouen
Sept 2024-         William Fleurat         Post-Doc
Sept 2024-         Adrianus Twigt         PhD student
Oct 2025-         Klara Krause         PhD student

Positions available, contact us!

Activities

We list here the main activities supported by the project such as the weekly seminar, expert visits, conferences...

Weekly SuPerGRandMa seminar.

Scientific visits

Dec 2023         Alessandra Caraceni and Robin Stephenson
Dec 2023         Irina Dankovic
Jan 2024         Jonas Kahn
Mar 2024         Thomas Budzinski
July 2024         Alessandra Caraceni and Robin Stephenson
Sept 2024         Wilfrid Kendall
10-11 Sep 2024         Thomas Budzinski
16 Dec 2024         Guillaume Blanc
26 Jan- 7 Feb 2025         Serte Donderwinkel
27-28 Jan 2025         Klara Krause
12-20 Oct 2025         Itai Benjamini
10 Nov 2025         Itai Benjamini
24-28 Nov 2025         Luzie Kupffer
24-28 Nov 2025         Guillaume Blanc
1-5 Dec 2025         Eva-Maria Hainzl
12-17 Jan 2026         Amanda Priestley

Conferences supported

Jan 2024         Planar map days in Pisa SNS, Pisa
July 2024         Workshop on Self-Similar Markov trees and random geometry CIRM, Luminy
August 2024         Probability with/on random graphs Nesin village, Turkey
Jan 2025         Annual conference of the GDR branchement
Jul 2025         Workshop on Combinatorial and Hyperbolic geometry

Publications

Dec 2023         Ideal Poisson-Voronoi tessellations on hyperbolic spaces         M. D'Achille, N. Curien, N. Enriquez, R. Lyons, M. Unel
Dec 2023         Random trees with local catastrophes: the Brownian case         A. Carrance, J. Casse, N. Curien
Jan 2024         Where do (random) trees grow leaves?         A. Caraceni, N. Curien, R. Stephenson
Feb 2024         Parking on supercritical geometric Bienayme--Galton--Watson trees         L. Chen, A. Contat
Mar 2024         The distance problem on measured metric spaces         D. Aldous, G. Blanc, N. Curien
Mar 2024         Local limit of massive spanning forests on the complete graph         M. D'Achille, N. Enriquez, P. Melotti
June 2024         Geodesics in planar Poisson roads random metric         G. Blanc, N. Curien and J. Kahn
July 2024         Self-Similar Markov trees and scaling limits         J. Bertoin, N. Curien and A. Riera
Sep 2024         Scaling limit of trees with vertices of fixed degrees and heights         A. Blanc-Renaudie and E. Kammerer
Nov 2024         Gaskets of O(2) loop-decorated random planar maps         E. Kammerer
Dec 2024         Scaling limit of first passage percolation geodesics on planar maps         E. Kammerer
Dec 2024         Ideal Poisson--Voronoi tessellations beyond hyperbolic spaces         M. D'Achille
Jan 2025         The scaling limit of planar maps with large faces         N. Curien and G. Miermont and A. Riera
March 2025         Universality for catalytic equations and fully parked trees         A. Contat and N. Curien
Avr 2025         Extremal Ising Gibbs States on Lobachevsky lattices         M. D'Achille and L. Coquille and A. Le Ny
Avr 2025         The height of the infection tree         E. Kammerer and I. Kortchemski and D. Senizergues
Aug 2025         Random punctured hyperbolic surfaces & the Brownian sphere         T. Budd and N. Curien
Oct 2025         A Tauberian approach to metric scaling limits of random discrete structures         W. Fleurat