Conférence JeanBernardIsEighty

24 sept. 2026, 09:30 → 25 sept. 2026, 18:00 Europe/Paris

Amphithéatre Hermite (Institut Henri Poincaré)

 

This conference will be in honor of Jean-Bernard Zuber, a leading figure of the french theoretical physics community for many years. It will cover a variety of topics dear to Jean-Bernard, including random matrix models, conformal theories, combinatorics, integrable models and the mathematical aspects of field theories. A conference dinner will be held on Thursday 24 evening, at the Restaurant Martin (Republique).

 

Invited speakers:

• Costas Bachas (Ecole Normale Supérieure Paris)
• Philippe Biane (U. Gustave Eiffel, Champs sur Marne)
• Mireille Bousquet-Mélou (LaBRI, U. Bordeaux)
• Andrea Cappelli (INFN Florence)
• Robert Coquereaux (I2M Marseille)
• Benoit Estienne (LPTHE, Sorbonne U. Paris)
• Alice Guionnet (UMPA, ENS Lyon) 
• Sylvain Lacroix (LPTHE, Sorbonne U. Paris)
• Marcos Marino (Université de Genève)
• Colin McSwiggen (Academia Sinica, Taiwan) 
• Paul Pearce (U. Melbourne) 
• Didina Serban (IPHT Saclay)
• Michel Talagrand (IMJ Paris)
• Paul Zinn-Justin (U. Melbourne) 

 

Organizers:

Denis Bernard, Philippe di Francesco, Sylvain Lacroix, Michela Petrini, Boris Pioline

Financial support is kindly provided by Fédération de Recherches Interactions Fondamentales (FRIF), Fondation Mathématiques Jacques Hadamard (FMJH), Institut Philippe Meyer (IPM) , Institut de Physique Théoriques du CEA (IPHT), and Laboratoire de Physique Théorique et Hautes Energies (LPTHE).

Attendance to the talks is open to everyone. The registration for the diner is now closed.

jeu. 24 septembre

09:30 → 10:15 Memories of Jean-Bernard

Orateurs: Andrea Cappelli (INFN Florence), Philippe di Francesco (IPhT Saclay and UIUC)

JBZ80-Cappelli.pdf

JBZ80-DiFrancesco.pdf

10:15 → 11:00 Coffee break

11:00 → 11:45 Nimreps, old and new

After recalling basic properties of fusion algebras and nimreps in a modern setting (module-categories), we describe exotic nimreps associated with an old exceptional invariant of F4 at level 6 that cannot be obtained from a conformal embedding of affine Lie algebras.

Orateur: Robert Coquereaux (I2M Marseille)

Coquereaux_JBZ80.pdf

11:45 → 12:30 Concentration of measure

Orateur: Michel Talagrand (IMJ-PRG, Sorbonne Université, CNRS)

JBZ80-Talagrand.pdf

12:30 → 14:00 Lunch break

14:00 → 14:45 Asymptotics and HCIZ integrals

Orateur: Alice Guionnet (UMPA, ENS de Lyon)

14:45 → 15:30 Entanglement at Quantum Criticality

Over the past twenty years, quantum entanglement has established itself as a central theme of research across a wide spectrum of physics, from high-energy theory to condensed matter and quantum information. In the context of this talk, the key point is that entanglement measures have proven to be a remarkably powerful tool for investigating the physics of one-dimensional quantum critical systems.

I will begin by introducing the relevant concepts and reviewing the replica approach to computing Rényi entropies. For one-dimensional quantum systems in particular, the entanglement entropy can be evaluated within two complementary frameworks. In the geometric perspective, the scaling limit reduces the problem to computing a partition function on a branched covering of certain Riemann surfaces—effectively a replication of space-time. In contrast, the algebraic perspective replicates the degrees of freedom themselves, leading to the formulation of a cyclic orbifold.

Following this review, I will highlight the main obstacles to evaluating entanglement entropies in one-dimensional quantum critical systems, and outline some recent developments.

Orateur: Benoit Estienne (LPTHE, Sorbonne Université)

JBZ80-Estienne.pdf

15:30 → 16:15 Coffee break

16:15 → 17:00 Counting trees and maps: Cyclic sieving phenomena

Some families of combinatorial objects, on which a cyclic group G acts, exhibit a "cyclic sieving phenomenon": this means that for any size n, there exists a nice polynomial P(q), with integer coefficients, such that the value of P at any primitive d-th root of unity gives... the number of objects of size n that are fixed by any element of G of order d. Strange! In particular, P(1) is the total number of objects of size n. We will show such phenomena for various actions of a cyclic group on families plane trees (this is joint work with Christian Krattenthaler, from Vienna) and on plane maps (this is joint work with Marie Albenque, from Paris).

