L’esprit des cartes : une conférence en l’honneur d’Emmanuel Guitter

15 mai 2025, 09:30 → 16 mai 2025, 17:30 Europe/Paris

Amphithéâtre Claude Bloch, Institut de Physique Théorique, Orme des Merisiers, CEA Paris-Saclay

Nous célébrerons les 60 ans de notre collègue et ami Emmanuel Guitter par une rencontre scientifique autour des thèmes qui lui sont chers.

Oratrices et orateurs invités :

• Mireille Bousquet-Mélou (LaBRI, CNRS/Université de Bordeaux)
• Mark Bowick (KITP, University of California Santa Barbara)
• Timothy Budd (IMAPP, Radboud Universiteit)
• Nicolas Curien (IMO, Université Paris-Saclay)
• François David (IPhT, CNRS/CEA Paris-Saclay)
• Éric Fusy (LIGM, CNRS/Université Gustave Eiffel)
• Charlotte Kristjansen (NBI, Université de Copenhague)
• Jean-François Le Gall (IMO, Université Paris-Saclay)
• Grégory Miermont (UMPA, École normale supérieure de Lyon)
• Jason Miller (DPMMS, University of Cambridge)
• Enzo Orlandini (DFA, Università degli Studi di Padova)
• Gilles Schaeffer (LIX, CNRS/École Polytechnique)
• Sofia Tarricone (IMJ-PRG, Sorbonne Université)

Comité d'organisation : Jérémie Bouttier, Philippe Di Francesco, Bertrand Duplantier, Bertrand Eynard, Camille Flouret, Laure Sauboy

Soutien financier : IPhT (CEA/CNRS), projet ERC-SyG ReNewQuantum

Affiche en français

Poster in English

jeu. 15 mai

09:30 → 10:45 Introduction, par les organisateurs

Nous retracerons la carrière et les travaux d'Emmanuel Guitter dans un exposé introductif à plusieurs voix.

10:45 → 11:15 Pause

11:15 → 12:00 Mark Bowick : Facets of Order

We are trained to exploit symmetry but I will discuss examples in which the solution to an analysis problem violates the obvious symmetries of the problem. Particular features are the emergence of non-trivial topology and non-trivial geometry, most notably where sharp structures arise from a smooth-looking starting point.

12:00 → 12:30 François David : Quantum Walks on Random Combs

The continuous time quantum walk on an infinite comb with infinite teeth has been shown to differ from the classical random walk on the same object. I will show that introducing randomness in the geometry of the comb leads to interesting effects and new questions. Some can be related to the standard theory of localization, and some are specific to the infinite comb.

Based on joint work (some in progress) with T. Jonsson (U. of Iceland)

12:30 → 14:30 Déjeuner

14:30 → 15:15 Mireille Bousquet-Mélou

15:15 → 15:45 Gilles Schaeffer

15:45 → 16:15 Pause

16:15 → 17:00 Charlotte Kristjansen : Quantum Quenches from Quantum Fields

An integrable spin chain underlies the celebrated Maldacena duality. Overlaps between matrix product states and Bethe eigenstates of the chain contain information both about correlation functions of the quantum field theory entering the duality and about the behavior of the spin chain after a quantum quench. I will explain how such overlaps can be calculated exactly.

17:00 → 17:30 Grégory Miermont

ven. 16 mai

09:30 → 10:15 Timothy Budd : A bijection between rigid and integer-labeled quadrangulations

In this talk I will introduce the combinatorial class of rigid
quadrangulations, which form a subclass of flat quadrangulations of the
disk, meaning that all non-boundary vertices are of degree 4.
Rigid quadrangulations are shown to be in bijection with certain
integer-labeled quadrangulations of the sphere, that were enumerated
recently by Bousquet-Mélou and Elvey Price. The bijection relates
several natural statistics on one side to equally natural, but rather
different, statistics on the other. Finally, I will touch upon the
question of scaling limits of large rigid quadrangulations and similar
models of random flat metrics on the disk, and their physics motivation.

10:15 → 10:45 Marie Albenque

10:45 → 11:15 Pause

11:15 → 12:00 Jason Miller : The scaling limit of the intrinsic metric and simple random walk on 2D critical percolation clusters

We show that the CLE(κ) gasket for each κ in (4,8), the range of κ values where the loops can hit each other, themselves, and the domain boundary, can be equipped with: 1) A canonical intrinsic metric and 2) A canonical "Brownian motion" (a continuous Markov process living in the gasket). We also consider critical percolation on the triangular lattice T and show that: 1) The shortest path distance and 2) The simple random walk on large clusters jointly converge in the scaling limit to our continuum metric and Brownian motion on CLE(6).

Based on joint works with Valeria Ambrosio, Irina Dankovic, Maarten Markering, and Yizheng Yuan.

12:00 → 12:30 Nicolas Curien : On the uniqueness of the infinite noodle

When trying to understand the wonderful (and still unproved) conjectures of Emmanuel and co-authors on the enumeration of meanders, we design a much much (much) simpler question which is still open:
Is there an infinite cluster in the gluing of two independent uniform noncrossing matchings?
I will discuss the partial progresses we made and discuss another related problem on loop model on random quadrangulations.
Based on a joint work with G. Kozma, L. Tournier, and V. Sidoravicius.

noodle.pdf

12:30 → 14:30 Déjeuner

14:30 → 15:15 Enzo Orlandini : Combinatorics and topological weights of chromatin loop networks

The 3D folding of mammalian DNA (chromatin) is tightly linked to its transcriptional activity, hence, understanding constitutes an important goal in biophysics. In this talk I will present a polymer model to study the 3D folding of a chromatin segment. By using combinatorial arguments, one can enumerate the emergent chromatin loop networks, both in the case where transcription factors are labeled and where they are unlabeled. These mathematical results, once combined with those of computer simulations, show that networks featuring local loops are statistically more likely with respect to networks including more nonlocal contacts.

This surprising result, which can be rationalised by analytically computing the Boltzmann weight of different loop networks, lays down some basic rules to understand the topological alphabet of chromatin folding in mammalian genomes.

15:15 → 15:45 Éric Fusy : Schnyder orientations for d-irreducible maps

I will review a bijective approach for planar maps developed in joint work with Olivier Bernardi. It relies on certain orientations and draws its inspiration from the Bouttier Di Francesco Guitter bijection between maps and mobiles, and from a bijection by Bernardi for tree-rooted maps. We have applied this method to simple triangulations, relying on orientations with vertex outdegrees 3, so-called Schnyder orientations, and more generally to d-angulations of girth d, and to planar maps of girth d with controlled face-degrees. I will also describe how the method can be extended to d-irreducible maps (recent joint work with Olivier Bernardi and Shizhe Liang), which have been previously counted bijectively by Bouttier and Guitter via slice decompositions.

15:45 → 16:15 Pause

16:15 → 16:45 Sofia Tarricone : Distance dans les cartes planaires et polynômes orthogonaux

Dans cet exposé nous revisitons des propriétés de la fonction à deux points pour les cartes planaires avec des faces de degrés bornés. En particulier, nous verrons comment la relier à une famille de polynômes orthogonaux et comment cela permet de donner des preuves analytiques alternatives de ses propriétés intégrables, comme son écriture déterminantale et les équations discrètes qu'elle satisfait, qui avaient été prouvés originellement via des moyens combinatoires par Emmanuel Guitter et ses collaborateurs Jérémie Bouttier et Philippe Di Francesco. Basé sur un travail en cours avec Jérémie Bouttier.

16:45 → 17:30 Jean-François Le Gall