Orateur: Mireille Bousquet-Mélou (LaBRI, U. Bordeaux)

JBZ80-Bousquet-Melou.pdf

17:00 → 17:45 Greedy Tamari intervals and constellations

We prove a conjecture of Bousquet-Mélou and Chapoton about the enumeration of intervals of a greedy version of the Tamari order, by providing a recursive bijection with rooted bipartite planar maps. This bijection extends to constellations. Joint work with W. Fang.

Orateur: Philippe Biane (Universite Gustave Eiffel, Paris)

JBZ80-Biane.pdf

ven. 25 septembre

09:30 → 10:15 Knot enumeration and crossing loop models coupled to gravity

24 years ago, Jean-Bernard suggested we work together on the enumeration of knots, tangles and links using matrix models and related combinatorial tools. Though we managed to derive some exact results, many questions remain unanswered, including the important issue of the asymptotic enumeration of knot diagrams as the number of crossings goes to infinity. In this talk I will give an update on these questions, both on the theoretical side (precise predictions from QFT coupled to 2D gravity) and on the numerical side.

Orateur: Paul Zinn-Justin (University of Melbourne)

JBZ80-Zinn-Justin.pdf

10:15 → 11:00 Coffee break

11:00 → 11:45 Cryptozoology of Special Functions

Cyptozoology is the study of cryptids, animals whose existence has been conjectured but never proven. Well-known cryptids include the Loch Ness monster, the jackalope, the chupacabra, and — perhaps most famously — the sasquatch, AKA bigfoot, believed by many enthusiasts to be a "missing link" between apes and humans. This talk will introduce the cryptozoology of integral representations for special functions, beginning with the HCIZ integral formula proved by our dear friend Jean-Bernard, and ending with new results from joint work with Siddhartha Sahi. Reference: https://arxiv.org/abs/2606.15185

Orateur: Colin McSwiggen (Academia Sinica, Taiwan)

JBZ80-McSwiggen.pdf

11:45 → 12:30 Taking a trip to cumuland with Jean-Bernard

In this talk, I will discuss our recent work with Jean-Bernard Zuber on finite N precursors of the free cumulants. These are polynomials on the space of NxN matrices, invariant under conjugations and extracted from the so-called HCIZ integral. Their main feature is their additivity with respect to the average over sums of U(N)-conjugacy orbits. Moreover, they admit natural expansions in terms of Newton and Schur polynomials, related to the representation theory of the unitary and symmetric groups and recovering a previous construction by Capitaine and Casalis. I will further discuss their large N limit, which yields the free cumulants, with 1/N² corrections expressed in terms of Hurwitz numbers. Finally, expanding on the main additivity property of these objects, I will describe the behaviour of general U(N)-invariant polynomials under sums of conjugacy orbits.

Orateur: Sylvain Lacroix (LPTHE, Sorbonne Université)

JBZ80-Lacroix.pdf

12:30 → 14:00 Lunch break

14:00 → 14:45 From divergent series to moduli spaces

Jean-Bernard Zuber has made contributions to an extraordinarily broad range of topics. Among these are two apparently distant subjects: the large-order behavior of perturbative series in quantum field theory, and integration over moduli spaces of Riemann surfaces. In this talk, I will describe recent developments that bring these two subjects together. In particular, I will show how physical ideas about large-order behavior lead to predictions for enumerative invariants of moduli spaces.

Orateur: Marcos Marino (Université de Genève)

14:45 → 15:30 Jean-Bernard and his defects

Defects, to whose study JB has made pioneering contributions, are ubiquitous in modern Quantum Filed Theory. I will present a curious identity obeyed by all superconformal defects, and discuss its physics implications.

Orateur: Costas Bachas (ENS Paris)

JBZ80-Bachas.pdf

15:30 → 16:15 Coffee break

16:15 → 17:00 JBZ, ADE, Defects & All That: A Lattice Perspective

Jean-Bernard has always been passionate about all things ADE. In this talk I will consider the construction of defects in the context of Yang-Baxter integrable classical, affine and twisted affine ADE RSOS lattice models. I will also discuss their associated fusion algebras with an emphasis on the $E_6$ and $D_4^{(1)}$ examples. For the classical ADE models, the defects satisfy the Ocneanu algebra for arbitrary system sizes and thus reproduce, in the continuum scaling limit, the well known CFT results of Petkova and Zuber 2001 for topological defects.

Orateur: Paul Pearce (University of Melbourne)

JBZ80-Pearce.pdf

17:00 → 17:45 Large N is solvable — and even integrable : correlation functions in N=4 SYM at strong coupling

Orateur: Didina Serban (IPHT Saclay)

JBZ80-Serban.pdf